Deliverable 6.2 Description of nexus workflow and case study
Deliverable 6.2 Guidelines on the design for...
Transcript of Deliverable 6.2 Guidelines on the design for...
DEVELOPING INNOVATIVE SYSTEMS
FOR REINFORCED MASONRY WALLS
COOP-CT-2005
CONTRACT N 018120
Design of masonry walls D62 Page 1 of 106
Deliverable 62
Guidelines on the design for end-users
Due date July 2007 Draft submission July 2007
Final submission date January 2008 Issued by TUM
WORKPACKAGE 6 Design of masonry walls (Leader TUM)
PROJECT Ndeg COOP-CT-2005-018120
ACRONYM DISWall
TITLE Developing Innovative Systems for Reinforced Masonry Walls
COORDINATOR Universitagrave di Padova (Italy)
START DATE 16 January 2006 DURATION 24 months
INSTRUMENT Co-operative Research Project
THEMATIC PRIORITY Horizontal Research activities involving SMEs
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm)
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd
[kN
]
0 30 60
90 120 150
180 210 240
270 Loadings
V-M domain (left) M-N domain (middle) V (M-N) domain for concrete perforated clay and hollow clay unit
reinforced masonry
Dissemination level PU Rev FINAL
Design of masonry walls D62 Page 2 of 106
INDEX
INDEX 2 1 INTRODUCTION 5
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE 5 12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE 5
2 TYPES OF CONSTRUCTION 6 21 RESIDENTIAL BUILDINGS 6 22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS 7
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS 10 31 PERFORATED CLAY UNITS 10
311 Perforated clay units for in-plane masonry walls 10 312 Perforated clay units for out-of-plane masonry walls 11
32 HOLLOW CLAY UNITS 12 33 CONCRETE MASONRY UNITS 14
4 GENERAL DESIGN ASPECTS 16 41 LOADING CONDITIONS 16
411 Vertical loading 16 412 Wind loading 18 413 Earthquake loading 19 414 Ultimate limit states load combinations and partial safety factors 22 415 Loading conditions in different National Codes 25
42 STRUCTURAL BEHAVIOUR 27 421 Vertical loading 27 422 Wind loading 27 423 Earthquake loading 28
43 MECHANISM OF LOAD TRANSMISSION 31 431 Vertical loading 31 432 Horizontal loading 31 433 Effect of openings 32
5 DESIGN OF WALLS FOR VERTICAL LOADING 34 51 INTRODUCTION 34 52 PERFORATED CLAY UNITS 35
521 Geometry and boundary conditions 35 522 Material properties 39 523 Design for vertical loading 41 524 Design charts 42
Design of masonry walls D62 Page 3 of 106
53 HOLLOW CLAY UNITS 44 531 Geometry and boundary conditions 44 532 Material properties 45 534 Design for vertical loading 52 534 Design charts 53
54 CONCRETE MASONRY UNITS 54 541 Geometry and boundary conditions 54 542 Material properties 55 543 Design for vertical loading 55 544 Design charts 56
6 DESIGN OF WALLS FOR IN-PLANE LOADING 57 61 INTRODUCTION 57 62 PERFORATED CLAY UNITS 59
621 Geometry and boundary conditions 59 622 Material properties 59 623 In-plane wall design 60 624 Design charts 63
63 HOLLOW CLAY UNITS 68 631 Geometry and boundary conditions 68 632 Material properties 69 633 In-plane wall design 69 634 Design charts 71
64 CONCRETE MASONRY UNITS 78 641 Geometry and boundary conditions 78 642 Material properties 80 643 In-plane wall design 81 644 Design charts 83
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING 87 71 INTRODUCTION 87 72 PERFORATED CLAY UNITS 87
721 Geometry and boundary conditions 87 722 Material properties 88 723 Out of plane wall design 88 724 Design charts 91
73 HOLLOW CLAY UNITS 93 731 Geometry and boundary conditions 93 732 Material properties 93 733 Out of plane wall design 94 734 Design charts 95
Design of masonry walls D62 Page 4 of 106
74 CONCRETE MASONRY UNITS 97 741 Geometry and boundary conditions 97 742 Material properties 97 743 Out-of-plane wall design 98 744 Design charts 98
8 OTHER DESIGN ASPECTS 101 81 DURABILITY 101 82 SERVICEABILITY LIMIT STATE 101
REFERENCES 103 ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE 105
Design of masonry walls D62 Page 5 of 106
1 INTRODUCTION
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE
The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The
validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the
study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this
studies by means of design and production of materials development and construction of reinforced
masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at
producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and
horizontal reinforcement including design charts and a software code for the design of masonry walls made
with the proposed construction systems These products of the WP6 are of crucial importance to ensure the
commercial expansion and the exploitation of the intended technology as they provide the potential users
(designer architects and engineers and construction companies) with understandable easy to use and
sound design tools These rules and tools should provide the average user with easy criteria to safely design
masonry walls for most of the expected situations Moreover the interaction and the incorporation of these
recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the
use of the intended structural solutions For special cases the designer will be addressed to scientific and
technical reports and the use of more complex software The workpackage 6 is mainly based on the
experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under
service and ultimate conditions subjected to diverse possible actions has been gained
12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE
These guidelines give general recommendations for the structural design of reinforced masonry walls
They cover the main aspects related to how to calculate and design masonry walls built with perforated clay
units hollow clay units and concrete units and also include design charts They are not intended to cover any
other type of reinforced masonry besides those above mentioned and any other aspect of design such as
acoustic thermal etc The aspect related to the construction are covered by D75
The recommendations in these guidelines are based on literature research and code recommendations and
on the experience gained through the testing and modelling of masonry wall specimens in the framework of
the DISWall project They are intended in particular for those end-users (architects engineers construction
companies etc) that are involved with the conception and the design of the buildings
The guidelines are structured into seven main sections After the introduction there is a short reference to
the type of buildings that can be built with the proposed construction systems and a description of the
systems Following some general aspects of the structural design are reported and the aspects of design
for in-plane and out-of-plane loadings are described Other design aspects related to the structural
performance of the buildings are briefly described Finally some reference publications and relevant
standards are listed
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 2 of 106
INDEX
INDEX 2 1 INTRODUCTION 5
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE 5 12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE 5
2 TYPES OF CONSTRUCTION 6 21 RESIDENTIAL BUILDINGS 6 22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS 7
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS 10 31 PERFORATED CLAY UNITS 10
311 Perforated clay units for in-plane masonry walls 10 312 Perforated clay units for out-of-plane masonry walls 11
32 HOLLOW CLAY UNITS 12 33 CONCRETE MASONRY UNITS 14
4 GENERAL DESIGN ASPECTS 16 41 LOADING CONDITIONS 16
411 Vertical loading 16 412 Wind loading 18 413 Earthquake loading 19 414 Ultimate limit states load combinations and partial safety factors 22 415 Loading conditions in different National Codes 25
42 STRUCTURAL BEHAVIOUR 27 421 Vertical loading 27 422 Wind loading 27 423 Earthquake loading 28
43 MECHANISM OF LOAD TRANSMISSION 31 431 Vertical loading 31 432 Horizontal loading 31 433 Effect of openings 32
5 DESIGN OF WALLS FOR VERTICAL LOADING 34 51 INTRODUCTION 34 52 PERFORATED CLAY UNITS 35
521 Geometry and boundary conditions 35 522 Material properties 39 523 Design for vertical loading 41 524 Design charts 42
Design of masonry walls D62 Page 3 of 106
53 HOLLOW CLAY UNITS 44 531 Geometry and boundary conditions 44 532 Material properties 45 534 Design for vertical loading 52 534 Design charts 53
54 CONCRETE MASONRY UNITS 54 541 Geometry and boundary conditions 54 542 Material properties 55 543 Design for vertical loading 55 544 Design charts 56
6 DESIGN OF WALLS FOR IN-PLANE LOADING 57 61 INTRODUCTION 57 62 PERFORATED CLAY UNITS 59
621 Geometry and boundary conditions 59 622 Material properties 59 623 In-plane wall design 60 624 Design charts 63
63 HOLLOW CLAY UNITS 68 631 Geometry and boundary conditions 68 632 Material properties 69 633 In-plane wall design 69 634 Design charts 71
64 CONCRETE MASONRY UNITS 78 641 Geometry and boundary conditions 78 642 Material properties 80 643 In-plane wall design 81 644 Design charts 83
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING 87 71 INTRODUCTION 87 72 PERFORATED CLAY UNITS 87
721 Geometry and boundary conditions 87 722 Material properties 88 723 Out of plane wall design 88 724 Design charts 91
73 HOLLOW CLAY UNITS 93 731 Geometry and boundary conditions 93 732 Material properties 93 733 Out of plane wall design 94 734 Design charts 95
Design of masonry walls D62 Page 4 of 106
74 CONCRETE MASONRY UNITS 97 741 Geometry and boundary conditions 97 742 Material properties 97 743 Out-of-plane wall design 98 744 Design charts 98
8 OTHER DESIGN ASPECTS 101 81 DURABILITY 101 82 SERVICEABILITY LIMIT STATE 101
REFERENCES 103 ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE 105
Design of masonry walls D62 Page 5 of 106
1 INTRODUCTION
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE
The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The
validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the
study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this
studies by means of design and production of materials development and construction of reinforced
masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at
producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and
horizontal reinforcement including design charts and a software code for the design of masonry walls made
with the proposed construction systems These products of the WP6 are of crucial importance to ensure the
commercial expansion and the exploitation of the intended technology as they provide the potential users
(designer architects and engineers and construction companies) with understandable easy to use and
sound design tools These rules and tools should provide the average user with easy criteria to safely design
masonry walls for most of the expected situations Moreover the interaction and the incorporation of these
recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the
use of the intended structural solutions For special cases the designer will be addressed to scientific and
technical reports and the use of more complex software The workpackage 6 is mainly based on the
experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under
service and ultimate conditions subjected to diverse possible actions has been gained
12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE
These guidelines give general recommendations for the structural design of reinforced masonry walls
They cover the main aspects related to how to calculate and design masonry walls built with perforated clay
units hollow clay units and concrete units and also include design charts They are not intended to cover any
other type of reinforced masonry besides those above mentioned and any other aspect of design such as
acoustic thermal etc The aspect related to the construction are covered by D75
The recommendations in these guidelines are based on literature research and code recommendations and
on the experience gained through the testing and modelling of masonry wall specimens in the framework of
the DISWall project They are intended in particular for those end-users (architects engineers construction
companies etc) that are involved with the conception and the design of the buildings
The guidelines are structured into seven main sections After the introduction there is a short reference to
the type of buildings that can be built with the proposed construction systems and a description of the
systems Following some general aspects of the structural design are reported and the aspects of design
for in-plane and out-of-plane loadings are described Other design aspects related to the structural
performance of the buildings are briefly described Finally some reference publications and relevant
standards are listed
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 3 of 106
53 HOLLOW CLAY UNITS 44 531 Geometry and boundary conditions 44 532 Material properties 45 534 Design for vertical loading 52 534 Design charts 53
54 CONCRETE MASONRY UNITS 54 541 Geometry and boundary conditions 54 542 Material properties 55 543 Design for vertical loading 55 544 Design charts 56
6 DESIGN OF WALLS FOR IN-PLANE LOADING 57 61 INTRODUCTION 57 62 PERFORATED CLAY UNITS 59
621 Geometry and boundary conditions 59 622 Material properties 59 623 In-plane wall design 60 624 Design charts 63
63 HOLLOW CLAY UNITS 68 631 Geometry and boundary conditions 68 632 Material properties 69 633 In-plane wall design 69 634 Design charts 71
64 CONCRETE MASONRY UNITS 78 641 Geometry and boundary conditions 78 642 Material properties 80 643 In-plane wall design 81 644 Design charts 83
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING 87 71 INTRODUCTION 87 72 PERFORATED CLAY UNITS 87
721 Geometry and boundary conditions 87 722 Material properties 88 723 Out of plane wall design 88 724 Design charts 91
73 HOLLOW CLAY UNITS 93 731 Geometry and boundary conditions 93 732 Material properties 93 733 Out of plane wall design 94 734 Design charts 95
Design of masonry walls D62 Page 4 of 106
74 CONCRETE MASONRY UNITS 97 741 Geometry and boundary conditions 97 742 Material properties 97 743 Out-of-plane wall design 98 744 Design charts 98
8 OTHER DESIGN ASPECTS 101 81 DURABILITY 101 82 SERVICEABILITY LIMIT STATE 101
REFERENCES 103 ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE 105
Design of masonry walls D62 Page 5 of 106
1 INTRODUCTION
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE
The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The
validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the
study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this
studies by means of design and production of materials development and construction of reinforced
masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at
producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and
horizontal reinforcement including design charts and a software code for the design of masonry walls made
with the proposed construction systems These products of the WP6 are of crucial importance to ensure the
commercial expansion and the exploitation of the intended technology as they provide the potential users
(designer architects and engineers and construction companies) with understandable easy to use and
sound design tools These rules and tools should provide the average user with easy criteria to safely design
masonry walls for most of the expected situations Moreover the interaction and the incorporation of these
recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the
use of the intended structural solutions For special cases the designer will be addressed to scientific and
technical reports and the use of more complex software The workpackage 6 is mainly based on the
experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under
service and ultimate conditions subjected to diverse possible actions has been gained
12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE
These guidelines give general recommendations for the structural design of reinforced masonry walls
They cover the main aspects related to how to calculate and design masonry walls built with perforated clay
units hollow clay units and concrete units and also include design charts They are not intended to cover any
other type of reinforced masonry besides those above mentioned and any other aspect of design such as
acoustic thermal etc The aspect related to the construction are covered by D75
