Transcript of Lecture 2 3 Compression, Condition Assess
Classnotes for ROSE School Course in: Classnotes for ROSE
School Course in: Masonry Structures Masonry Structures Lesson 2
and 3: Properties of Masonry Materials Introduction, compressive
strength, modulus of elasticity condition assessment, movements
Notes Prepared by: Daniel P. Abrams Willett Professor of Civil
Engineering University of Illinois at Urbana-Champaign October 7,
2004 Masonry Structures, Lectures 2-3, slide 1 Historical Use of
Masonry as a Structural Material Masonry Structures, Lectures 2-3,
slide 2
The First Building Material The first masonry structures were
constructed of mud, sun- dried brick. The people of Jericho were
building with brick more than 9000 years ago. Sumerian and
Babylonian builders covered brick walls with kiln-baked glazed
brick. Mesopotamian builders Etemenanki Ziggurat constructed temple
towers from height 91 meters 4000 BC to 600 BC. Masonry Structures,
Lectures 2-3, slide 3 The First Building Material Stone masonry was
used for Egyptian pyramids c. 2500 BC. Pyramid of Khufu at Giza
measured 147 m. high and 230 m. square. Pyramid of Khafre at Giza
was constructed without cranes, pulleys or lifting tackle. No
mortar or adhesive was used. Ancient examples of Cyclopean masonry
found throughout Pyramid of Khafre at Giza Europe, China and Peru.
Egyptian houses made of mud- brick walls. Masonry Structures,
Lectures 2-3, slide 4
Greek and Roman Architecture Early Greek architecture (3000 to
700 BC) used massive stone blocks for walls, and early vaults and
domes. Greeks constructed with limestone and marble. Romans
constructed with concrete, terra cotta and El Puente Aqueduct fired
clay bricks. near Segovia Spain Romans refined arch, vault 1st
Century AD and dome construction to two tiers of arches 28. 5m tall
construct great aqueducts, coliseums and palaces were built with
clay brick. Masonry Structures, Lectures 2-3, slide 5 Applications
in China The Great Wall of China was constructed from 221 to 204
BC. The wall winds 2400 km from Gansu to the Yellow Sea, and is the
longest human-made structure in the world. The wall is constructed
of Great Wall of China earth and stone with a brick 6 to 15m. tall
facing in the eastern part. 4.6 to 9.1m wide at base ave. 3.7 m
wide at top Masonry Structures, Lectures 2-3, slide 6
Byzantine Architecture Huge domed churches were built on a
scale far larger than achieved with the Romans. Innovative
Byzantine technology allowed architects to design a basilica with
an immense dome over an open, square space. Isalmic architects
developed a rich variety of Hagia Sophia, Istanbul pointed,
scalloped, constructed 532-537 AD horseshoe and S-curved dome fell
after earthquake in 563 arches for mosques and palaces. Masonry
Structures, Lectures 2-3, slide 7 Masonry in the Americas Early
pyramids built c. 1200 BC at the Olmec site of LaVenta in Tabasco
Mexico. Later monuments constructed by the Maya, Toltecs and Aztecs
in central Mexico, the Yucatan, Guatemala, Honduras, El Salvador
and Peru were based on the Olmec plan. Four-sided, flat-topped
Pyramid of the Sun polyhedrons with stepped Teotihuacan Mexico
sides. 66-m. high 2nd century AD Masonry Structures, Lectures 2-3,
slide 8
Masonry in the Americas Aztec, Mayan and other Indian cultures
relied on masonry for housing and monuments. Stone veneers used by
Mayans at Uxmal in 9th century. Slight outward lean of these
buildings made them appear light and elegant. Pueblo Bonito housed
up to Pueblo Bonito 1000 residents. Chaco Canyon, NM Anasazi
constructed 10th Century AD multistory pueblos from stone, covers
more than 3 acres mud and beams during period of 1100-1300 AD.
Masonry Structures, Lectures 2-3, slide 9 Romanesque, Gothic and
Renaissance With Romanesque architecture (10th to 12th century),
large internal spaces were spanned with barrel vaults supported on
thick, squat columns and piers. Gothic architecture (12th to 16th
century) used a pointed arch which minimized outward thrust and
resulted in lighter and thinner walls. Santa Maria degli Angeli
Renaissance architecture was Firenza, Italy influenced by the round
arch, constructed 1420-61 AD the barrel vault, and the dome. 39 m.
