Deliverable 1.2 Calculation Model determining mechanical ... · Iy moment of inertia IT torsional...

REPORT

Deliverable 1.2

Calculation Model determining mechanical strength of sandwich

panels with openings with and without additional internal frame

structure

Publisher:

Felicitas Rädel

Jörg Lange

This report includes 54 pages.

Date of issue: September 12th, 2011

EASIE WP1 Deliverable 1.2 2

Project co-funded under the European Commission Seventh Research and Technology

Development Framework programme (2007-2013)

Theme 4 NMP – Nanotechnologies, materials and new production technologies

Prepared by

Felicitas Rädel, TU Darmstadt Drafting history

Draft version 1 05.01.2011 Draft version 2 28.01.2011 Draft version 3 04.02.2011 Draft version 4 28.03.2011 Draft version 5 08.07.2011 Final 12.09.2011 Dissemination Level

PU Public X PP Restricted on the other programme participants (including

the Commission Services)

RE Restricted to a group specified by the Consortium (including the Commission Services)

CO Confidential, only for members of the Consortium (including the Commission Services)

Verification and approval Coordinator Industrial Project Leader Management Committee Industrial Committee

Deliverable

D1.2 Calculation model determining mechanical strength of sandwich panels with openings with and without additional internal frame structure

Due date: Month 30 Completed: Month 30


Table of contents

1 Introduction __________________________________________________________ 4

1.1 General ________________________________________________________________ 4

1.1.1 State of the art _______________________________________________________________ 4

1.1.2 Lay-out and types of openings __________________________________________________ 6

1.2 Symbols and notations ___________________________________________________ 7

1.3 Definitions ______________________________________________________________ 7

1.4 Design aspects __________________________________________________________ 8

2 Resistance of panels with openings without reinforcement ________________ 9

2.1 Resistance of single panels with flat faces _________________________________ 9

2.2 Transferring of loads to adjacent panels __________________________________ 13

2.2.1 Principles ___________________________________________________________________ 13

2.2.2 Modelling of static system of panels ____________________________________________ 14

2.2.3 Cross-sectional values of sandwich panels _______________________________________ 15

2.2.4 Resistance and stiffness of the longitudinal joints ________________________________ 19

2.2.5 Simplified test and design procedure ___________________________________________ 21

2.2.6 Verification _________________________________________________________________ 21

2.3 Resistance of single panels with profiled faces ____________________________ 22

2.3.1 Experimental investigations ___________________________________________________ 22

2.3.2 Design procedure ____________________________________________________________ 26

3 Resistance of panels with openings with reinforcement __________________29

3.1 Experimental Investigations with small openings __________________________ 29

3.1.1 Test set-up __________________________________________________________________ 29

3.1.2 Results _____________________________________________________________________ 29

3.1.3 Comparison with existing methods of calculation ________________________________ 30

3.2 Additional tests with small openings _____________________________________ 31

3.2.1 Test set-ups _________________________________________________________________ 31

3.2.2 Results _____________________________________________________________________ 32

3.3 Experimental investigations with large openings (TKS – FSI) _______________ 34

3.3.1 Test set-up __________________________________________________________________ 34

3.3.2 Results _____________________________________________________________________ 34

3.3.3 Comparison with existing methods of calculation ________________________________ 35

3.4 Experimental investigations with Fech - windows _________________________ 36

3.4.1 Test set-up __________________________________________________________________ 36

3.4.2 Results _____________________________________________________________________ 36

3.5 Calculation models for large openings____________________________________ 39

3.5.1 Types of large openings _______________________________________________________ 39

3.5.2 Ribbon windows with adapter profiles __________________________________________ 39

3.5.3 Ribbon windows with punctual fixing __________________________________________ 48

3.5.4 Windows with bonded frames _________________________________________________ 49

4 Conclusions __________________________________________________________53


1 Introduction

1.1 General

The report contains part of the Preliminary European Recommendations for design of sandwich panels with openings, which will be published in 2011. This part of the text is marked with italic style.

Self-supporting sandwich panels are known building components used to cover external and internal walls and roofs. Most of the walls and roofs of buildings include openings due to the doors, windows, HVAC lines and other technical inlets. Thus, also the covering components in walls and roofs are often penetrated and cut with openings of different sizes and geometries. European product standard EN 14509 gives guidance for manufacturing and design of complete sandwich panels made in factories. It does not include any information about the influence of the openings and detailing in the behaviour or resistance of panels. A partial reason may be the fact that many of the openings are made on building site, thus being outside of the control of the phase of the manufacture. This report includes the current information about the influence of the openings in the behaviour and resistance of sandwich panels. The intention of the report is to complete the directions given in European product standard EN 14509. Thus, the report may give useful information for the design of sandwich panels with openings but also for the cutting, forming and placing of the openings in practice. The report introduces solid technical information such as the calculation models and experimental arrangements which is based on research reports and reviewed publications. The report introduces also useful practical directions based on the experience and guidance from companies in practice. The latter information is presented in note boxes in order to make a difference between the technical information based on experiments and theoretical modelling and on the other hand, on the knowledge from practice. The report covers mainly the mechanical design aspects.