The recommendations in these guidelines are based on literature research and code recommendations and
on the experience gained through the testing and modelling of masonry wall specimens in the framework of
the DISWall project They are intended in particular for those end-users (architects engineers construction
companies etc) that are involved with the conception and the design of the buildings
The guidelines are structured into seven main sections After the introduction there is a short reference to
the type of buildings that can be built with the proposed construction systems and a description of the
systems Following some general aspects of the structural design are reported and the aspects of design
for in-plane and out-of-plane loadings are described Other design aspects related to the structural
performance of the buildings are briefly described Finally some reference publications and relevant
standards are listed
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 4 of 106
74 CONCRETE MASONRY UNITS 97 741 Geometry and boundary conditions 97 742 Material properties 97 743 Out-of-plane wall design 98 744 Design charts 98
8 OTHER DESIGN ASPECTS 101 81 DURABILITY 101 82 SERVICEABILITY LIMIT STATE 101
REFERENCES 103 ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE 105
Design of masonry walls D62 Page 5 of 106
1 INTRODUCTION
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE
The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The
validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the
study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this
studies by means of design and production of materials development and construction of reinforced
masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at
producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and
horizontal reinforcement including design charts and a software code for the design of masonry walls made
with the proposed construction systems These products of the WP6 are of crucial importance to ensure the
commercial expansion and the exploitation of the intended technology as they provide the potential users
(designer architects and engineers and construction companies) with understandable easy to use and
sound design tools These rules and tools should provide the average user with easy criteria to safely design
masonry walls for most of the expected situations Moreover the interaction and the incorporation of these
recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the
use of the intended structural solutions For special cases the designer will be addressed to scientific and
technical reports and the use of more complex software The workpackage 6 is mainly based on the
experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under
service and ultimate conditions subjected to diverse possible actions has been gained
12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE
These guidelines give general recommendations for the structural design of reinforced masonry walls
They cover the main aspects related to how to calculate and design masonry walls built with perforated clay
units hollow clay units and concrete units and also include design charts They are not intended to cover any
other type of reinforced masonry besides those above mentioned and any other aspect of design such as
acoustic thermal etc The aspect related to the construction are covered by D75
The recommendations in these guidelines are based on literature research and code recommendations and
on the experience gained through the testing and modelling of masonry wall specimens in the framework of
the DISWall project They are intended in particular for those end-users (architects engineers construction
companies etc) that are involved with the conception and the design of the buildings
The guidelines are structured into seven main sections After the introduction there is a short reference to
the type of buildings that can be built with the proposed construction systems and a description of the
systems Following some general aspects of the structural design are reported and the aspects of design
for in-plane and out-of-plane loadings are described Other design aspects related to the structural
performance of the buildings are briefly described Finally some reference publications and relevant
standards are listed
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 5 of 106
1 INTRODUCTION
11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE
The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The
validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the
study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this
studies by means of design and production of materials development and construction of reinforced
masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at
producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and
horizontal reinforcement including design charts and a software code for the design of masonry walls made
with the proposed construction systems These products of the WP6 are of crucial importance to ensure the
commercial expansion and the exploitation of the intended technology as they provide the potential users
(designer architects and engineers and construction companies) with understandable easy to use and
sound design tools These rules and tools should provide the average user with easy criteria to safely design
masonry walls for most of the expected situations Moreover the interaction and the incorporation of these
recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the
use of the intended structural solutions For special cases the designer will be addressed to scientific and
technical reports and the use of more complex software The workpackage 6 is mainly based on the
experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under
service and ultimate conditions subjected to diverse possible actions has been gained
12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE
These guidelines give general recommendations for the structural design of reinforced masonry walls
They cover the main aspects related to how to calculate and design masonry walls built with perforated clay
units hollow clay units and concrete units and also include design charts They are not intended to cover any
other type of reinforced masonry besides those above mentioned and any other aspect of design such as
acoustic thermal etc The aspect related to the construction are covered by D75
The recommendations in these guidelines are based on literature research and code recommendations and
on the experience gained through the testing and modelling of masonry wall specimens in the framework of
the DISWall project They are intended in particular for those end-users (architects engineers construction
companies etc) that are involved with the conception and the design of the buildings
The guidelines are structured into seven main sections After the introduction there is a short reference to
the type of buildings that can be built with the proposed construction systems and a description of the
systems Following some general aspects of the structural design are reported and the aspects of design
for in-plane and out-of-plane loadings are described Other design aspects related to the structural
performance of the buildings are briefly described Finally some reference publications and relevant
standards are listed
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 6 of 106
2 TYPES OF CONSTRUCTION
Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in
the deliverable D75 section 8 In the following the different building typologies are divided according to the
typical structural behaviour that can be recognized for each of them
21 RESIDENTIAL BUILDINGS
The common form of residential construction in Europe varies from the single occupancy house (Figure 1)
one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are
commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach
relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate
types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses
(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete
floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is
generally low around 270 m
Figure 1 One-family house in San Gregorio
nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto
(MN Italy)
Figure 3 Two-family house in Peron di Sedico
(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto
(PR Italy)
In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with
the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 7 of 106
forces from wind are taken into account in the design by calculating the correspondent eccentricity in the
vertical forces and by reducing accordingly the compression strength of masonry in the vertical load
verifications or can be carryed out directly out-of-plane bending moment verification in the case of
reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is
generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing
the resisting out-of-plane bending moment with the design bending moment However the in-plane shear
forces are generally the governing actions where earthquake forces are high
In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family
houses the roof structures can be made of wooden beams and can be deformable even in new buildings In
these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs
can be governed by resistance to out-of-plane forces
22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS
In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls
with non-structural function their structural design is usually governed only by the resistance to wind and
earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings
the walls must have sufficient in-plane flexural resistance to span between frame members and other
supports Deflection compatibility between frames and walls has to be taken into account in particular if
these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane
earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of
the building but would prejudice the safety of people
A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-
storey high made with load bearing reinforced masonry instead of infill walls In this case compared to
residential buildings with the same number of storeys the inter-storey height will be generally quite high
(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities
etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions
suitable for food processing (Figure 5) or for recreational activities (Figure 6)
In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to
the construction system chosen by the designer The presence of one or the other will influence the
behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded
walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their
own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the
building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In
this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively
considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of
both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are
represented in Figure 9
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 8 of 106
Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)
Gluelam beams and metallic cover
Precast RC double T-beams
Precast RC shed
Figure 7 Sketch of the three deformable roof typologies
RC slabs with lightening clay units
Composite steel-concrete slabs
Steel beams and collaborating RC slab
Figure 8 Sketch of the three rigid roof typologies
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 9 of 106
Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 10 of 106
3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS
31 PERFORATED CLAY UNITS
Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost
entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of
perforated clay units are largely used for the construction of residential buildings as well as larger buildings
with industrial or services destination Within this project one of the studied construction system is aimed at
improving the behaviour of walls under in-plane actions for medium to low size residential buildings
characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at
improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m
high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect
312)
311 Perforated clay units for in-plane masonry walls
This reinforced masonry construction system with concentrated vertical reinforcement and similar to
confined masonry is made by using a special clay unit with horizontal holes and recesses for the
accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining
columns that contain the vertical reinforcement (Figure 10 Figure 11)
Figure 10 Construction system with horizontally
perforated clay units Front view and cross sections
Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner
detail
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 11 of 106
The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of
horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the
Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar
with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is
developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints
Figure 10 and Figure 11 show the developed masonry system
The system which makes use of horizontally perforated clay units that is a very traditional construction
technique for all the countries facing the Mediterranean basin has been developed mainly to be used in
small residential buildings that are generally built with stiff floors and roofs and in which the walls have to
withstand in-plane actions This masonry system has been developed in order to optimize the bond of the
horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the
reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also
possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the
vertical confining columns
312 Perforated clay units for out-of-plane masonry walls
This construction system is made by using vertically perforated clay units and is developed and aimed at
building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of
structures have to resist out-of-plane actions in particular when they are in the presence of deformable
roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the
bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be
easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed
masonry system
Figure 12 Construction system with vertically perforated clay units Front view and cross sections
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password
Design of masonry walls D62 Page 12 of 106
The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far
from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane
behaviour assuring at the same time an appropriate confining effect on the small reinforced column The
developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and
adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal
joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there
is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses
can be also used for the horizontal and vertical reinforcement respectively They can have some
advantages compared to the rebars for example the easier and better placing and the direct collaboration of
the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour
32 HOLLOW CLAY UNITS
The hollow clay unit system is based on unreinforced masonry systems used in Germany since several
years mostly for load bearing walls with high demands on sound insulation Within these systems the
concrete infill is not activated for the load bearing function
Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard
DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities
necessary Therefore the development focused on the application of reinforcement to increase the in-plane-
shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in
common types of construction not relevant as the these types of reinforced masonry are used for internal
walls and the exterior walls are usually build using vertically perforated clay units with a high thermal
insulation
For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical
columns and load distribution) Therefore the bricks were modified amongst others to enable the application