in diameter, 91 m. high Filippo Brunelleschi Masonry Structures,
Lectures 2-3, slide 10
Masonry at the Turn of the Century URM brick bearing-wall
construction used for multistory buildings. Design based on
empirical rules. URM construction popular for low-rise buildings in
inner core of cities, many of which are still standing today. In
1908, the Nat. Assoc. of Cement Users developed the first
specification for concrete block. Fifty million cmus produced in
1919 which grew to 467 million in Monadnock Building 1941. Chicago,
1891 D. Burnham and J. Root Masonry Structures, Lectures 2-3, slide
11 Rational Structural Design Masonry compressive strength
standardized by 1910. Empirical design still prominent through
first half of twentieth century. Research on structural masonry
done at the Structural Clay Products Association and Portland
Cement Association. BIA in the 1966 and NCMA in 1970 developed
standards for structural code of Hammurabi design of brick and
block. Babylon, 1780 BC Masonry Structures, Lectures 2-3, slide
12
Recent Code Developments TMS developed first standard for
brick/block masonry, and became Chapter 24 of 1985 UBC. Further
revised in 1988, 1991 and 1994 (as Chapter 21). ACI-ASCE 530 code
published in 1988. Further revised in 1992 and 1995 as MSJC code.
Strength design introduced into 1985 UBC. New chapter on strength
design in 2002 MSJC. MSJC Building Code Requirements for Masonry
Masonry Structures, Lectures 2-3, slide 13 Masonry Seismic
Provisions Chapters 8 and 8A of NEHRP Recommended Seismic
Provisions for New Buildings (FEMA 222A, 1994) Appendix C of NEHRP
Handbook for Seismic Evaluation of Existing Buildings (FEMA 178,
1992) FEMA 273/356 Guidelines for Seismic Rehabilitation of
Buildings NEHRP Provisions for New Buildings Masonry Structures,
Lectures 2-3, slide 14
Present Applications The use of masonry as a structural
material has been developing rapidly in the western US over the
last two decades. Tall buildings of structural masonry are now
being constructed. A slow revolution in the Excaliber Hotel, Las
Vegas east. tallest building of structural masonry URM still used
for new construction. Tall, slender walls compete with tilt-up
construction. Masonry Structures, Lectures 2-3, slide 15 Masonry
Compressive Strength Masonry Structures, Lectures 2-3, slide
16
Mechanics of Masonry in Compression P = y l A P zb xb masonry
unit tj xb stresses shown for zb tb mortar > unit y y zm xm
mortar P xm zm y Masonry Structures, Lectures 2-3, slide 17 Biaxial
Strength of Masonry Units flat-wise compressive strength of unit
from test fut y compression fut brick splits when: y fut xb = f
'udt (1 ) f 'ut direct tensile strength of unit from test fudt xb
tension fudt fudt Masonry Structures, Lectures 2-3, slide 18
Biaxial Strength of Mortar fjt mortar crushes when: - f'
uniaxial compressive y jt xm = strength from test 4.1 y compression
fjt 4.1 1.0 y multiaxial f' jt compressive xm xm strength xm
compression y Masonry Structures, Lectures 2-3, slide 19 Masonry
Compressive Strength equilibrium relation: P xb( tbl ) = xm( t jl )
tj xb = xm tb tj if mortar crushes: tb ( y f ' jt ) xm = or 4.1 t j
/ tb t j / tb xb = ( y f ' jt ) = ( y f ' jt ) where = 4.1 4.1 P if
brick splits: y xb = f 'udt (1 - ) f 'ut Masonry Structures,
Lectures 2-3, slide 20
Masonry Compressive Strength if mortar crushes and brick splits
simultaneously: y ( y f ' jt ) = f'udt (1 ) f ' ut f'udt y f' jt =
f'udt y f'ut f ' +f ' jt y = udt Hilsdorf equation f 'ut f 'udt +f
'ut y f'm = prism strength = Uu where Uu = coefficient of
non-uniformity (range 1.1 to 2.5) Masonry Structures, Lectures 2-3,
slide 21 Nonlinear Mortar Behavior y 1000 psi triaxial test y zm 30
psi = xm = xm xm zm zm y v y 1000 psi l x 30 psi z Masonry
Structures, Lectures 2-3, slide 22
Unit Splitting vs. Mortar Crushing Linear Mortar y mortar unit
stress path stress path fut mortar failure envelope unit mortar
crushes failure fjt envelope failure compression tension xb xm fudt
Masonry Structures, Lectures 2-3, slide 23 Unit Splitting vs.
Mortar Crushing Nonlinear Mortar y unit fut stress path mortar
failure unit splits envelope unit fjt mortar failure stress path
envelope failure compression tension xb xm fudt Masonry Structures,
Lectures 2-3, slide 24
Incremental Lateral Tensile Stress on Masonry Unit Assuming
linear behavior for masonry unit, and nonlinear mortar behavior: Eb
y b - m( xm,zm ) Ej ( xm, z m ) xb = Eb tb Eb tb - b - m ( xm,zm )
1 + Ej ( xm, z m ) t j Ej ( xm, z m ) t j where : = Poisson s ratio
for masonry unit b m = Poisson s ratio for mortar = Young s modulus
for masonry unit E b E j = Young s modulus for mortar t b =
thickness of masonry unit = tj thickness of mortar joint = xm , zm
lateral mortar compressiv e stresses From Atkinson and Noland A
Proposed Failure Theory for Brick Masonry in Compression,
Proceedings, Third Canadian Masonry Symposium, Edmonton, 1983, pp.