1.1.1 State of the art

Because of the windows, doors and different kinds of technical inlets in typical walls, there are

obvious needs to make openings in the wall panels. The openings reduce the structural cross-

section of the faces and core of the panels, and thus, may have influence on load-bearing capacity

of the panels.

The "official" state of the art concerning the openings within the wall constructions made of self-

supporting sandwich panels is a "replacement", i.e. an additional support to the wall panels in the


area of the openings. Thus, all the applied loads on the window and door openings are to be

transferred to the spaced structural supports, e.g. framework, by longitudinal beams and cross

beams (Fig. 1.1). The replacing concept results in additional structural components and is a

substantial effort. According to the technical information of today the additional supports are not

always needed, which is also often in agreement to requirements of the visual and architectural

appearance.

In Nordic Countries, especially in Finland, since late 80’ies it has been a common practice to base

the design to transfer loads from panels with openings to adjacent panels on the manufacturer’s

directive. This procedure has been used with success and it has reduced significantly the need of

additional supporting structures.

Figure 1.1 Large openings require additional supporting of sandwich panels in the wall

The report introduces new possibilities to design sandwich panels with openings, having in mind

the following purposes.

• no additional supports shall be installed if really not needed

• sandwich panel shall have an adequate load bearing capacity and allowable span also

with openings

• careful analysis of stresses covering all load cases and the resistance in the area of

openings shall be made


1.1.2 Lay-out and types of openings

Typical lay-outs and alternatives of the openings depend on the intended use of them. For wall panels they may differ in following ways:

• Size of the opening (Fig. 1.2a)

• Location of the opening (Fig. 1.2b)

• Direction of the span of the panels (Fig. 1.2c and d)

a: size of the openings b: location of openings

c: vertical alignment d: horizontal span direction

Figure 1.2 Openings in sandwich wall panels may vary a) in size and b) in location. Openings

may be cut in panels c) installed in vertical direction or d) in horizontal direction.

Based on the various arrangements shown in Fig 1.2, it is obvious, that the structural behaviour

and resistance of the panels varies in different cases which have to be taken into account in

structural design.

In roof panels the main reasons for openings are HVAC lines. Large openings for ventilation or roof lights need a substructure in any case. Due to that the investigations regarding openings in profiled panels are limited to openings with a width of less than 40 % of the panel in this report.


1.2 Symbols and notations

A area B overall width of the panel D overall depth of the panel E E-Modulus EIy bending stiffness Fj load bearing capacity oft he joint G G-Modulus Iy moment of inertia IT torsional rigidity My bending moment MT torsional moment N normal force Q shear force V shear force Vs,max maximum shear force (design value) b width of the opening inside a panel eC distance between centroids of faces fCv shear strength of the core kC reduction factor of shear stress kF reduction factor of wrinkling stress k2 reduction factor due to low cross-panel tensile strength tFd design thickness of the face γM material safety factor β = b/B, parameter σw wrinkling strength of the face σF normal stress of a face layer tc shear stress of the core

tcd design value of shear strength of the core

tcd,max maximum shear strength in the core (design value)

1.3 Definitions

additional support support of sandwich panel, which is needed additionally

because of the reduced resistance due to the opening

core layer of material, which is bonded between the internal

and external faces

face layer flat, lightly profiled or profiled thin metal sheet firmly

bonded to the core

fastening a point of connection between the sandwich panel and its

supporting framework or a point of connection in a face of


a sandwich panel

nominal thickness thickness given in the product information table

large opening width of the opening is equal to or larger than the width

of the sandwich panel

opening opening may have a shape of a rectangular, circular or

non-regular hole, which perforates the face and core of a

sandwich panel

reinforcement stiffening and load bearing structure around the opening

or around the sandwich panel

remaining cross-section gross cross-section minus the cross-section of the opening

replacement resistance of the sandwich panel with opening is neglected

and the loads are carried by additional structures

sandwich panel building product consisting of two metal faces positioned

on either side of a core and firmly bonded to it so as to act

compositely under load

small opening width of the opening is smaller than the width of the

sandwich panel and the opening does not cut nor reach the

longitudinal joint of the panel

steel core thickness The thickness of the pure metal sheet layer alone.

In case of zinc-coated steel faces, the steel core thickness is

the nominal thickness minus the thickness of zinc layers.

sub-structure structure into which the fasteners of the sandwich panel

are fixed

1.4 Design aspects

In many cases the openings are located in places, in which the sandwich panel may have a reserve

of strength of a variable degree. The strength reserve may be caused by several reasons;

- opening may not be in a most stressed part of the panel,

- the panel may not be located in the corner or on the top floor of the building, where the

loads are typically at the highest, and

- the depth of the panel may have been determined by other requirements such as the

thermal insulation power.

Regardless of the reason of the strength reserve, the degree of the utilization of the strength of the

face and core shall be taken account of when evaluating the resistance of the panel with openings.


2 Resistance of panels with openings without reinforcement

2.1 Resistance of single panels with flat faces

The term “small opening” is used in this report to describe openings, the width of which is smaller

than the width of the sandwich panel. A small opening shall not cut nor meet the longitudinal

joint of the panel.