of horizontal reinforcement
The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to
avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of
the horizontal and also the vertical reinforcement is ensured
Design of masonry walls D62 Page 13 of 106
Figure 13 Construction system with hollow clay units
The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of
25cm ie 425 mmsup2m
Figure 14 Reinforcement for the hollow clay unit system plan view
Figure 15 Reinforcement for the hollow clay unit system vertical section
The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of
the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the
RC structural member before or glued in after it At the top of the wall also single reinforcement bars are
fixed into the clay elements before placing the concrete infill into the wall
Design of masonry walls D62 Page 14 of 106
33 CONCRETE MASONRY UNITS
Portugal is a country with very different seismic risk zones with low to high seismicity A construction system
is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with
moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is
based on concrete masonry units whose geometry and mechanical properties have to be specially designed
to be used for structural purposes Two and three hollow cell concrete masonry units were developed in
order to vertical reinforcements can be properly accommodated For this construction system different
possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16
and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly
spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor
RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends
In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to
the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important
aspect of this construction system is the filling of the vertical reinforced joints with a modified general
purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the
masonry can be reached and thus an effective stress transfer mechanism between both materials can be
obtained
(a)
(b)
Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical
joints (b) vertical reinforcements placed in the hollow cells
Design of masonry walls D62 Page 15 of 106
Figure 17 Detail of the intersection of reinforced masonry walls
Design of masonry walls D62 Page 16 of 106
4 GENERAL DESIGN ASPECTS
41 LOADING CONDITIONS
The size of the structural members are primarily governed by the requirement that these elements must
adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the
building components or permanent construction and machinery inside the building and the vertical loads
related to the building occupancy due to the use of the building but not related to wind earthquake or dead
loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure
which generate in-plane shear loads and out-of-plane face loads on individual members While both loading
types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of
building elements whereas earthquake loads arise due to the inertia inherent in the building when the
ground moves Consequently the relative forces induced in various building elements are different under the
two types of loading [Lawrence and Page 1999]
In the following some general rules for the determination of the load intensity for the different loading
conditions and the load combinations for the structural design taken from the Eurocodes are given These
rules apply to all the countries of the European Community even if in each country some specific differences
or different values of the loading parameters and the related partial safety factors can be used Finally some
information of the structural behaviour and the mechanism of load transmission in masonry buildings are
given
411 Vertical loading
In this very general category the main distinction is between dead and live load The first can be described
as those loads that remain essentially constant during the life of a structure such as the weight of the
building components or any permanent or stationary construction such as partition or equipment Therefore
the dead load is the vertical load due to the weight of all permanent structural and non-structural components
of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally
reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience
and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean
values of density of construction materials such as concrete mortar and masonry other materials such as
wood metals plastics glass and also possible stored materials can be found from a number of sources
and in particular in EN 1991-1-1
The live loads are also referred to as occupancy loads and are those loads which are directly caused by
people furniture machines or other movable objects They may be considered as short-duration loads
since they act intermittently during the life of a structure The codes specify minimum floor live-load
requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads
can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these
loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by
Design of masonry walls D62 Page 17 of 106
the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be
evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground
sk given for each site according to the climatic region and the altitude the shape of the roof and in certain
cases of the building by means of the shape coefficient microi the topography of the building location by means
of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1
Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow
load for the persistenttransient design situation is thus given by
s = microi Ce Ct sk (41)
Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]
Table 2 Density of constructions materials masonry [after EN 1991-1-1]
Design of masonry walls D62 Page 18 of 106
Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]
412 Wind loading
According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external
surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or
directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces
normal to the surface of the structure or of individual cladding components Generally the wind action is
represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of
the turbulent wind
Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm
determined from the basic wind velocity vb at 10 m above ground level in open country terrain which
depends on the wind climate given for each geographical area and the height variation of the wind
determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))
vm = vb cr(z) co(z) (42)
To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first
converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)
and the basic velocity pressure qp
(43)
the peak velocity pressure qp(z) at height z is equal to
(44)
Design of masonry walls D62 Page 19 of 106
where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the
corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the
external surfaces we and on the internal surfaces wi of buildings can be respectively found as
we = qp (ze) cpe (45a)
wi = qp (zi) cpi (45b)
where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of
the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal
pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size
factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of
the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from
vibrations due to turbulence in resonance with the structure are used
413 Earthquake loading
Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake
These movements induce inertial forces in the structure related to the distributions of mass and rigidity and
the overall forces produce bending shear and axial effects in the structural members For simplicity
earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic
characteristics of the structure foundation conditions etc [Lawrence and Page 1999]
This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic
response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of
SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock
The resulting plot can then be used to pick off the response of any linear system given its period (the
inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum
lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response
spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of
the soil characteristics besides the values of the structural damping To take into account in a simplified way
of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour
factors lsquoqrsquo and the design response spectra are obtained
The process for calculating the seismic action according to the EN 1998-1-1 is the following First the
national territories shall be subdivided into seismic zones depending on the local hazard that is described in
terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR
The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic
action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years
PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference
return period For return periods other than the reference related to the importance classes of the building
the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)
Design of masonry walls D62 Page 20 of 106
where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E
described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for
the influence of local ground conditions on the seismic action
For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the
following expressions
(46a)
(46b)
(46c)
(46d)
where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the
design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant
spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch
TD is the value defining the beginning of the constant displacement response range of the spectrum S is the
soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and
equal to for different values of viscous damping ξ
In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is
adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of
probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure
18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic
response spectra and the corresponding spectra (for 5 viscous damping)
Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN
1998-1-1]
Design of masonry walls D62 Page 21 of 106
Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]
When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct
transformation of the elastic acceleration response spectrum Se(T) using the following expression normally
for vibration periods not exceeding 40 s
(47)
The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the
vertical component of the seismic action
(48a)
(48b)
(48c)
(48d)
where Table 5 gives the recommended values of parameters describing the vertical elastic response
spectra
Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]
Design of masonry walls D62 Page 22 of 106
As already explained the capacity of the structural systems to resist seismic actions in the non-linear range
generally permits their design for resistance to seismic forces smaller than those corresponding to a linear
elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo
behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the
design spectrum Sd(T) shall be defined by the following expressions
(49a)
(49b)
(49c)
(49d)
where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the
lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical
component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the
design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the
other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a
behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas
in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6
Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]
414 Ultimate limit states load combinations and partial safety factors
According to EN 1990 the ultimate limit states to be verified are the following
a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body
Design of masonry walls D62 Page 23 of 106
b) STR Internal failure or excessive deformation of the structure or structural members where the strength
of construction materials of the structure governs
c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in
providing resistance
d) FAT Fatigue failure of the structure or structural members
At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be
determined by combining the values of actions that are considered to occur simultaneously Each
combination of actions should include a leading variable action (such as wind for example) or an accidental
action The fundamental combination of actions for persistent or transient design situations and the
combination of actions for accidental design situations are respectively given by
(410a)
(410b)
where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions
Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action
and ψ0i is the combination coefficient given in Table 8
Table 7 Recommended values of γ factors for buildings [after EN 1990]
EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)
Factor γG γQ γG γQ γG γQ
favourable 090 000 100 000 100 000
unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted
In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into
account the presence of the masses associated with the gravity loads appearing in the following combination
of actions
(411)
where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the
variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-
1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic
actions shall be computed from the following expression
ψEi = φ ψ2i (412)
Design of masonry walls D62 Page 24 of 106
where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of
buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the
the recommended values for φ are listed in Table 9
Table 8 Recommended values of ψ factors for buildings [after EN 1990]
Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]
The combination of actions for seismic design situations for calculating the design value Ed of the effects of
actions in the seismic design situation according to EN 1990 is given by
(413)
where AEd is the design value of the seismic action
Design of masonry walls D62 Page 25 of 106
415 Loading conditions in different National Codes
In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of
seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]
The novelties introduced in the seismic design of buildings has been integrated into a general structural code
in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of
vertical wind and earthquake loading including the load combinations are the same that can be found in the
Eurocodes with differences found only in the definition of some parameters The seismic design is based on
the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration
(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic
zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of
the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of
the seismic action for buildings with different importance factors is made explicit as the code require
evaluating the expected building life-time and class of use on the bases of which the return period for the
seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra
are given also with reference to the different return periods and probability of exceedance
In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind
loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149
Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))
For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with
the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)
The wind loadings increased compared to the pervious standard from 1986 significantly Especially in
regions next to the North Sea up to 40 higher wind loadings have to be considered
The seismic design is based on the assumption of 3 main seismic area characterized by values of design
(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g
(seismic zone 1) up to 008g (seismic zone 3)
In Portugal the definition of the design load for the structural design of buildings has been made accordingly