5-1 to 5-17. Masonry Structures, Lectures 2-3, slide 25 Effect of
Mortar on Compression Weaker Mortars M S y weaker mortars result in
weaker prism strength because ratio of vmortar/vunit is larger N
weaker mortars result in greater extents of nonlinear prism
behavior O y Masonry Structures, Lectures 2-3, slide 26
Effect of Mortar on Compression Stronger Mortars M may not
adhere to units as well. S y a larger scatter of experimental data
with the stronger mortars. N create a stiffer prism which is more
sensitive to alignment problems during testing and more brittle. O
more variable masonry compressive strength. y Masonry Structures,
Lectures 2-3, slide 27 Guidelines for Prism Testing UBC Sec.
2105.3.2: Masonry Prism Testing A set of five prisms shall be built
and tested prior to construction in accordance with UBC Std. 21-17.
At least three prisms per 5,000 sq. feet of wall area shall be
built and tested during construction. Test values for prism
strength shall exceed design values. Note that testing is not
required if half of allowable stresses are used for design. NCMA
TEK 18-1 Concrete Masonry Prism Testing Masonry Structures,
Lectures 2-3, slide 28
Guidelines for Prism Testing UBC Standard 21-17: Test Method
for Compressive Strength of Masonry Prisms Methods for prism
construction, transportation and curing. h Preparation for testing,
test procedures, etc. Calculation for compressive stress. Net area,
correction factors. tp Table 21-17A prism h/tp 1.3 1.5 2.0 2.5 3.0
4.0 5.0 correction 0.75 0.86 1.00 1.04 1.07 1.15 1.22 factor Use
lesser of average strength or 1.25 times least strength. Masonry
Structures, Lectures 2-3, slide 29 Code Values for Prism Strength
UBC Sec. 2105.3.4: Unit Strength Method Use test values per UBC
21-17. Take fm equal to 75% of average prism record value.
(2105.3.3) Take fm from Table 21-D if no prisms are tested.
Associated BIA Technical Note: 35 Early Strength of Brick Masonry
Masonry Structures, Lectures 2-3, slide 30
Compressive Strength of Masonry per UBC UBC Table 21-D
Specified compressive strength of clay masonry, fm Specified
Compressive Strength Compressive Strength of Masonry, fm, (psi) of
Clay Masonry Units (psi) Type M/S mortar Type N mortar 14,000 or
more 5,300 4,400 12,000 4,700 3,800 10,000 4,000 3,300 8,000 3,350
2,750 6,000 2,700 2,200 4,000 2,000 1,600 Masonry Structures,
Lectures 2-3, slide 31 Compressive Strength of Masonry per UBC UBC
Table 21-D Specified compressive strength of concrete masonry, fm
Specified Compressive Strength Compressive Strength of Masonry, fm,
(psi) of Concrete Masonry Units (psi) Type M/S mortar Type N mortar
4,800 or more 3,000 2,800 3,750 2,500 2,350 2,800 2,000 1,850 1,900
1,500 1,350 1,250 1,000 950 Masonry Structures, Lectures 2-3, slide
32
MSJC Specifications for Prism Strength Sec. 1.4.B Compressive
Strength Determination Sec. 1.4B.2 Unit Strength method Table 1
Compressive Strength for Clay Masonry Table 2 Compressive Strength
for Concrete Masonry Sec. 1.4B.3 Prism Test Method ASTM C 1314
Masonry Structures, Lectures 2-3, slide 33 Compressive Strength of
Masonry per MSJC MSJC Specification Table 1 Compressive strength of
clay masonry by unit strength method Net Area Compressive Strength
Net Area of Clay Masonry Units (psi) Compressive Strength of
Masonry Type M/S Mortar Type N Mortar (psi) 1,700 2,100 1,000 3,350
4,150 1,500 4,950 6,200 2,000 6,600 8,250 2,500 8,250 10,300 3,000
9,900 - 3,500 13,200 - 4,000 Masonry Structures, Lectures 2-3,
slide 34
Compressive Strength of Masonry per MSJC MSJC Specification
Table 2 Compressive strength of concrete masonry by unit strength
method Compressive Strength Net Area of Concrete Masonry Units
(psi) Compressive Strength of Masonry Type N Mortar Type M/S Mortar
(psi) 1,250 1,300 1,000 1,900 2,150 1,500 2,800 3,050 2,000 3,750
4,050 2,500 4,800 5,250 3,000 MSJC values of compressive strength
from Table 1 and Table 2 are intended to be used in lieu of prism
tests to estimate needed mortar types and unit strengths for a
required compressive strength. Masonry Structures, Lectures 2-3,
slide 35 Comparison of Default Prism Strengths UBC Table 21-D vs.