The remaining cross-section of a sandwich panel with small openings may be able to carry the

loads exposed to a sandwich panel, if the size of the opening is small or the opening is located in a

less-stressed cross-section of the panel. The evaluation of the remaining resistance is obviously the

first useful task to be made in design. The remaining cross section is described by the difference of

the overall width (B) and the width of the opening (b) (Fig 2.1). The task is to check, whether the

bending moment and the shear force in the area of the opening can be carried by the cross-section

weakened by the opening.

Figure 2.1 Remaining cross section in the area of an opening in a sandwich panel.

It has to be pointed out that a simple calculation based on the pure remaining cross section leads

to an unsafe side, because of the substantial stress concentrations, which arise in the corners of

the opening. Thus, the design can not be based on the pure remaining cross-section, but the stress

concentrations have to be taken into account in calculations.

The remaining cross-section of a sandwich panel (B-b) is classified to be able to carry the loads

exposed to a sandwich panel with an opening, if the following verifications of the wrinkling

strength of the face and the shear strength of the core are fulfilled.

Verification of the wrinkling strength σFcd of a flat or a slightly profiled face with openings placed

symmetrically along the mid-line of the sandwich panel shall be made using the expression 1a


and 1b. The first expression (1a) is the usual verification of the full cross section in the point of

the highest bending moment of the panel. The second expression (1b) describes the verification in

the point of the highest bending moment in the area of the opening.

L

x1, critical cross-section to shear resistance, normally close to a support

x2 , critical cross-section to resistance of bending resistance,

normally close to the mid-span

b B

Fig. 2.2 Coordinates describing the location of an opening

≤=

≤=

M

Fck

F

FdC

od

Fcd

M

Fck

FdC

d

Fcd

fkk

tBe

xM

fk

tBe

M

γσ

γσ

2

2max.

)(

(1a,b)

where

( )( )

≤<−

≤≤−=

8.04.016.0

4.0012

ββ

ββ

if

ifkF (2a,b)

k2 = (6.10 fCt +0.39) < 1.0 (3)

b = b/B (4)

In expressions fCt is characteristic cross panel tensile strength of the core in MPa. Md.max represent

the highest design bending moment of the sandwich panel and Mod(x) is the highest design

bending moment in the area of the opening.

Factor k2 is defined in the Section A.5.5.5 of EN 14509.

The cutting of the openings in the faces of the panel with low bonding strength is a sensitive task

and may reduce the strength of the bond and core and thus, cause a clear risk of delamination.

If the opening is located non-symmetrically to the mid-line of the sandwich panel with flat or

slightly profiled faces, the reduction factor kF.ecc expressed in 5a and 5b shall be used instead of the

factor kF in expressions 2a, 2b (Fig 2.3).


( )( )

( )( )

≤<−

+

−

≤≤−

+

−

=

8.04.01

1

16.0

4.001

1

12

.

ββ

β

ββ

β

if

I

yyB

if

I

yyB

k

z

eS

z

eS

eccF (5a.b)

oS ebB

by

−= (6)

Byy Se 5.0−= (7)

( ) ( ) ( )2

22

2

11

3

2

3

1 5.05.05.05.012

1byBbbyBbbbI SSz −++−−++=

(8)

01 5.05.0 ebBb +−= (9)

oebBb −−= 5.05.02 (10)

where eo is the eccentricity of the mid-line of the opening to the mid-line of the cross-section. The

sign of eo shall be taken into account (Fig. 2.3).

L

x1, critical cross-section to shear resistance

x2 , critical cross-section to resistance

of bending resistance

B

B/2

B/2 eo

b/2

b/2

y b1

b2

yS

Figure 2.3 Definition of the eccentricity of the opening

Verification of the shear strength of a sandwich panel with flat or lightly profiled faces with

openings placed symmetrically along the mid-line of the sandwich panel shall be made using the

expression 11a and 11b. The first expression (11a) is the usual verification of the full cross

section in the point of the shear force of the panel. The second expression (11b) is the verification

in the point of the highest shear force in the area of the opening.


( )

≤=

≤=

M

Cvk

C

C

od

Cd

M

Cvk

C

d

Cd

fk

Be

xV

f

Be

V

γτ

γτ max,

(11a,b)

in which

( ) 8.001 ≤≤−= ββ ifkC (12)

In the expression Vd.max represents the highest design shear force of the sandwich panel and Vod(x)

is the highest design shear force in the area of the opening.

In verification of the shear strength of a sandwich panel with flat or slightly profiled faces having

openings which are placed non-symmetrically along the mid-line of the sandwich panel, the

reduction factor kC has to be modified.

Table 2.1. Numerical values of the reduction factors kF and kC

β=b/B kF kC

0,0 1,0 1,0

0,1 0,81 0,9

0,2 0,64 0,8

0,3 0,49 0,7

0,4 0,36 0,6

0,5 0,3 0,5

0,6 0,24 0,4

0,7 0,18 0,3

0,8 0,12 0,2


2.2 Transferring of loads to adjacent panels

2.2.1 Principles

Openings in a sandwich panel reduce the cross-section and the bending and shear stiffness of the

panel. Due to the difference of the stiffness, the loads or a part of the loads exposed directly to the

panel with openings will be transferred via the longitudinal joints to the adjacent panels (case A

in Fig. 2.4). The most severe case is the load transfer from a completely cut sandwich panel (case

B in Fig. 2.4). While in case “A” the panel might have enough capacity still to withstand the load,

case “B” relies on the load transfer. In both cases the neighbouring panels will receive additional

loads due to compatibility of the deflections in the longitudinal joints (Fig. 2.5). These loads are

transferred by the longitudinal joints and therefore, the assessment of the strength and stiffness of

the joints is important. Furthermore, the load transfer will result in an eccentric line load to the panel without an opening activating its torsional rigidity and causing additional shear stresses in the core material and additional normal stresses in the faces due to the eccentric loads.