to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a
process to the adaptation to the European codes has also been started The calculation of the design loads
are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is
under preparation where new seismic zones are defined according to the type of seismic action For close
seismic action three seismic areas are defines with peak ground acceleration (with a probability of
exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g
(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground
acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic
zone 2) and 005g (seismic zone 5) see Figure 20
Design of masonry walls D62 Page 26 of 106
Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]
Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)
Design of masonry walls D62 Page 27 of 106
42 STRUCTURAL BEHAVIOUR
421 Vertical loading
This section covers in general the most typical behaviour of loadbearing masonry structures In these
buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without
any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live
load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical
load In other words they rely on their compressive load resistance to support other parts of the structure
The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but
there can also be concentrated loads and effects arising from composite action between walls and lintels and
beams
Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the
wall supports determine the compressive capacity of each individual wall Strength properties of masonry
are difficult to predict from known properties of the mortar and masonry units because of the relatively
complex interaction of the two component materials However such interaction is that on which the
determination of the compressive strength of masonry is based for most of the codes Not only the material
(unit and mortar) properties but also the shape of the units particularly the presence the size and the
direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]
422 Wind loading
Traditionally masonry structures were massively proportioned to provide stability and prevent tensile
stresses In the period following the Second World War traditional loadbearing constructions were replaced
by structures using the shear wall concept where stability against horizontal loads is achieved by aligning
walls parallel to the load direction (Figure 21)
Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]
Design of masonry walls D62 Page 28 of 106
Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of
concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to
resist horizontal load For these structures the walls subjected to face loading must be designed to have
sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry
walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]
423 Earthquake loading
In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic
forces because of dynamic effects and are therefore more susceptible to damage caused by face loading
The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are
more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised
by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is
characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the
compressed masonry toes These failure modes do not usually result in wall collapse but can cause
considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent
defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the
strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation
capacity in-plane flexural failure mode are preferred and according to the capacity design should occur
first Shear damage can also occur in structures with masonry infills when large frame deflections cause
load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid
torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular
shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN
1998-1-1 for a building to be categorised as being regular in plan the following conditions should be
satisfied
1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately
symmetrical in plan with respect to two orthogonal axes
2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in
plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being
satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the
area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5
of the floor area
3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the
vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of
the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be
carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to
that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph
should be considered for the global behaviour of the building
Design of masonry walls D62 Page 29 of 106
4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are
respectively the larger and smaller in plan dimension of the building measured in orthogonal directions
5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional
radius r shall be in accordance with the two conditions below which are expressed for the direction of
analysis y
eox le 030 rx (414a)
rx ge ls (414b)
where eox is the distance between the centre of stiffness and the centre of mass measured along the x
direction which is normal to the direction of analysis considered rx is the square root of the ratio of the
torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of
the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with
respect to the centre of mass of the floor to (b) the floor mass)
Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following
conditions should be satisfied
1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption
from their foundations to the top of the building or if setbacks at different heights are present to the top of
the relevant zone of the building
2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually
without abrupt changes from the base to the top of a particular building
3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis
should not vary disproportionately between adjacent storeys
4- When setbacks are present the following additional conditions apply
a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of
the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)
b) for a single setback within the lower 15 of the total height of the main structural system the setback
shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of
the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at
least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base
enlargement
c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not
greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid
basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see
Figure 22d)
Design of masonry walls D62 Page 30 of 106
Figure 22 Criteria for regularity of buildings with setbacks
Design of masonry walls D62 Page 31 of 106
43 MECHANISM OF LOAD TRANSMISSION
431 Vertical loading
Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to
avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially
under seismic loadings
432 Horizontal loading
The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding
for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in
combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane
restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as
a cantilever beam is generally too unfavourable describing a shear wall in a common construction
The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005
553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased
correspondingly and assuming equilibrium
Figure 23 Spacial structural system under combined loadings
Design of masonry walls D62 Page 32 of 106
Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs
433 Effect of openings
Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution
significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic
behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design
process wall can be separated into stripes
Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings
For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several
combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg
extra reinforcement in the corners (diagonal and orthogonal)
Design of masonry walls D62 Page 33 of 106
Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]
Design of masonry walls D62 Page 34 of 106
5 DESIGN OF WALLS FOR VERTICAL LOADING
51 INTRODUCTION
According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical
loading allowance in the design should be made not only for the vertical loads directly applied to the wall
but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the
interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and
differences in the material properties of individual components The definition of the masonry wall capacity is
thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their
typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved
by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to
evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load
verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections
Design of masonry walls D62 Page 35 of 106
52 PERFORATED CLAY UNITS
521 Geometry and boundary conditions
Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the
presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced
masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef
and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls
The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the
EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning
from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a
bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness
of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the
same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the
wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and
bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two
vertical edges
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In that case the effective thickness is measured as
tef = ρt t (51)
where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27
Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]
Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]
Design of masonry walls D62 Page 36 of 106
In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The
effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction
factor ρn that changes according to the above mentioned wall boundary conditions
hef = ρn h (52)
For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at
the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least
23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the
wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and
stiffened on one vertical edge (with one free vertical edge)
if hl le 35
(53a)
if hl gt 35
(53b)
For walls restrained at the top and bottom and stiffened on two vertical edges
if hl le 115
(54a)
if hl gt 115
(54b)
These cases that are typical for the constructions analyzed have been all taken into account Figure 28
gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not
restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025
times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major
than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective
height for walls restrained at the vertical edges varying the height to length ratio of the wall The
corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the
walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even
more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two
vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the
slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical
application therefore for the design the out of plane bending moment of resistance should be evaluated
Design of masonry walls D62 Page 37 of 106
Slenderness ratio for walls not restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
50 54 58 62 66 70 74 78 82 86 90 94 98 102
106
110
114
118
122
126
130
134
138
142
146
150
154
158
162
166
170 ht
λ
λ2 (e le 025 t)λ2 (e gt 025 t)
wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t
wall h = 6000 mm t = 380 mmdeformable roof
Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness
ratio)
Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges
00
01
02
03
04
05
06
07
08
09
10
053
065
080
095
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
380
395
410
425
440
455
470
485
500 hl
ρ
ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)
Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical
edges (varying the wall height to length ratio)
Design of masonry walls D62 Page 38 of 106
Slenderness ratio for walls restrained at the vertical edges
0
1
2
3
4
5
6
7
8
9
10
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm
Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying
thickness and wall length)
Slenderness ratio for walls restrained at the vertical edges
0
2
4
6
8
10
12
14
16
18
20
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600
l (cm)
λ
h=600 cm t=30 cmh=600 cm t=34 cmh=600 cm t=38 cmh=600 cm t=42 cmh=600 cm t=46 cm
Figure 31 Slenderness ratio for walls restrained at the vertical edges (walls with h=6000 mm varying
thickness and wall length)
The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has
been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers
500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of
masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length
equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from
walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)
Design of masonry walls D62 Page 39 of 106
522 Material properties
The materials properties that have to be used for the design under vertical loading of reinforced masonry
walls made with perforated clay units concern the materials (normalized compressive strength of the units fb
mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain
εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive
the design values the partial safety factors for the materials are required For the definition of the
compressive strength of masonry the EN 1996-1-1 formulation can be used
(55)
where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main
parameters adopted for the creation of the design charts
Table 11 Material properties parameters and partial safety factors used for the design
ALAN Material property CISEDIL Horizontal Holes
(G4) Vertical Holes
(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the
characteristics of both the types of unit have been taken into account to define the strength of the entire
masonry system Once the characteristic compressive strength of each portion of masonry (masonry made
with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has
been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of
a simple geometric homogenization
vh
kvvkhhk AA
fAfAf
++
= (56)
Design of masonry walls D62 Page 40 of 106
where A is the gross cross sectional area of the different portions of the wall Considering that in any
masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about
315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the
compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be
seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of
experimental compressive strength fexp were derived for the masonry columns made with vertically perforated
units the masonry panels made with horizontally perforated units and for the whole system Table 12
compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength
Table 12 Experimental and theoretical values of the masonry system compressive strength
Masonry columns
Masonry panels
Masonry system
l (mm) 630 920 1550
fexp (Nmm2) 559 271 390
fth (eq 56) (Nmm2) - - 388
Error () - - 0005
Factored compressive strength
10
15
20
25
30
35
40
45
50
55
60
500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250
lw (mm)
f (Nmm2)
fexpfdα fd
Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of
the wall
Design of masonry walls D62 Page 41 of 106
523 Design for vertical loading
The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the
determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see
Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from
500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take