MSJC Specifications Table 1 C lay-U nit Masonry 6 M/S, UBC 5 Pr is
m St re ngt h, f'm ksi N, UBC 4 M /S, M SJC 3 N , M SJC 2 1 0 0 5
10 15 20 Unit Strength, ksi Default prism strengths are lower
bounds to expected values. Masonry Structures, Lectures 2-3, slide
36
Comparison of Default Prism Strengths UBC Table 21-D vs. Table
2 MSJC-Spec. Concrete-Unit Masonry 3.5 M/S, UBC 3 M/S, MSJC N, UBC
P rism Strength, f'm ksi 2.5 N, MSJC 2 1.5 1 0.5 0 0 2 4 6 8 10
Unit Strength, ksi Note: MSJC and UBC values are almost identical
for concrete masonry. Default prism strengths are lower bounds to
expected values. Masonry Structures, Lectures 2-3, slide 37 Masonry
Elastic Modulus Masonry Structures, Lectures 2-3, slide 38
Elastic Modulus of Masonry in Compression Basic Mechanics j =
deformation of mortar = j t j = E t j [1] y P = y Anet j t b =
deformation of unit = b t b = [2] y E b b = deformation of masonry
= E ( t j + t b ) y [3] m y = j + b = E t j + E tb y [4] tj j b tb
t t = thickness ratio = t j [5] b E m = modulus ratio = E j [6] b t
j + tb = ( 1 + t )tb [7] Masonry Structures, Lectures 2-3, slide 39
Elastic Modulus of Masonry in Compression Basic Mechanics y y from
3 and 7 : = ( t j + tb ) = ( 1 + t )tb [8] P = y Anet m m y y from
1,5 and 6 : j = t tb tj = [9] m Eb Ej y y y tj ( 1 + t )t b = t tb
+ [10] from 4, 8 and 9 : tb m Eb Em Eb tb (1+ t ) 1 t = +1) ( [11]
Eb m Em (1+ t ) m = b t [12] (1+ ) m Reference: Structural Masonry
by S. Sahlin, Section D.2 Masonry Structures, Lectures 2-3, slide
40
Elastic Modulus of Masonry in Compression (1 + t ) = Em t Em
Emasonry Eb (1 + = ) m Eb Eunit 1.2 1.0 t= 0.152 0.8 concrete block
masonry 0.76 (typical for brick masonry) t= 0.0498 0.6 clay-unit
masonry (typical for concrete block masonry) 0.4 0.2 E mortar m =
0.0 E unit 0 0.5 1 1.5 2 Masonry Structures, Lectures 2-3, slide 41
Code Assumptions for Elastic Modulus UBC Sec. 2106.2.12 and
2106.2.13 & MSJC Sec. 1.8.2.2.1 and 1.8.2.2.2 secant method
estimate without prism test data UBC Sec. 2106.2.12.1 for clay-unit
or concrete masonry fm Em = 750 fm < 3000 ksi Em fmt MSJC Sec.
1.8.2.1.1 for clay-unit masonry Em = 700 fm for concrete-unit
masonry 0.33 fmt Em = 900 fm UBC 2106.2.13 0.05 fmt MSJC Sec.
1.8.2.2.2 m G = 0.4 Em Masonry Structures, Lectures 2-3, slide
42
Strength of URM Bearing Walls Masonry Structures, Lectures 2-3,
slide 43 Unreinforced Bearing and Shear Walls Structural Walls have
3 functions: floor or roof loads (bearing wall) resist vertical
compression resist bending from eccentric vertical loads and/or
transverse wind, earthquake, or blast loads ds oa e l wall) resist
in-plane shear and ers in-plane sv lane bending from lateral loads
ran-of-p shear and t applied to building system t moment (ou in
direction parallel with (shear wall) plane of wall Ref: BIA Tech.