Figure 2.4 Small and full-width openings in walls covered with sandwich panels

Figure 2.5 Line loads in the longitudinal join between neighbouring sandwich panels with

different bending and shear stiffness.

A

B

A

B


2.2.2 Modelling of static system of panels

The intensity of the load, which can be transferred through the longitudinal joints to adjacent

panels, depends on the bending, shear and torsional rigidity of the panels and in addition, on the

shear rigidity of the longitudinal joint. On the basis of the geometry and the stiffness parameters

of the panels, a numerical model can be generated to evaluate the internal forces and deflections

with software for 3D beam structures. As an example, a strut model of a three-panel-system is

shown in Fig. 2.6

Figure 2.6 A finite element beam model describing a three-panel-system. The panel in the middle

has an opening.

The finite element model shown in Fig. 2.6 consists of

- beam elements representing the complete sandwich panels (No 1),

- beam elements representing the partial elements along the opening (No 2 and 3),

- rigid load distribution struts (No 4),

- transfer struts representing the stiffness perpendicular to the main span (No 5),

- transfer struts with reduced size due to the opening (No 6 + 7) and

- transfer struts representing the joint stiffness (No 8 + 9).

Additional panels might be included in the model. The main goal of this model is the assessment

of the loads in the struts representing the joints. The derivation of the required cross-section

values of the beam elements can be made experimentally or by calculations as shown in following

sections.

Z

Y

X

1

9

8

1

5

1

5

5

4

43

2

6

7

Z

Y

X

11

99

88

11

55

11

55

55

44

4433

22

66

77


Alternatively, the approximate intensity of the shear loads in the longitudinal joint can be

evaluated using an analytical approach introduced in refs [Höglund 1986] and [Davies 2001].

The approach is based on the assumption of the compatibility of the deflections caused by the

bending and torsional moments and the shear forces in the mid-points in the longitudinal joints

and on the known, typically uniform distribution of shear loads in the joints. Thus, the approach

is valid for a system with openings, which are distributed over the span of the panel such as

regular lines of windows in a wall.

2.2.3 Cross-sectional values of sandwich panels

3.2.3.1 Torsional stiffness

The value of the torsional stiffness of a sandwich panel is needed for an analysis of the complete

wall structures consisting of sandwich panels with and without openings. The existing expressions

(13) and (14) have been derived in refs [Stamm, Witte 1974] and [Höglund 1986].

⋅

⋅−⋅

+

⋅⋅⋅⋅⋅==

B

B

tt

ttBeGIGV CFTFS

λ

λ

5.0

)5.0tanh(14

21

21211. (13)

+

===

∫BG

e

tG

B

eB

t

ds

AGIGV

C

C

FdF

C

s

FTS3

3

22

3

24

4

22

20

2. 2 (14)

21

21

ttd

tt

G

G

cF

C +⋅=λ and ( )215,0 tted cc +−= (15)

in which IT is the torsional rigidity, GF and GC the shear modulus of the face and core materials,

and t1 and t2 the design thickness of the external and internal faces.

Expression to the distribution of the shear stresses caused by the torsional moment has been

derived in ref [Höglund]

33

24

3.

Be

B

M

C

TTC

=τ (16)

Shear stress caused by the torsional moment shall be combined with the shear stress caused by

shear force (17)

28

27

Be

M

Be

V

C

T

CCTCv +=+ττ (17)


At the moment of the drafting of the report, the expressions (13 - 17) have been verified to foam

cored sandwich panels.

All the expressions above are based on the theory of St. Venant. Recent investigations showed that this theory is not valid for sandwich panels. Within EASIE two panel tests with one loaded panel have been done. They showed that the theory of Stamm-Witte brings good correlation with test results regarding the deflection, but for determining the stresses the model is not useful. Also for other kinds of loading like point loads the formulas do not lead to good results. At TU Darmstadt lightly profiled panels with eccentric point loads in midspan were tested. These tests demonstrate that the equations (13-14) overestimate the torsional stiffness of sandwich panels for this kind of load. If the effect of the longitudinal joint is neglected for point loads at midspan the following expression can be used:

( )

⋅⋅+

⋅⋅

⋅

⋅⋅=

C

c

F

c

TF

GB

e

Gt

B

BeIG

1010

9

62,12

(18)

The additional effect of the longitudinal joint is depending on its geometry. In the tests it varied between 5 and 10 % of the torsional stiffness of the panel. At the moment only a few tests were done. So the factor for the influence of the joint has to be verified by further tests. According to the theory of St. Venant, the torsional moment causes only shear stresses. This assumption leads to the expressions (16, 17). In recent tests at TU Darmstadt also additional axial stresses in the faces were measured. These stresses cannot be neglected. They depend on the stiffness of the panel, on the shear modulus of the core material and on the aspect ratio of the panels. For a lot of applications the load transfer to the neighbouring panel is similar to a sinus curve like shown in Figure 2.7.