into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated
locally in the vertical columns the reinforced section has been considered as having a width of not more
than two times the width of the reinforced column multiplied by the number of columns in the wall No other
limitations have been taken into account in the calculation of the resisting moment as the limitation of the
section width and the reduction of the compressive strength for increasing wall length appeared to be
already on the safety side beside the limitation on the maximum compressive strength of the full wall section
subjected to a centred axial load considered the factored compressive strength
Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]
In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in
this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12
mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there
are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be
calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to
1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical
for real building site conditions In this case the reinforcement percentage is that resulting from the
constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm
Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one
knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design
vertical load resistance of the wall The top left figure gives these values for walls of different length provided
with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall
length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical
Design of masonry walls D62 Page 42 of 106
reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two
rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the
vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous
524 Design charts
NRd for walls of different length min vert reinf and varying eccentricity
750 mm1000 mm
1250 mm1500 mm
1750 mm2000 mm
2250 mm2500 mm
2750 mm3000 mm3250 mm3500 mm
4000 mm4250 mm
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
3750 mm
500 mm
wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-
150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash14 mm
2oslash16 mm
2oslash18 mm2oslash20 mm
4oslash16 mm
wall l = 2000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash16 mm
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 2500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50
200
350
500
650
800
950
1100
1250
1400
1550
1700
1850
2000
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 43 of 106
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
11001250
140015501700
185020002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
NRd for walls with fixed length varying vert reinf and eccentricity
50200
350500650
800950
110012501400
155017001850
20002150
23002450
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1
Murfor RNDZ-5-150 400 mm
Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance
of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement
(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm
3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity
NRd for walls of different length and varying eccentricity
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
000 005 010 015 020 025 030 035 040 045 050
et (-)
NRd (kN)
1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm
wall t = 380 mm steel 4oslash12 780 mm Feb 44k
Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load
resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying
eccentricity
Design of masonry walls D62 Page 44 of 106
53 HOLLOW CLAY UNITS
531 Geometry and boundary conditions
The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on
walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is
taken typical of housing construction with 25m (10 rows high)
The design under dominant vertical loadings has to consider the boundary conditions at the top and the base
of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical
edges are in the following not considered (safe side) Also the effects of partially increased effective
thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of
the UNIPOR-system is designated for wall with rectangular plan view
Figure 36 Geometry of the hollow clay unit and the concrete infill column
Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls
should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the
wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor
slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075
Design of masonry walls D62 Page 45 of 106
532 Material properties
The material properties of the infill material are characterized by the compression strength fck Generally the
minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant
compression also long term effects are taken into consideration
Table 13 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2 SCC 25 Nmmsup2 (min demand)
γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2
For the design under vertical loadings only the concrete infill is considered for the load bearing design In the
analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the
hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced
corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with
a reduction of 08
The effective compression strength fd_eff is calculated
column
column
M
ccckeffd s
lff sdotsdot
=γ
α (57)
with lcolumn=02m scolumn=025m
In the context of the workpackage 5 extensive experimental investigations were carried out with respect to
the description of the load bearing behaviour of the composite material clay unit and concrete Both material
laws of the single materials were determined and the load bearing behaviour of the compound was
examined under tensile and compressive loads With the aid of the finite element method the investigations
at the compound specimen could be described appropriate For the evaluation of the masonry compression
tests an analytic calculation approach is applied for the composite cross section on the assumption of plane
remaining surfaces and neglecting lateral extensions
The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure
37 to Figure 40 in accordance with Deliverable 54
Design of masonry walls D62 Page 46 of 106
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 05 10 15 20 25 30 35 40
compressive stress in Nmmsup2
compressive strain in mmm Figure 37 Standard unit material compressive
stress-strain-curve Figure 38 DISWall unit material compressive
stress-strain-curve
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm
0
5
10
15
20
25
30
35
40
00 20 40 60 80 100 120 140 160
compressive stress in Nmmsup2
compressive strain in mmm Figure 39 Standard concrete compressive
stress-strain-curve
Figure 40 Standard selfcompating concrete
compressive stress-strain-curve
The compressive ndashstressndashstrain curves of the compound are simplified computed with the following
equation
( ) ( ) ( )c u sc u s
A A AE
A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)
σ (ε) compressive stress-strain curve of the compound
σu (ε) compressive stress-strain curve of unit material (see figure 1)
σc (ε) compressive stress-strain curve of concrete (see figure 2)
A total cross section
Ac cross section of concrete
Au cross section of unit material
ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)
fy yield strength
Design of masonry walls D62 Page 47 of 106
The estimated cross sections of the single materials are indicated in Table 14
Table 14 Material cross section in half unit
area in mmsup2 chamber (half unit) material
Standard unit DISWall unit
Concrete 36500 38500
Clay Material 18500 18500
Hole 5000 3000
In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and
application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in
comparison with the experimental and the numerical computed curves Figure 44 shows the numerically
computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)
for the investigated material combinations The influence of the different material combinations on the stress-
strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values
according to equation (58) are about 7-8 smaller compared to the numerical results The difference may
be caused among others things by the lateral confinement of the pressure plates This influence is not
considered by equation (58)
In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial
test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to
standard) which were manufactured with the wall specimens as well as the masonry compressive strength
(single and average values) are given The masonry compressive strength was calculated according to
equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4
Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered
if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the
experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated
stress-strain-curves of the composite material are depicted in Figure 45
Within the tests for the determination of the fundamental material properties the mean value of the cube
strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and
the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The
compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values
(upward and downward) To consider these deviations roughly in the calculations with equation (58) the
stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression
stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength
determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio
fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are
depicted in Figure 46
Design of masonry walls D62 Page 48 of 106
For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive
strength amounts for the adjusted values between 057 and 069 (average value 064) The difference
between the calculated and experimental values may have different causes Among other things the
specimen geometry and imperfections as well as the scatter of the material properties affect the compressive
strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made
of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio
for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete
in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry
walls with Normal Concrete within the experimental investigations
For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084
respectively The higher values can be attributed to the positive effect of the horizontal reinforcement
elements (longitudinal bars binder) which are not considered in equation (58)
Table 15 Comparison of calculated and tested masonry compressive strengths
description fccubedry fcmas cal fc
fcmas
cal fcmas corr cal fcmas
fcmas
corr cal fcmas
- Nmmsup2 Nmmsup2 - Nmmsup2 -
182 SU-VC-NM
136
163 SU-VC
353
168
mean 162
327 050 283 057
236 SU-SCC 445
216
mean 226
327 069 346 065
247 DU-SCC
438 175
mean 211
286 074 304 069
223 DU-SCC-DR 399
234
mean 229
295 078 272 084
261 DU-SCC-SR 365
257
mean 259
321 081 317 082
Design of masonry walls D62 Page 49 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compessive strain in mmm
final compressive strength
Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
Design of masonry walls D62 Page 50 of 106
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation
compressive stress in Nmmsup2
compressive strain in mmm
final compressive strength
Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-
simulation and analytical calculation (equation)
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen
Design of masonry walls D62 Page 51 of 106
0
5
10
15
20
25
30
35
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 45 Results of analytical calculation (equation) masonry walls
0
5
10
15
20
25
30
35
40
0 05 1 15 2 25 3 35
SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)
compressive stress σD in Nmmsup2
compressive strain εD in mmm
Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls
Design of masonry walls D62 Page 52 of 106
534 Design for vertical loading
The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments
can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of
the wall ie M1d M2d and Mmd
The design is performed by checking the axial force
SdRd NN ge (58)
for rectangular cross sections
dRd ftN sdotsdotΦ= (59)
The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the
wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple
approach is done by taking the maximum bending moment for all design checks ie at the mid height and
the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured
Especially when the bending moment at the mid height is significantly smaller than the bending moment at
the top resp bottom of the wall it might be favourable to perform the design with the following charts only for
the moment at the mid height of the wall and in a second step for the bending moment at the top resp
bottom of the wall using equations (64) and 65)
For the following design procedure the determination of Φi is done according to eq (64) and Φm according to
eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following
comparison
Design of masonry walls D62 Page 53 of 106
534 Design charts
Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here different heights h and restraint factors ρ
Figure 48 N-M diagram Load bearing capacity of walls under dominant axial compression with different
geometry and material parameters here strength of the infill
Design of masonry walls D62 Page 54 of 106
54 CONCRETE MASONRY UNITS
541 Geometry and boundary conditions
The design for vertical loads of masonry walls with concrete units was based on walls with different lengths
proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of
joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about
280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts
Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in
the design charts
The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and
bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the
capacity of transversal walls to stiff the walls
The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless
the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the
actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall
h times a reduction factor ρn that changes according to the wall boundary condition as already explained in
sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety
side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is
105 (lt12)
Design of masonry walls D62 Page 55 of 106
542 Material properties
The value of the design compressive strength of the concrete masonry units is calculated based on the
values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce
real scale masonry units with a normalized compressive strength close to the one obtained by experimental
tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the
compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in
the calculation of the design compressive strength of concrete masonry
Table 16 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300
543 Design for vertical loading
The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on
the determination of the design out-of-plane bending moment resistance that divided for possible values of
vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In
determining the design value of the moment of resistance of the walls a rectangular stress distribution as
been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly
to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length
(from 160 mm to 560 mm) taking thus into account the factored design compressive strength
Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows
the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical
load resistance of the wall For the obtainment of the design charts also the variation of the vertical
reinforcement is taken into account
Design of masonry walls D62 Page 56 of 106
544 Design charts
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
Nrd
(kN
)
(et)
L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm
Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load
resistance of the wall NRd for walls of different length
00 01 02 03 04 050
500
1000
1500
2000
2500
3000L=160cm
As = 0036 As = 0045 As = 0074 As = 011 As = 017
Nrd
(kN
)
(et)