Note 24 The Contemporary Bearing Wall Masonry Structures, Lectures
2-3, slide 44
Unreinforced Bearing and Shear Walls Historically walls were
sized in terms of h/t ratio which was limited to 25. 2 M = wh = F S
= F t 2 6 8 b b h = 8 F = 8 (50 psi) ( 144 ) 2 b t 6 w 6 (15 psf) 2
wind = 15 psf h h = 25.3 t Empirical design of masonry UBC 2105.2 h
< 35 Associated BIA Technical Note: 24 series The Contemporary
Bearing Wall Building Masonry Structures, Lectures 2-3, slide 45
Concentric Axial Compression Buckling Load Euler buckling load: P =
y Anet Pcr = Em2I cr = Em I 2 2 ( kl ) ( kl ) A 2 for rectangular
section: h = kl bt 3 A = bt I= 12 bt 3 t2 I r= = = = 0.289t A 12bt
12 t Masonry Structures, Lectures 2-3, slide 46
Concentric Axial Compression 3 2 m( bt ) 0 .82 m 12 = cr = 2 kl
2 y (kl) bt () t if Em =750 f 'm and h' = kl, then cr = 615 f'2m (
h' ) fm t 24.8 Euler curve cutoff at f 'm = cr = 615f'2 , or h' /t
= 24 .8 m ( h' ) 615f' m cr = t ( h' ) 2 t 0.25 fm MSJC/UBC h/t 100
25 50 75 Note: for MSJC and UBC plot, r=0.289t is assumed Masonry
Structures, Lectures 2-3, slide 47 Code Allowable Compressive
Stress Fa MSJC Section 2.2.3 and UBC Section 2107.3.2: f 'm 0.3 for
h/r < = 99: Fa = 0.25 fm [1 - (h/140r)2] MSJC Eq. 2-12 and UBC
Eq. 7-39 for h/r > 99 : Fa = 0.25 fm [(70r/h)2] MSJC Eq. 2-13
and UBC Eq. 7-40 0.2 0.1 h' 0 r 0 50 100 150 200 Masonry
Structures, Lectures 2-3, slide 48
Concentric Axial Compression UBC 2106.2.4: Effective Wall
Height no sidesway restraint translation restrained h=kh h rotation
rotation rotation rotation k = h/h unrestrained restrained
unrestrained restrained 1.0 0.70 2.0 2.0 MSJC 2.2.3: Buckling Loads
2EmI ( 1 0.577 e )3 P 1 Pe Pe = (2 11 / 2 - 15) 4 r h' 2 e =
eccentricity of axial load Masonry Structures, Lectures 2-3, slide
49 Concentric Axial Compression UBC 2106.2.3: Effective Wall
Thickness C. Cavity Walls A. Single Wythe t = specified thickness
both wythes loaded one wythe loaded P B. Multiwythe P1 P2 t mortar
or air space grout filled collar joint wire joint reinforcement t2
t1 t2 t1 each wythe t = t1 + t 2 2 2 considered separate Masonry
Structures, Lectures 2-3, slide 50
Concentric Axial Compression UBC 2106.2.5: Effective Wall Area
Effective area is minimum area of mortar bed joints plus any
grouted area. face shell raked joint effective thickness effective
thickness Neglect web area if face-shell bedding is used. Masonry
Structures, Lectures 2-3, slide 51 Example: Concentric Axial
Compression Determine the allowable vertical load capacity of the
unreinforced cavity wall shown below per both the UBC and the MSJC
requirements. Pa Case A: Prisms have been tested. fm = 2500 psi for
block wall 8CMU 4 brick fm = 5000 psi for brick wall face-shell
metal ties bedding Case B: No prisms have been tested. 20-0 fm =
1500 psi for block wall (Type I CMUs and 7.63 Type S mortar will be
specified.) 3.63 Per NCMA TEK 14-1A for face shell bedding:
concrete footing Anet = 30.0 in2 Inet = 308.7 in4 r = 2.84 in. (r
based only on loaded wythe) Masonry Structures, Lectures 2-3, slide
52
Example: Case A MSJC Section 2.2.3 & UBC 2107.3.2 h' 12(
20') = = 84 .5 r 2 .84 in. for h'/r < 99: Fa = 0 .25 f'm [ 1
(h'/ 140 r)2 ] Fa = 0 .159 f'm = 0 .159( 2500 psi) = 397 psi Pa = (
0 .397 ksi)( 2 x 1.25 in. x 12 in.) = 11.9 kip/ft MSJC Section