Figure 2.7 Eccentric loaded panel

For this case a parametric study with finite elements has been performed. In the following diagrams one can find the maximum normal stresses in the face for two different shear


moduli of the core material. They are given as a ratio to a not eccentric loaded panel with the same load. In the following formula this value is called ks.

Figure 2.8 Parametric studies for eccentric loaded panels

1,00

1,10

1,20

1,30

1,40

1,50

1,60

1,70

3 4 5 6 7 8 9 10

ma

x. s

tre

ss i

n t

he

face

co

mp

are

d t

o a

no

t

ecc

en

tric

lo

ade

d p

an

el

length of the panel in m (width 1m)

max . normal stress in the face for an eccentric "Sinus-load"

Gc= 3 N/mm2

B = 20000 kNcm²/cm

B = 35000 kNcm²/cm

B = 50000 kNcm²/cm

B = 75000 kNcm²/cm

B = 100000 kNcm²/cm

B = 150000 kNcm²/cm

B = 200000 kNcm²/cm

B = 250000 kNcm²/cm

B = 300000 kNcm²/cm

1,00

1,10

1,20

1,30

1,40

1,50

1,60

3 4 5 6 7 8 9 10

ma

x. s

tre

ss i

n t

he

face

co

mp

are

d t

o a

no

t

ecc

en

tric

lo

ad

ed

pan

el

length of the panel in m (width 1m)

max. normal stress in the face for an eccentric "Sinus-load"

Gc= 4 N/mm2

B = 20000 kNcm²/cm

B = 35000 kNcm²/cm

B = 50000 kNcm²/cm

B = 75000 kNcm²/cm

B = 100000 kNcm²/cm

B = 150000 kNcm²/cm

B = 200000 kNcm²/cm

B = 250000 kNcm²/cm

B = 300000 kNcm²/cm


The maximum normal stress in the face due to the eccentric load can be calculated as:

σ�� ,��, ��∙��∙�∙�� (19)

with M�,��,�� ∙��

q = max. value of “sinus-load” at midspan The maximum value of the sinus-load can be derived from calculations like e.g. shown in figure 2.6. Together with the uniform load of the panel itself, it results in the maximum normal stress of the face:

σ�� ,��,��, ��∙��∙�∙�� (20)

For the additional shear stress, the panel can be calculated with an effective width of 250 mm.

The eccentric load leads to the following additional shear stress:

τ ! � "�,��, ��∙#$%�� (21)

So the resulting shear stress is:

τ � "�,��∙� & "�,��, ��

��∙#$%�� (22)

3.2.3.2 Bending and shear stiffness in direction of span

∫ +== 2

2211

22112Cx

xFFxFF

xFFxFFxxSx e

AEAE

AEAEdzzB (23)

CCxx GeBS = (24)


3.2.3.3 Bending and shear stiffness perpendicular to the span

∫ +== 2

2211

22112Cy

yFFyFF

yFFyFFyySy e

AEAE

AEAEdzzB (25)

CCyy GeBS = (26)

2.2.4 Resistance and stiffness of the longitudinal joints

The longitudinal joints of the panels are loaded with shear forces, if the load is transferred

through the joint between the panels. Figure 2.9 shows the typical crack pattern that occurs when

the joint is overloaded. The panel on the left is the one with a reduced stiffness. It rests on the

panel on the right hand side of the picture. This produces a line load to the joint, which has to be

transmitted by the tongues and grooves of the metal sheet faces and the core. Ultimate load is

reached due to a combined failure of the core material and the delamination of the faces.

Figure 2.9 Cracks in the longitudinal joint due to the load transfer.

Modern sandwich panels usually have a joint geometry that allows a sufficient load transfer.

However, experimental information is needed in order to verify the shear resistance of the

longitudinal joints of the panels. Fig. 2.10 shows a test arrangement to measure the shear

resistance of the longitudinal joint. Panel No. 1 is a panel that was cut in longitudinal direction

in two halves. Both halves are restrained by steel profiles no. 3, a pair of load bearing structures,

e.g. U-sections with foamed rubber for soft load introduction. The load bearing structures are

fixed to a stiff structure (no. 4) by threaded rods (no 3). The specimen is fixed in sideway

direction with threaded rods (no. 7) in order to avoid the decomposition of the specimen, which

corresponds to the boundary conditions in wall panels in practice. The rod (no. 7) is preloaded

with a load, which provides a contact for the end plates (no 7) and the joints of the specimen. The


rod (no. 7) shall not be prestressed. A normal panel (no. 2) is fixed between the two halves. The

load is introduced into two loading beams (no. 5) by a spreader beam (no. 6). The typical length

of the panels in the test rig is app 800 mm.

The load deflection curve obtained in the test with this setup allows the derivation of the stiffness

and ultimate load of the longitudinal joint. Because of the different geometry, the load-deflection

curves and the ultimate loads may be different to the two joints of the specimen. However, the test

set up shows the lowest ultimate load, only. These properties can be used in further calculations.