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0035 As = 0045 As = 0070 As = 011 As = 018
Nrd
(kN
)
(et)
L=280cm
(a) (b)
Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=400cm
00 01 02 03 04 050
500
1000
1500
2000
2500
3000
3500
As = 0022 As = 0034 As = 0045 As = 0070 As = 010
Nrd
(kN
)
(et)
L=560cm
(a) (b)
Figure 51 Design charts for reinforced concrete masonry system Design values of the vertical load
resistance of the wall NRd for walls (a) L= 400cm (b) L= 560cm
Design of masonry walls D62 Page 57 of 106
6 DESIGN OF WALLS FOR IN-PLANE LOADING
61 INTRODUCTION
The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the
presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when
the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical
reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a
contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of
vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between
the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]
Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of
reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions
These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)
contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical
reinforcement (VR3) as in eq (61)
1 2 3R R R RV V V V= + + (61)
Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for
example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian
standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530
2005] are based on some similar concepts but the expressions for the strength contribution is more complex
and based on the calibration of experimental results Generally the codes omit the dowel-action contribution
that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are
reported in Table 17
In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively
the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the
design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear
strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of
the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N
is the design vertical load M and V the design bending moment and shear α is the angle formed by the
applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the
percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different
approach for the evaluation of the reinforced masonry shear strength based on the contribution of the
various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios
(1988) The comparison between the experimental values of shear capacity and the theoretical values given
by some of these formulations has been carried out in Deliverable D12bis (2006)
Design of masonry walls D62 Page 58 of 106
Table 17 Shear strength contribution for reinforced masonry
Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1
(2005) tlf vd sdot ydSw fA sdot90 0
AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0
BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0
DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0
NZS 4230 (2004) ltfC
ltN
vd 8080tan90
02 sdot⎟⎠
⎞⎜⎝
⎛+
sdotα lt
stfA
fC ydswvd 80)
80( 01 sdot
sdot+ 0
ACI 530 (2005) Nftl
VLM
d 250)7514(0830 +minus slfA ydsw 50 0
Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060
The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from
those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same
variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the
maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-
strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular
whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
Design of masonry walls D62 Page 59 of 106
62 PERFORATED CLAY UNITS
621 Geometry and boundary conditions
The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN
system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from
short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing
construction for which the system has been developed (2700 mm) The study has been limited to masonry
piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical
reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie
whether it is a cantilever or a wall with double fixed end as this condition change the value of the design
applied in-plane bending moment The design values of the resisting shear and bending moment are found
on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement
and the material properties
Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm
each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been
taken into account in the following calculations This is equal to a percentage of steel on the wall cross
section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As
demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb
44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each
other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm
Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905
2007] upwards has been taken into account into the calculations When the 005 of the masonry wall
section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical
reinforcement [DM 140905 2007]
622 Material properties
The materials properties that have to be used for the design under in-plane horizontal loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values
the partial safety factors for the materials are required The compressive strength of masonry is derived as
described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as
described by Figure 32 to take into account the different properties of the unit with vertical and with
horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts
Design of masonry walls D62 Page 60 of 106
Table 18 Material properties parameters and partial safety factors used for the design
Material property Horizontal Holes (G4) Vertical Holes (G2)
fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922
fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design
compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used
(62)
with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then
inferred from fvk dividing by γM
623 In-plane wall design
The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units
(ALAN system) has been based on the determination of the design in-plane bending moment resistance and
the design in-plane shear resistance
In determining the design value of the moment of resistance of the walls for various values of design
compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a
rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the
reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has
been computed by studying the limit conditions between different fields and limiting for cross-sections not
fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1
for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250
Design of masonry walls D62 Page 61 of 106
mm) taking thus into account the factored design compressive strength (reduced to take into account the
stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation
method has been carried out by comparing the experimental values of maximum bending moment in the
tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design
values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to
get the trend of the strength for varying applied compressive stresses and gives value of predicted bending
moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method
is reliable
The prediction of the design value of the shear resistance of the walls has been also carried out for various
values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01
Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum
of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal
reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the
horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear
strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the
strength for varying applied compressive stresses Therefore it was decided to use a similar formulation
proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40
[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient
of 110 (blue dots in Figure 53)
MRd for walls with fixed length and varying vert reinf
0
50
100
150
200
250
0 50 100 150 200 250 300 350 400
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-
5-150 400 mm
VRd varying the influence of hor reinf
NTC 1500 mm
EC6 1500 mm
100
150
200
250
300
0 100 200 300 400 500 600
NEd (kN)
VRd (kN)
06 Asy fyd09 Asy fydExperimental
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment
Figure 53 Comparison of design shear resistance and experimental values of maximum shear force
Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum
percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of
the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and
finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value
of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-
Design of masonry walls D62 Page 62 of 106
N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the
length of the wall and the value of the design applied bending moment and axial load enters the diagram
and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57
gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the
applied design compressive stresses If one knows the design value of the applied compressive stresses or
axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or
cantilever) can calculate the design values of the applied shear and bending moment At this point heshe
enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall
section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm
1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement
(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm
each 400 mm or 1 Murfor RNDZ-5-150 400 mm)
Design of masonry walls D62 Page 63 of 106
624 Design charts
MRd for walls of different length and min vert reinf
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
00 02 04 06 08 10 12 14σd (Nmm2)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
MRd for walls of different length and min vert reinf
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm
2250 mm2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of
resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design
compressive stresses (left) and design axial load (right)
VRd for walls of different length
500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm
100
150
200
250
300
350
400
450
500
550
00 02 04 06 08 10 12 14
σd (Nmm2)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
VRd for walls of different length
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm2750 mm
3000 mm3250 mm
3500 mm
3750 mm4000 mm
4250 mm
100
150
200
250
300
350
400
450
500
550
0 200 400 600 800 1000 1200 1400 1600
NEd (kN)
VRd (kN)
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the
wall VRd for varying design compressive stresses (left) and design axial load (right)
Design of masonry walls D62 Page 64 of 106
M-N domain for walls of different length and minimum vertical reinforcement
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
NRd (kN)
MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
500 mm750 mm
1000 mm1250 mm
1500 mm1750 mm
2000 mm2250 mm
2500 mm
2750 mm
3000 mm
3250 mm
3500 mm
3750 mm
4000 mm
4250 mm
Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and
minimum vertical reinforcement (FeB 44k)
V-M domain for walls with different legth and different applied σd
100
150
200
250
300
350
400
450
500
550
0 250 500 750 1000 1250 1500 1750 2000
MRd (kNm)
VRd (kN)
σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm
wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and
minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses
Design of masonry walls D62 Page 65 of 106
M-N domain for walls with fixed length and varying vert reinf
0
10
20
30
40
50
60
70
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
-400 -200 0 200 400 600 800 1000 1200
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800 1000 1200 1400
NRd (kN)
MRd (kNm)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
-400 -200 0 200 400 600 800 1000 1200 1400 1600
NRd (kN)
MRd (kNm)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
100
200
300
400
500
600
700
800
900
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800
NRd (kN)
MRd (kNm)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
NRd (kN)
MRd (kNm)
2oslash18 mm
2oslash20 mm
4oslash16 mm
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Design of masonry walls D62 Page 66 of 106
M-N domain for walls with fixed length and varying vert reinf
0
200
400
600
800
1000
1200
1400
-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
M-N domain for walls with fixed length and varying vert reinf
0
300
600
900
1200
1500
1800
-600 -300 0 300 600 900 1200 1500 1800 2100 2400
NRd (kN)
MRd (kNm)
2oslash20 mm
4oslash16 mm
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm
Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for
walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm
1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2
wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
100
110
120
130
140
150
160
170
180
190
200
0 25 50 75 100 125 150 175 200 225 250
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
150
160
170
180
190
200
210
220
230
240
250
50 100 150 200 250 300 350 400 450
MRd (kNm)
VRd (kN)
2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
160
180
200
220
240
260
280
300
150 200 250 300 350 400 450 500 550 600 650
MRd (kNm)
VRd (kN)
2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Design of masonry walls D62 Page 67 of 106
V-M domain for walls with fixed legth varying vert reinf and σd
200
220
240
260
280
300
320
340
360
250 300 350 400 450 500 550 600 650 700 750 800 850
MRd (kNm)
VRd (kN)
2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 2500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
220
240
260
280
300
320
340
360
380
400
420
350 450 550 650 750 850 950 1050 1150
MRd (kNm)
VRd (kN)
2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2
wall l = 3000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
240
260
280
300
320
340
360
380
400
420
440
460
550 650 750 850 950 1050 1150 1250 1350 1450
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 3500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
V-M domain for walls with fixed legth varying vert reinf and σd
280
300
320
340
360
380
400
420
440
460
480
500
520
650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
MRd (kNm)
VRd (kN)
2oslash20 mm
4oslash16 mm
σd = 01 Nmmsup2
σd = 02 Nmmsup2
σd = 03 Nmmsup2
σd = 04 Nmmsup2σd = 05 Nmmsup2
σd = 06 Nmmsup2
σd = 07 Nmmsup2
σd = 08 Nmmsup2
σd ge 09 Nmmsup2
wall l = 4000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor
RNDZ-5-150 400 mm
Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for
walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive
stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm
Design of masonry walls D62 Page 68 of 106
63 HOLLOW CLAY UNITS
631 Geometry and boundary conditions
The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-
plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured
Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint
effects at the top of the wall (left) and without (cantilever system right)
The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential
housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in
the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is
limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common
residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not
relevant
Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The
developed hollow clay units system allows generally also additional reinforcement but in the following the
design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners
next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling
and the necessary compaction of the concrete infill is not affected by this additional reinforcement
significantly
Design of masonry walls D62 Page 69 of 106
632 Material properties
For the design under in-plane loadings also just the concrete infill is taken into account The relevant
property is here the compression strength
Table 19 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
εuk - 25permil ES Nmm2 200000 γS - 115
633 In-plane wall design
The in-plane wall design bases on the separation of the wall in the relevant cross section into the single