2.2.3: check buckling * 2 m I 1 e ( 1 0 .577 )3 P< Pe = 0 .25 h2
4 r Em = 900 f'm MSJC Section 1.8 .2 .2 .1 Em = 900 2500 = 2 ,250
,000 psi = 2250 ksi 2( 2 .25 x 10 3 )( 308.7 ) P = 0 .25 = 29 .8
kip/ft buckling doesn't govern ( 240 )2 Pa = 11.9 kip / ft for both
codes * no buckling check per UBC. Masonry Structures, Lectures
2-3, slide 53 Example: Case B MSJC Section 2.2.3 & UBC 2107.3.2
h' 12( 20' ) = = 84.5 r 2.84 in . for h' / r < 99 : Fa = 0.25 f
'm [ 1 ( h' / 140r )2 ] Fa = 0 .159 f 'm = 0.159( 1500 psi ) = 283
psi Governs for MSJC, take 1/2 for UBC since no Pa = ( 0.283 ksi )(
2 x 1.25 in . x 12 in .) = 7.2kip / ft special inspection is
provided. MSJC Section 2.2.3: check buckling 2 m I 1 e P< Pe =
0.25 ( 1 0.577 )3 h2 4 r m = 900 f 'm MSJC Section 1.8.2.2.1 m =
900 1500 = 1350,000 psi = 1350 ksi 2 ( 1.35 x 10 3 )( 308.7 ) P =
0.25 = 17.85kip / ft buckling doesn' t govern ( 240 )2 Masonry
Structures, Lectures 2-3, slide 54
Eccentric Axial Compression e axial stress bending stress P M =
Pe P Pe P Mc M fa = fb = = A I S h combined axial stress plus
bending -fa + fb fa + fb t Ref: NCMA TEK 14-4 Eccentric Loading of
Nonreinforced Concrete Masonry Masonry Structures, Lectures 2-3,
slide 55 Eccentric Axial Compression UBC Section 2107.2.7 and MSJC
2.2.3: Unity Formula fa f limiting compressive stress + b < 1 .0
(controls for small es) Fa Fb where Fa= allowable axial compressive
stress (UBC 2107.3.2 or MSJC Sec. 2.2.3) Fb= allowable flexural
compressive stress = 0.33 fm (UBC 2107.3.3 or MSJC Sec 2.2.3) UBC
2107.3.5 or MSJC 2.2.3: Allowable Tensile Stress limiting tensile
stress -fa + fb < Ft (controls for large es) where Ft =
allowable tensile stress References Associated NCMA TEK Note 31
Eccentric Loading of Nonreinforced Concrete Masonry (1971)
Associated BIA Technical Note 24B Design Examples of Contemporary
Bearing Walls 24E Design Tables for Columns and Walls Masonry
Structures, Lectures 2-3, slide 56
Allowable Tensile Stresses, Ft MSJC Table 2.2.3.2 and UBC Table
21-I Mortar Type Direction of Tension Portland Cement/Lime and
Masonry Cement/Lime or Mortar Cement Type of Masonry N M or S N M
or S all units are (psi) tension normal to bed joints 24 15 30
solid units 40 15 9 19 hollow units 25 41* 26* 58* fully grouted
units 68* tension parallel to bed joints 48 30 60 solid units 80 30
19 38 hollow units 50 48* 29* 60* fully grouted units 80* * grouted
masonry is addressed only by MSJC Masonry Structures, Lectures 2-3,
slide 57 Allowable Flexural Tensile Stresses, Ft flexural tension
normal to bed joints Note: direct tensile stresses across wall
thickness is not allowed per UBC or MSJC. flexural tension parallel
to bed joints strong units weak units No direct tensile strength
assumed normal to head joints, just shear strength along bed joint.
Masonry Structures, Lectures 2-3, slide 58
Example: Eccentric Axial Compression Determine the allowable
vertical load capacity per UBC and MSJC. e = 3.0 fm = 2000 psi
(from tests) Pa Type S mortar Ft = 25 psi per UBC 2107.3.5 and MSJC
Table 2.2.3.2 1.25 face-shell 20-0 bedding 8CMU Per NCMA Tek 141A:
ungrouted (per running foot) Anet = 30.0 in2 7.63 Ix= 309 in4 Sx =
81.0 in3 concrete footing r= 2.84 Masonry Structures, Lectures 2-3,
slide 59 Example Tension controlling: - fa + fb = Ft = 25 psi Pa Pe
+ a = Ft h - Anet Snet Pa P ( 3 .0quot;) +a = 25 psi Pa = 6750 lbs.