Tests within EASIE showed that it is not possible to calculate the resistance of the joint itself. The maximum load depends on various parameters like the exact geometry, the quality of the foaming, the adhesive strength between core and face material etc. So tests are necessary for each type of panel.

Figure 2.10 Test set up for the assessment of the shear stiffness and resistance of the longitudinal

joint

The thickness of the panel used in the tests shall represent the small, large and a medium

thickness of the sandwich panel product. The specimen is loaded with monotonously increasing

static load up to failure. The test series consists of minimum three similar tests. Measurements

and observations concerning the deformations and tightness may give useful information for

verification of the serviceability limit state. Repeated loading with an intensity of app ½ of the

ultimate load may give further interesting information for the verification of the joint.

In order to test the influence of glued joints, within EASIE also a test series with panels with different faces (steel and glass fibre reinforced plastic) and different types of joints (without glue, glued faces, glued cores, glued faces and cores) has been implemented. The results showed that any kind of bonding has a positive effect on the resistance and stiffness of the joint. The level of improvement depends on various factors. One factor is the face material. So for steel and glass fibre reinforced plastic with glued faces and a glued core, the joint was not the determining factor for failure anymore.

1

F

6

1

33 3 3

4

5 5

2

7

7

11

F

66

11

3333 33 33

44

55 55

22

77

77


2.2.5 Simplified test and design procedure

A simplified procedure to test the shear resistance of the longitudinal joint and thus the ability to

transfer loads from the panel with openings to the adjacent panel, is to place two simply

supported panels side by side on the supports. The panels are fixed to each other in the joints on

the supports. One panel is loaded up to the failure, while the second panel remains unloaded. The

ultimate load is compared to the ultimate load of a single panel. The increase of the load carrying

capacity in the term of the bending moment is marked as M joint (or shear force capacity as V joint)

and will be used as the load capacity able to be transferred to adjacent panels in the following

design procedure. The characteristic value and the corresponding design value of the increase of

the bending moment capacity M joint,d (or shear force capacity V joint,d) is determined on the basis

of three tests as a minimum. In the following the load increase capacity will be treated as increase

in bending moment capacity:

1. The bending moment capacity of the panel with opening Mod is determined according

to chapter 2.1.

2. If the bending moment capacity of the panel with opening is not adequate, the

additionally needed bending moment capacity ∆M and corresponding needed

additional load capacity ∆q is determined from the basic design procedure EULS:d < Rd

3. It is assumed that half of the additional load is distributed to each side of the panel

with opening.

4. If the additional needed bending moment capacity ∆M is less than 2*Mjoint,d no

additional supporting frame structure is needed

5. The panel, where half of the bending moment ∆M is transferred to over the joint is to

be designed with the transferred bending moment ∆M/2 in addition to the actual

bending moment on the panel.

6. If the additionally needed load capacity ∆M is bigger than 2*Mjoint additional

supporting frame structure has to be introduced according to chapter 3.3

In case the load transfer to the neighbouring panel has to be determined for a system with three

panels connected to each other it has to be loaded with same procedure as given above. The

transferred load to the third panel is marked as Mjoint2,d and the procedure is repeated as above.

Within EASIE, such tests with two panels were performed with different panels. Two different types of panels with two different thicknesses were tested. In each series 3 single panels and 3 test set-ups with two panels were tested. For all of these tests the load could be increased from 35% up to 50% compared to the tests with single panels.

2.2.6 Verification


Verification of the resistance to transfer the load through longitudinal joints shall follow the usual

practice of design and be made at serviceability and ultimate limit states with relevant load and

material safety factors. Criteria for serviceability limit state verification are the deformation and

tightness of the longitudinal joint and for ultimate limit state verification, the ultimate shear load

carried through the joint.

Ultimate limit state verification includes the bending and shear resistance of the panel with

opening and the adjacent panels and the resistance of the joint.

2.3 Resistance of single panels with profiled faces

In the chapters before openings in panels with flat or lightly profiled faces were studied. Within EASIE WP1 also profiled panels with small openings have been assessed. Based on the rigidity of the faces profiled panels are usually used as roof covering. The term “small opening“ describes again an opening with a width smaller than the panel. The most common reason for cutting openings in profiled panels are HVAC lines, so the investigations within EASIE were concentrated on openings with a maximum width of 400 mm, which is also the limit for the formulae given in this section. The load bearing capacity of the remaining cross section of profiled panels depends severely on the position of the opening. It has to be distinguished between openings in the flat part of the section and openings through the profiled part of the section, like shown in figure 2.11. Further a differentiation between panels with mineral wool and PUR core is necessary.

Figure 2.11a Opening in the flat part of a profiled panel

Figure 2.11b Opening in the profiled part of a profiled panel

2.3.1 Experimental investigations

Within EASIE WP1 different test series were implemented. The following distinctions were made:


• Core Material (mineral wool and PUR)

• Position of the opening (flat and profiled part of the panel)

• Failure mode (influence on bending moment capacity and shear capacity)

• Size of opening (200 mm and 400 mm)

• Geometry of the opening (circular, square and rectangular)

For the effect on the bending capacity a total of 18 panels were tested. 9 panels had a core of mineral wool, 9 panels a core of PUR. In these tests all the openings were circular and had a diameter of 200 mm.