columns Here the local strain and stress distribution is determined
Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section
into several columns (left) and determination of the corresponding state in the column (right)
Design of masonry walls D62 Page 70 of 106
bull For columns under tension only vertical tension forces can be carried by the reinforcement The
tension force is determined depending to the strain and the amount of reinforcement
Figure 62 Stress-strain relation of the reinforcement under tension for the design
It is assumed the not shear stresses can be carried in regions with tension
bull For columns under compression the compression stresses are carried by the concrete infill The
force is determined by the cross section of the column and the strain
Figure 63 Stress-strain relation of the concrete infill under compression for the design
The shear stress in the compressed area is calculated acc to EN 1992 by following equations
(63)
(64)
(65)
(66)
Design of masonry walls D62 Page 71 of 106
The determination of the internal forces is carried out by integration along the wall length (= summation of
forces in the single columns)
Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section
634 Design charts
Following parameters were fixed within the design charts
bull Thickness of the system 24cm
bull Horizontal and vertical reinforcement ratio
bull Partial safety factors
Following parameters were varied within the design charts
bull Loadings (N M V) result from the charts
bull Length of the wall 1m 25m and 4m
bull Compression strength of the concrete infill 25 and 45 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Design of masonry walls D62 Page 72 of 106
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2
Figure 65 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250
Md [kNm]
Nd [
kN]
0 10 20
30 40 50
60 70 80
90 Loadings
Figure 66 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 73 of 106
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 67 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
0 50 100 150 200 250 300 350 400 450
Md [kNm]
Nd [
kN]
0 20 40
60 80 100
120 140 160
180 Loadings
Figure 68 Design chart for UNIPOR-System under in-plane loadings
Length = 1m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 74 of 106
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 69 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-5000
-4000
-3000
-2000
-1000
0
1000
0 200 400 600 800 1000 1200 1400 1600
Md [kNm]
Nd [
kN]
0 30 60
90 120 150
180 210 240
270 Loadings
Figure 70 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 75 of 106
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 71 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 72 Design chart for UNIPOR-System under in-plane loadings
Length = 25m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 76 of 106
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 73 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 500 1000 1500 2000 2500 3000 3500 4000
Md [kNm]
Nd [
kN]
0 40 80
120 160 200
240 280 320
360 Loadings
Figure 74 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=25Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 77 of 106
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 75 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=500Nmmsup2
Vd (MdNd) [kN]-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
0 1000 2000 3000 4000 5000 6000 7000
Md [kNm]
Nd [
kN]
0 70 140
210 280 350
420 490 560
630 Loadings
Figure 76 Design chart for UNIPOR-System under in-plane loadings
Length = 4m fck=45Nmmsup2 fyk=600Nmmsup2
Design of masonry walls D62 Page 78 of 106
64 CONCRETE MASONRY UNITS
641 Geometry and boundary conditions
The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential
buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions
both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs
The design for in-plane horizontal load of masonry made with concrete units was based on walls with
different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190
mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is
commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of
the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal
reinforcement was taken into account in the design charts
Figure 77 Geometry of concrete masonry walls (Variation of HL)
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical
reinforcement in all holes of the wall which becomes the construction time consuming
Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously
the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100
is presented in Figure 78
Design of masonry walls D62 Page 79 of 106
Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)
Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing
limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is
presented in Figure 79
Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)
Design of masonry walls D62 Page 80 of 106
642 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts
Table 20 Material properties parameters and partial safety factors used for the design
Material properties
fb Nmm2 1000
fm Nmm2 1000
K - 045
α - 070
β - 030
fk Nmm2 450
γM - 150
fd Nmm2 300
fyk0 Nmm2 020
fyk Nmm2 500
γS - 115
fyd Nmm2 43478
E Nmm2 210000
εyd permil 207
Design of masonry walls D62 Page 81 of 106
643 In-plane wall design
According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry
subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls
subjected to flexure shall be based on the following assumptions
bull the reinforcement is subjected to the same variations in strain as the adjacent masonry
bull the tensile strength of the masonry is taken to be zero
bull the tensile strength of the reinforcement should be limited by 001
bull the maximum compressive strain of the masonry is chosen according to the material
bull the maximum tensile strain in the reinforcement is chosen according to the material
bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or
rectangular (λ = 08x)
bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1
bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater
than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units
The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains
(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively
Figure 80 Stress and strain distribution in wall section (EN1996-1-1)
xdx i
sim
minus=
minus εε (67)
sissi E εσ = (68)
summinus=i
sim FFN (69)
xtfF wam 80= (610)
Design of masonry walls D62 Page 82 of 106
svisisi AF σ= (611)
sum ⎟⎠⎞
⎜⎝⎛ minus+⎟
⎠⎞
⎜⎝⎛ minus==
i
wisi
wmfR
bdFx
bFzHM
240
2 (612)
In case of the shear evaluation EN1996-1-1 proposes equation (7)
wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)
σ400 += vv ff bv ff 0650le (614)
where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is
the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit
Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of
masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the
cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit
of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some
part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit
seems to represent the rupture of a strut
Design of masonry walls D62 Page 83 of 106
644 Design charts
According to the formulation previously presented some design charts can be proposed assisting the design
of reinforced concrete masonry walls see from Figure 81 to Figure 87
These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear
capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the
reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force
only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear
stress of 2 MPa
-500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) (a)
-500 0 500 1000 1500 2000 2500 3000 3500 40000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Shea
r (kN
)
Normal (kN) (b)
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
She
ar (k
N)
Moment (kNm) (c)
Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and
(c) V x M
Design of masonry walls D62 Page 84 of 106
As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the
horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the
masonry walls but the flexure capacity should be take in account
-500 0 500 1000 1500 2000100
150
200
250
300
350
400
450
500
ρh = 0035 ρ
h = 0049
ρh = 0098
Shea
r (kN
)
Normal (kN) (a)
0 100 200 300 400 500 600 700 800 900 1000
150
200
250
300
350
400
450
ρh = 0035 ρh = 0049 ρh = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio
to HL=100) (a) V x N and (b) V x M
According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls
Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 400 800 1200 1600 2000 2400 2800 3200 3600
200
250
300
350
400
450
500
550
600
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=050) (a) M x N and (b) V x M
Design of masonry walls D62 Page 85 of 106
-500 0 500 1000 1500 2000 2500 30000
200
400
600
800
1000
1200
1400
1600
1800
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN) (a)
-200 0 200 400 600 800 1000 1200 1400 1600 1800150
200
250
300
350
400
450
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Shea
r (kN
)
Moment (kNm) (b)
Figure 84 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=070) (a) M x N and (b) V x M
-500 0 500 1000 1500 20000
100
200
300
400
500
600
700
800
900
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN) (a)
0 200 400 600 800 1000100
150
200
250
300
350
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Shea
r (kN
)
Moment (kNm) (b)
Figure 85 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=100) (a) M x N and (b) V x M
Design of masonry walls D62 Page 86 of 106
-300 0 300 600 900 12000
50
100
150
200
250
300
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN) (a)
-50 0 50 100 150 200 250 300
120
150
180
210
240
ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086
Shea
r (kN
)
Moment (kNm) (b)
Figure 86 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=175) (a) M x N and (b) V x M
-100 0 100 200 300 400 500 6000
10
20
30
40
50
60
70
ρv = 0049 ρv = 0070 ρv = 0098M
omen
t (kN
m)
Normal (kN) (a)
-10 0 10 20 30 40 50 60 7090
100
110
120
130
140
150
ρv = 0049 ρv = 0070 ρv = 0098
Shea
r (kN
)
Moment (kNm) (b)
Figure 87 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio
HL=350) (a) M x N and (b) V x M
Design of masonry walls D62 Page 87 of 106
7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING
71 INTRODUCTION
Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls
in the basement with earth pressure For masonry structural elements the resulting bending moment can be
suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity
can be assured by reinforcement
If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash
the bending is dominant and the effect of additional axial force can be neglected This approach is also
allowed acc EN 1996-1-1 2005
72 PERFORATED CLAY UNITS
721 Geometry and boundary conditions
Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are
regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use
of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m
In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of
deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable
D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and
a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural
configurations for out of plane loads are as represented in Figure 88
Figure 88 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)
Design of masonry walls D62 Page 88 of 106
722 Material properties
The materials properties that have to be used for the design under out-of-plane loading of reinforced
masonry walls made with perforated clay units concern the materials (normalized compressive strength of
the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and
ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength
fk) To derive the design values the partial safety factors for the materials are required The compressive
strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main
parameters adopted for the creation of the design charts
Table 21 Material properties parameters and partial safety factors used for the design
To have realistic values of element deflection the strain of masonry into the model column model described
in the following section sect723 was limited to the experimental value deduced from the compressive test
results (see D55 2008) equal to 1145permil
723 Out of plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1
the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-
plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the
Material property
CISEDIL
fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10
Design of masonry walls D62 Page 89 of 106
slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both
ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors
In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if
the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any
case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading of the CISEDIL system as shown in sect 724
When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when
they are not retained by reinforced concrete or other rigid floors the design should follow the same
provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into
account the effects of the second order by means of an additional design moment
(71)
However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane
tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is
developed with some constructive details that allow improving their out-of-plane behaviour even if the
second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter
of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is
calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account
only the geometry of the wall but do not take into account the real eccentricity due to the section properties
These effects and their strong influence on the wall behaviour were on the contrary demonstrated by
means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)
Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and
the vertical load eccentricity in the particular case of cantilever boundary conditions The model column
method which can be applied to isostatic columns with constant section and vertical load was considered It
is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛minus=
Lxvy
2cos1max
π (72)
where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall
Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0
(at the base of the wall) it is obtained (eq 73)
max2
2
41 v
LEJM
ry
base
π==⎟
⎠⎞
⎜⎝⎛=primeprime (73)
By inverting this equation the maximum (top) displacement is obtained and from that the second moment
order The maximum first order bending moment MI that can be sustained by the wall can be thus easily
calculated by the difference between the sectional resisting moment M calculated as above and the second
order moment MII calculated on the model column
Design of masonry walls D62 Page 90 of 106
The validity of the proposed models was checked by comparing the theoretical with the experimental data
see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without
using any safety factor On the base of this moment by means of the model column method the top
deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)
From this value it is possible to obtain the MII which shows the same good agreement and from the
underestimated value of MR a conservative value of MI
Table 22 Comparison of experimental and theoretical data for out-of-plane capacity
Experimental Values Out-of-Plane Compared
Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118
vmax mm 310 310 310 Theoretical Values
Out-of-Plane Compared Parameters MIdeg MIIdeg MR
N kN 50 50 50 M kNm 702 148 85
vmax mm 296 296 296
The design charts were produced for different lengths of the wall Being the reinforcement constituted by
4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position
there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls
can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length
equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm
considered typical for real building site conditions In this case the reinforcement percentage is that resulting
from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides
these geometrical aspects also the mechanical properties of the materials were kept constant The height of
the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from
one case to the other In this case also the vertical load that produces the second order effect was changed
in order to take into account indirectly of the different roof dead load and building spans
Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions
Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights
taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in
the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into
account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane
flexural design of the masonry section or in case the slenderness is higher than 12 and the second order
effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91
Design of masonry walls D62 Page 91 of 106
724 Design charts
M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)
TensionCompression
Limit 2-3
Limit 3-4
Limit 4-5
Limit 5-6
Limit 60
50
100
150
200
250
300
350
-10000 -8000 -6000 -4000 -2000 0 2000 4000
NRd (kN)
MRd (kNm)
l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm
Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of
the wall and for fixed percentage of vertical reinforcement
Design of masonry walls D62 Page 92 of 106
Variation of the Moments with different vertical loads
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
N (kN)
MRD (kNm)
rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg
t = 380 mm λ ge 12 Feb 44k
Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for
walls of different heights taking into account the second order effects (dashed lines)
Variation of the Lateral load from MIdeg for different height and different vetical loads
0
1
2
3
4
5
6
7
0 10 20 30 40 50
N (kN)
LIdeg (kN)
rmC-45m
rmC-5m
rmC-6m
rmC-7m
rmC-8m
t = 380 mm λ gt 12 Feb 44k
Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for
walls of different heights taking into account the second order effects
Design of masonry walls D62 Page 93 of 106
73 HOLLOW CLAY UNITS
731 Geometry and boundary conditions
Generally the mentioned structural members are full storey high elements with simple support at the top and
the base of the wall The height of the wall is adapted to the use of the system eg in housing structures
generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the
effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663
Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66
The use and consideration of flanges is generally possible but simply in the following neglected
732 Material properties
For the design under out-plane loadings also just the concrete infill is taken into account The relevant
property for the infill is the compression strength
Table 23 Material properties parameters and partial safety factors used for the design
Material property UNIPOR
fck Nmm2SCC
25 Nmmsup2 (min demand)measured 275 Nmmsup2
γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085
fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)
γS - 115
Design of masonry walls D62 Page 94 of 106
733 Out of plane wall design
The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can
be assumed according to following figure
Figure 93 Behaviour of a reinforced masonry structural element under dominant
out-of-plane bending in the ULS
According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress
exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1
(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)
The bending resistance is determined
(74)
with
(75)
A limitation of MRd to ensure a ductile behaviour is given by
(76)
The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of
ndashplane shear loadings appear following failure modes have to be checked
bull Friction sliding in the joint VRdsliding = microFM
bull Failure in the units VRdunit tension faliure = 0065fb λx
If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200
with the formulation already given in section sect723 eq 71
Design of masonry walls D62 Page 95 of 106
734 Design charts
Following parameters were fixed within the design charts
bull Reference length 1m
bull Partial safety factors 20 resp 115
Following parameters were varied within the design charts
bull Thickness t=20 cm and 30cm (d=t-4cm)
bull Loadings MRd result from the charts
bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m
bull Compression strength 4 and 10 Nmmsup2
bull Yield strength of the reinforcement 500 and 600 Nmmsup2
Table 24 Properties of the regarded combinations A ndash L of in the design chart
Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2
Design of masonry walls D62 Page 96 of 106
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12
as [cmsup2m]
MR
d [kN
mm
]
ABCDEFGHIJKL
Figure 95 Design chart for dominant out-of-plane bending moments in the ULS fyk=600Nmmsup2
Design of masonry walls D62 Page 97 of 106
74 CONCRETE MASONRY UNITS
741 Geometry and boundary conditions
In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral
loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action
due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-
plane resistance of the wall
The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with
the geometry and vertical reinforcement distribution already presented in section 64 Walls with different
lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1
mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly
about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design
charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of
vertical and horizontal reinforcement was taken into account in the design charts
One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement
ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits
of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in
Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value
used in Portuguese buildings
In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2
edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)
742 Material properties
All properties used in this analysis are referred to the desirable design properties of the real scale units to be
used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the
mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1
From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength
under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate
strain εu) were considered to be the same the ones obtained in the experimental campaign according to the
results pointed out in D55 To derive the design values the partial safety factors for the materials are
required Table 20 gives the main parameters adopted for the creation of the design charts see section
642
Design of masonry walls D62 Page 98 of 106
743 Out-of-plane wall design
In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the
effect of shear can be negligible in most cases because the thickness of wall is several times lower than the
other dimensions and on the other hand the shears loads can not be significant
According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same
formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the
reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a
slenderness ratio greater than 12 may be designed using the principles and application rules for
unreinforced members taking into account second order effects by an additional design moment
xεm
εsc
εst
Figure 96 ndash Strain distribution in out-of-plane wall section
In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made
based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive
resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane
loading as shown in 744
744 Design charts
According to the formulation previously presented some design charts can be proposed to help the design of
reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced
masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane
walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97
Design of masonry walls D62 Page 99 of 106
-500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
hL = 050 hL = 070 hL = 100 hL = 175 hL = 350
Mom
ent (
kNm
)
Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL
According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls
Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural
behaviour of the walls independent of the aspect ratio
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000
20
40
60
80
100
120
ρv = 0035
ρv = 0049 ρv = 0070 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(a)
-500 0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
80
90
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088
Mom
ent (
kNm
)
Normal (kN)(b)
-500 0 500 1000 1500 200005
101520253035404550556065
ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091
Mom
ent (
kNm
)
Normal (kN)(c)
-300 0 300 600 900 12000
5
10
15
20
25
30
35
40
ρv = 0037
ρv = 0049 ρv = 0070 ρv = 0086
Mom
ent (
kNm
)
Normal (kN)(d)
Design of masonry walls D62 Page 100 of 106
-100 0 100 200 300 400 500 6000
2
4
6
8
10
12
14
16
18
20
ρv = 0049
ρv = 0070 ρv = 0098
Mom
ent (
kNm
)
Normal (kN) (e)
Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350
Design of masonry walls D62 Page 101 of 106
8 OTHER DESIGN ASPECTS
81 DURABILITY
For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it
can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in
mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions
moisture) the level of protection for reinforcing steel has to be determined
The demands are give in the following table (EN 1996-1-1 2005 433)
Table 25 Protection level for the reinforcement steel depending on the exposure class
(EN 1996-1-1 2005 433)
82 SERVICEABILITY LIMIT STATE
The serviceability limit state is for common types of structures generally covered by the design process
within the ultimate limit state (ULS) and the additional code requirements - especially demands on the
minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio
Also the minimum thickness (corresponding slenderness) has to be checked
Relevant types of construction where SLS might become relevant can be
Design of masonry walls D62 Page 102 of 106
bull Very tall exterior slim walls with wind loading and low axial force
=gt dynamic effects effective stiffness swinging
bull Exterior walls with low axial forces and earth pressure
=gt deformation under dominant bending effective stiffness assuming gapping
For these types of constructions the loadings and the behaviour of the structural elements have to be
investigated in a deepened manner
Design of masonry walls D62 Page 103 of 106
REFERENCES
ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry
Standards Joint Committee
AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001
AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC
Press Boca Raton New York
AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of
the Army (Corps of Engineers)
BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and
prestressed masonry
DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-
2005-018120
DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls
the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-
018120
DM 14012008 (2008) Technical Standards for Constructions
EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo
EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight
imposed loads for buildingsrdquo
EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo
EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo
EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for
buildingsrdquo
EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and
unreinforced masonry structuresrdquo
EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules
seismic actions and rules for buildingsrdquo
LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver
Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-
EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute
Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-
C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals
NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New
Zeland Wellingston
OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and
subsequent updating in Italian)
Design of masonry walls D62 Page 104 of 106
OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in
Italian)
SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs
New Jersey
TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)
TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in
structures and Construction Elnashai A S amp Dowling P J
Design of masonry walls D62 Page 105 of 106
ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE
As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced
masonry walls verification Information on how to use the software are given in this annex as the software is
based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting
parameters of reinforced masonry walls made with the different construction technologies developed and
tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting
mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)
with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the
design values of the applied axial load shear and bending moment can carry out the masonry wall
verifications using the So-Wall
The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the
use of the software the execution of macros has to be enabled At the beginning the type of dominant
loading has to be chosen
bull in-plane loadings
or
bull out-of-plane loadings
As suitable design approaches for the general interaction of the two types of loadings does not exist the
user has to make further investigation when relevant interaction is assumed The software carries out the
design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the
Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by
the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions
or coating of the reinforcement according to what is reported in section sect 8
For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane
loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended
for axial tension forces this type of loading is not covered by this design software
When the type of loading for which carrying out the verification is inserted the type of masonry has to be
selected By doing this the software automatically switch the calculation of correct formulations according to
what is written in section from sect5 to sect7
Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane
loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to
be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software
and they reflect the configuration of the developed construction systems The amount of the horizontal and
vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding
value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements
has to be considered by dividing the whole wall in several sub-elements
Design of masonry walls D62 Page 106 of 106
Figure 99 Cross section for out-of-plane and in-plane loadings
A list of value of mechanical parameters has to be inserted next These values regard the unit mortar
concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory
and in any case each parameter found into the software is explained in detail into the present deliverable
D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the
Calculate f_k button) or entered directly by the user as input parameter For the compression strength of
ALAN masonry the factored compressive strength is directly evaluated by the software given the material
properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account
including long term effect of the concrete
The choice of the partial safety factors are made by the user After entering the design loadings the
calculation is started pressing the Design-button The result is given within few seconds The result can also
be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with
different symbols and colours The design action is marked directly within the chart In the main page a
message indicates whereas the masonry section is verified or if not an error message stating which
parameter is outside the safety range is given
For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and
can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-
M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a
password