- 30.0 81.0 Masonry Structures, Lectures 2-3, slide 60
Example Compression controlling: UBC 2107.3.4 and MSJC 2.2.3 Fb
= 0.333 f 'm = 0.333( 2000 psi ) = 667 psi h 12.0 ( 20' ) = = 74.8
r 2.84 in. h 2 Fa = 0.25f m 1 - 140r Fa = 0.159 f m = 0.159(2000
psi) = 318 psi Pa Pa e Pa Pa e Anet Snet 30.0 + 81.0 1.0 + 1.0 Fa
Fb 318 psi 667 psi Pa = 6233 lbs . < 6750 lbs . compressio n
controls Masonry Structures, Lectures 2-3, slide 61 Example MSJC
Section 2.2.3: Check Buckling (no buckling check per UBC) Em = 900
f 'm per MSJC Sec. 1.8.2.1.1 3 2 Em I e 1 0.577 P < 0.25Pe =
0.25 h2 r 3 2 ( 1800 ksi)(308.7 in 4 ) 3.00 1 0.577 0.25 Pe = 0.25
(240 in)2 2.84 P < .25Pe = 1417 lbs < 6233 lbs. buckling
controls Pa (lbs) Code Compression Tension Buckling 6233 UBC -----
6750 1417 MSJC 6233 6750 Masonry Structures, Lectures 2-3, slide
62
Kern Distance for URM Wall Assuming Ft = 0 for solid section. e
- fa + fb = 0 P P Mc + =0 - AI I = bt 3 /12 A = bt P Pe(t/2) + =0 t
- bt bt 3 /12 b/3 fa e = t/6 + t t/3 kern fb = b -fa + fb = 0 fa +
fb If load is within kern, then no net tensile stress. Masonry
Structures, Lectures 2-3, slide 63 Kern Distance for URM Wall
Specific Tensile Strength, Ft, for solid section. e - f a + f b =
Ft P P Mc + = Ft - AI P Pe(t/2) -+3 = Ft b Ft b 2 t bt bt /12 + t 3
3P fa t Ft t 2 b e= + t Ft t 2 b t 6 6P kern + + 3 3P fb = b -fa +
fb = Ft If load is within kern, fa + fb then tensile stress <
Ft. Masonry Structures, Lectures 2-3, slide 64
Strength of Walls with no Tensile Strength Resultant load
inside of kern. P PM [1] fm = + AS P 6 Pe t fm = + [2] bt bt 2 e P
6e fm = (1+ [3] ) bt t fm f m Fa orFb Fb = 0.33 f 'm P Masonry
Structures, Lectures 2-3, slide 65 Strength of Walls with no
Tensile Strength Resultant load outside of kern. Neglect all
masonry in tension. Note: This approach is outside of UBC and P
MSJC since Ft may be exceeded. 2P fm = = compressiv e edge stress
< Fa or Fb [1] b t t = 3( e ) = e [2] t 2 3 2 t/2 2P 2P 1 fm = =
b 3 b( t e ) t 2 [3] e 2 t2 3 4P fm < Fa or Fb fm = e [4] 3bt(1
- 2 ) t Partially cracked wall is not prismatic along its height.
Stability of the P wall must be checked based on Euler criteria
modified to account for zones of cracked masonry. Analytical
derivation for this case is provided in Chapter E of Structural
Masonry by S. Sahlin. Masonry Structures, Lectures 2-3, slide
66
Example Determine the maximum compressive edge stress. Part (a)
e = 1.0 in. < t/6 = 1.27 in. within kern! P = 10 kip/ft. e P 6e
1+ fm = bt t 10,000 lbs. 6 ( 1.0 in.) 1+ = 195 psi fm = ( 12
in.)(7.63 in.) ( 7.63 in.) Part (b) e = 2.5 in. > t/6 = 1.27 in.
outside of kern! t = 7.63 4P fm = e 3bt 1 - 2 two-wythe brick wall
t 4 (10,000 lbs) fm = = 422 psi 2.5 in. 3( 12 in.)(7.63 in.) 1 - 2
7.63 in. Masonry Structures, Lectures 2-3, slide 67 Condition
Assessment Masonry Structures, Lectures 2-3, slide 68
Insitu Material Properties Compressive strength Elastic modulus
Flexural tensile strength Masonry Structures, Lectures 2-3, slide
69 Insitu Material Properties Shear strength Shear modulus
Reinforcement P 0.75 0.75 v te + CE An = v me 1 .5 Masonry
Structures, Lectures 2-3, slide 70
Condition Assessment Knowledge factor = 0.75 when visual exam
is done Visual examination measure dimensions identify construction
type identify materials identify connection types Masonry
Structures, Lectures 2-3, slide 71 Condition Assessment Knowledge
factor = 1.00 with comprehensive knowledge level Nondestructive
tests ultrasonic mechanical pulse velocity impact echo or
radiography Masonry Structures, Lectures 2-3, slide 72
Movements Masonry Structures, Lectures 2-3, slide 73
Differential Movements One common cause of cracking is differential
movement between wythes. Different materials expand or contract
different amounts due to: temperature humidity freezing elastic
strain Cementitious materials shrink and creep Clay masonry expands
Consider differential movements relative to steel or concrete
frames shrink expand Ref: BIA Tech. Note 18 Movement - Volume
Changes and Effect of Movement, Part I Masonry Structures, Lectures
2-3, slide 74
Coefficients of Thermal Expansion Thermal Expansion Ave.