In the following table, exemplary the results for the bending capacity of panels with PUR-core and 200 mm circular openings are shown.


Table 2.2 Bending capacity of PUR-panels with openings

Test Opening Max. load in kN

deviation to the mean value of a

complete panel in %

failure mode

1.1 no 13,38 0,45 wrinkling at load application

1.2 no 13,12 -1,53 wrinkling at load application

1.3 no 13,47 1,08 wrinkling at load application

2.1 flat part 12,93 -2,97 wrinkling around the opening



3.1 profiled

part 10,18 -23,60 wrinkling around

the opening

3.2 profiled


the opening

3.3 profiled


the opening

An opening in the flat part of the panel leads to a decrease of bending capacity of 3 % to 6 %, whereas openings in the profiled part of the panel effect a decrease of about 20%. Panels with mineral wool as core material show similar results for the openings in the flat part. For openings in the profiled part a load drop of up to 35 % was measured.


To assess the effect on the shear capacity another 30 panels with different positions and geometries of the openings were tested. In table 2.3 exemplary the results for the shear capacity of panels with PUR-core and 200 mm circular openings are shown.

Table 2.3: Shear tests on profiled panels with and without opening

Test position of opening

size of opening in

mm

max. load in kN

max. load in the core in kN

area of the core in mm²

max. stress in the core

in N/mm²

S_1_1 - no opening 28,97 10,03 99333 0,101

S_1_2 - no opening 27,02 9,34 99333 0,094

S_1_3 - no opening 30,41 10,53 99333 0,106

S_4_1 flat part d = 200 mm 22,64 7,09 80533 0,088

S_4_2 flat part d = 200 mm 21,41 6,69 80533 0,083

S_4_3 flat part d = 200 mm 23,39 7,33 80533 0,091

S_5_1 profiled

part d = 200 mm 18,59 6,14 79728 0,077

S_5_2 profiled

part d = 200 mm 17,80 5,90 79728 0,074

S_5_3 profiled

part d = 200 mm 17,21 5,74 79728 0,072

mean value from shear tests: 0,134

In table 2.3 a clear difference can be noticed for the core stresses between the panels with openings, the panels without openings and the shear tests. The maximum load in the core has been counted back with the formulas of Stamm/Witte. For the mineral wool panels no difference of the core stresses is noticeable between panels with and without openings.


2.3.2 Design procedure

Bending capacity

Comparable to panels with flat faces a simple calculation based on the pure remaining cross section leads to results on the unsafe side. Stress concentrations around the openings have to be taken into account in calculations. For openings within the flat part of the panel the influence of stress concentrations is very small. This is due to the fact that the stresses in the flat part are much lower than in the profiled part and the expansion of the stress peaks is stopped by the profiled parts. So the verification of the maximum bending moment MRd of a profiled face with openings in the flat part of the sandwich panel section (see figure 2.11a) shall be made using the expression (27).

Figure 2.12 Opening in a profiled panel

(27)

In expression (27) MRd represents the bending moment capacity of the sandwich panel and Mod(x) is the highest design bending moment in the area of the opening. This moment includes the moment due to loading and the moment due to temperature according to EN 14509, table E.10.2. Openings within the profiled part of the section have a much bigger influence on the bending moment capacity. In general the profiled areas of the panel carry almost the whole load. So the verification of the maximum bending moment MRd of a profiled faced panel with openings in the profiled part of the sandwich panel section (see figure 2.11b) shall be made using the expression (28).

L

x , critical cross-section for bending resistance,


b B

L

x , critical cross-section for bending resistance,


b B

( ) Rdod MB

bxM ⋅

⋅−≤ 5,01


(28)

where Mod(x) = highest bending moment in the area of the opening MRd = bending moment capacity of the sandwich panel k = number of crowns across the sandwich panel section a = number of missing crowns due to the opening Both expressions can be used for panels with the core materials PUR and mineral wool. The cutting of the openings in the faces of the panel with low bonding strength is a sensitive task and may reduce the strength of the bond and core and thus, cause a clear risk of delamination.

Shear capacity For profiled panels with PUR-foam as core material and openings, the effect of stress peaks around the corner further decreases the shear capacity. The degree of weakening is depending on the core material, the position and the geometry of the opening. The verification of the shear strength of a sandwich panel with profiled faces with openings shall be made using the expression 29.

(29)

In the expression VO(x) is the highest design shear force component in the sandwich panel core in the area of the opening. AO is the missing core area caused by the opening.

Table 2.4: m-Factor

m Flat part of section any opening

0,85

Profiled part of section, circular opening

0,70

Profiled part of section, rectangular opening

0,6

Rdod Mk

akxM ⋅

−≤

)()(

⋅≤⋅−

=M

Cvk

oC

O

oCd

fm

ABe

xV

γτ

)(,


All the expressions above are derived from test series within EASIE. They should be verified by further test results with different geometries and sizes of openings. The calculation model regarding the shear capacity is only valid for panels with PUR as core material. For panels with mineral wool as core material further investigations are necessary.