Coefficient of Linear Thermal Expansion (inches per 100 for
Material 100oF (x 10-6 strain/oF) temperature increase) Clay
Masonry clay or shale brick 3.6 0.43 fire clay brick or tile 2.5
0.30 clay or shale tile 3.3 0.40 Concrete Masonry dense aggregate
5.2 0.62 cinder aggregate 3.1 0.37 expanded shale aggregate 4.3
0.52 expanded slag aggregate 4.6 0.55 pumice or cinder aggregate
4.1 0.49 Stone granite 4.7 0.56 limestone 4.4 0.53 marble 7.3 0.88
Thermal coefficients for other structural materials can be found in
BIA Technical Note 18. Masonry Structures, Lectures 2-3, slide 75
Moisture Movements Many masonry materials expand when their
moisture content is increased, and then shrink when drying.
Moisture movement is almost always fully reversible, but in some
cases, a permanent volume change may result. Moisture Expansion of
Clay Masonry = 0.020% Moisture Expansion of Clay Masonry = 0.020%
Freezing Expansion of Clay Masonry = 0.015% Freezing Expansion of
Clay Masonry = 0.015% Masonry Structures, Lectures 2-3, slide
76
Moisture Movements in Concrete Masonry Because concrete masonry
units are susceptible to shrinkage, ASTM limits the moisture
content of concrete masonry depending on the units linear shrinkage
potential and the annual average relative humidity. For Type I
units the following table is given. Moisture Content, % of Total
Absorption (average of three units) Humidity Conditions at Job Site
Linear Shrinkage, % humid intermediate arid 0.03 or less 45 40 35
40 35 30 0.03 to 0.045 35 30 25 0.045 to 0.065 Masonry Structures,
Lectures 2-3, slide 77 Control Joints in Concrete Masonry Control
joints designed to control shrinkage cracking in masonry. Spacing
recommendations per ACI for Type I moisture controlled units.
Vertical S pacing of Joint Reinforcement Recommended control None
24 16 8 joint spacing Ratio of panel length 2 2.5 3 4 to height,
L/h Panel length in feet 40 45 50 60 (not to exceed L regardless of
H) Cut spacing in half for Type II and reduce by one-third for
solidly grouted walls. Masonry Structures, Lectures 2-3, slide
78
Control Joints in Concrete Masonry Control joints should be
placed at: all abrupt changes in wall height all changes in wall
thickness coincidentally with movement joints in floors, roofs and
foundations at one or both sides of all window and door openings
Masonry Structures, Lectures 2-3, slide 79 Control Joint Details
for Concrete Masonry paper grout fill control joint unit raked head
joint and caulk Ref. NCMA TEK 10-2A Control Joints in Concrete
Masonry Walls Masonry Structures, Lectures 2-3, slide 80
Expansion Joints in Clay Masonry Pressure-relieving or
expansion joints Pressure-relieving or expansion joints accommodate
expansion of clay masonry. accommodate expansion of clay masonry.
expansion joint Ref: Masonry Design and Detailing, Christine Beall,
McGraw-Hill BIA Tech. Note 18A Movement - Design and Detailing of
Movement Joints, Part II Masonry Structures, Lectures 2-3, slide 81
Spacing of Expansion Joints For brick masonry: W = [ 0.0002 +
0.0000045( Tmax Tmin )] L where W = total wall expansion in inches
0.0002 = coefficient of moisture expansion 0.0000043 = coefficient
of thermal expansion L = length of wall in inches Tmax= maximum
mean wall temperature, F Tmin = minimum mean wall temperature, F 24
,000( p ) S= Tmax Tmin S = maximum spacing of joints in inches p =
ratio of opaque wall area to gross wall area Masonry Structures,
Lectures 2-3, slide 82
Expansion Joint Details for Brick Veneer Walls 20 oz. copper
silicone or butyl sealant neoprene extruded plastic Masonry
Structures, Lectures 2-3, slide 83 Vertical Expansion of Veneer
flashing with weep holes rc beam steel shelf angle 1/4 to 3/8 min.
clearance concrete block compressible filler joint reinforcement or
wire tie clay-brick veneer Masonry Structures, Lectures 2-3, slide
84
Expansion Problems In cavity walls, cracks can form at an
external corner because the outside wythe experiences a larger
temperature expansion than the inside wythe. sun Masonry
Structures, Lectures 2-3, slide 85 Expansion Problems Diagonal
cracks often occur between window and door openings if differential
movement is not accommodated. Masonry Structures, Lectures 2-3,
slide 86
Expansion Problems Clay-unit masonry walls or veneers can slip
beyond the edge of a concrete foundation wall because the concrete
shrinks while the clay masonry expands. As a result, cracks often
form in the masonry at the corner of a building. Brick Veneer
Concrete Foundation Masonry Structures, Lectures 2-3, slide 87
Expansion Problems Brick parapets are sensitive to temperature
movements since they are exposed to changing temperatures on both
sides. Elongation will be longer than for wall below. sun parapet
roof Masonry Structures, Lectures 2-3, slide 88
End of Lessons 2 and 3 Masonry Structures, Lectures 2-3, slide
89