EASIE WP1 Deliverable 1.2

3 Resistance of panels with

3.1 Experimental Investigations with small openings

3.1.1 Test set-up

In a first test series in EASIE sandwich panels with a window at midspan have been tested in a six point bending test. Half of the panels were tested in a positive position (equates to wind pressure), the other half in a negative position (equates to w

3.1.2 Results

Displacements Comparing the displacements of the an unweakened panel results in the following table:

Table 3.1: Comparison of d

Load level F = 1 kN

midspan

Test Calculation

without opening

1 12,36 2 12,67 3 12,49

4 12,83

Resistance of panels with openings with reinforcement

Experimental Investigations with small openings

sandwich panels with a window at midspan have been tested in a six point bending test. Half of the panels were tested in a positive position (equates to wind pressure), the other half in a negative position (equates to wind suction).

Figure 3.1: Experimental set-up

Comparing the displacements of the 60 mm-test panels with the calculated displacements of in the following table:

Table 3.1: Comparison of deflections with and without window frame

midspan, deflection in mm corner of the window frame

deflection in mm

Calculation without opening

Deviation in %

Test Calculation

without opening

6,96 77,6 12,04 6,7 6,96 82,0 12,43 6,7 6,96 79,5 12,39 6,7

6,96 84,3 12,79 6,7

29

sandwich panels with a window at midspan have been tested in a six point bending test. Half of the panels were tested in a positive position (equates to wind

test panels with the calculated displacements of

eflections with and without window frame

corner of the window frame, deflection in mm

Deviation in %

79,7 85,5 84,9

90,9


Level of failure: All panels failed by wrinkling in the corner region of the opening. The following table shows a comparison between the failure load of the test panels with openings and calculated failure loads of unweakened panels. The calculation was done with the measured G- and E-moduli, according to the formulas in EN 14509.

Table 3.2: Comparison of failure loads with and without opening

Test Thickness

of the panel Failure load

in kN

Calculated failure load of the complete

panel in kN

Deviation in %

1 60 3,4 10,81 68,2 2 60 3,3 10,81 70,0 3 60 3,6 7,94 54,7 4 60 3,3 7,94 58,8 5 120 6,8 18,99 64,2 6 120 4,9 13,06 62,8

3.1.3 Comparison with existing methods of calculation

Different calculation proposals exist for single sandwich panels with openings. In table 3.3, the failure loads of the tests are compared to calculation results for openings without frames according to calculation proposals of Böttcher (2005) and Courage/Toma (1998).

Table 3.3: Comparison of the failure load in kN between test and calculation

Failure load

in kN

Tests Böttcher Deviation in

% Courage/Toma

Deviation in %

60_1 3,44 1,92 +79 2,37 +45

60_2 3,25 1,92 +69 2,37 +37

60_3 3,60 1,41 +155 1,74 +106

60_4 3,27 1,41 +132 1,74 +88

120_1 6,80 3,37 +102 4,17 +63

120_2 4,85 2,32 +109 2,87 +69

The comparison shows, that window frames have a positive effect on the load bearing capacity. The panels carry up to 155 % more load than the calculation results without window-frames suggest.


3.2 Additional tests with small openings

3.2.1 Test set-ups

Based on the first test series (see chapter before) some additional tests regarding the shear and bending capacity of panels with openings have been performed. Also tests regarding the bonding between the panel and the window frames were included in this series. Altogether the following test series have been performed:

Table 3.4: Comparison of failure loads with and without opening

Series Description of the test Number of tests

Series 0 6 point bending test, span 6 m, complete panel 3 Series 1 6 point bending test, span 6 m, width 700 mm (without

joints) 3

Series 2 6 point bending test, span 6 m, window at midspan 700 x 700 mm

3

Series 3 6 point bending test, span 6 m, width 700 mm (without joints), window at midspan 700 x 700 mm

3

Series 4 4 point bending test, span 1.2 m, width 700 mm 3 Series 5 4 point bending test, span 1.2 m, width 700 mm, window

at midspan 700 x 700 mm 3

Series 6 Shear tests of the bonding 3

As an example the test set-ups of series 1 and 5 are shown in figure 3.2:

Figure 3.2: Experimental set-ups


3.2.2 Results

In the following table the mean values of the failure loads in each series are shown.

Table 3.5: Failure loads of the different test series

Test series

Failure load in kN

Failure mode

0 14,68 wrinkling of the upper face 1 9,85 wrinkling of the upper face 2 3,28 wrinkling with delamination of the face 3 < 0,50 failure of the bonding 4 16,11 shear failure in the core 5 1,02 failure of the bonding

6 2,20 failure of the bonding

The different failure modes are shown in the figures 3.3 and 3.4:

Figure 3.3: Failure modes (wrinkling series 1, wrinkling series 2 and shear failure series 4)

Figure 3.4: Failure of the bonding series 6, test set up and failure mode series 7


In test series 6 the bonding itself was tested. The strength of the bond is very low and that is the principle reason for very small maximum loads in series 3 and 5. A comparison between the tests with openings (series 2) and the tests with openings and frames (see chapter 3.1) further showed a nearly identical distribution of stress in the upper face:

Figure 3.5: Comparison of the stress distribution with and without window-frame

All these determinations lead to the conclusion that the bonding that was tested is not able to transfer loads from the panels to the window frames. Nevertheless, the window frames have a positive effect on the load bearing capacity of the panels by stabilising the faces in the high stressed regions around the opening. For example, test 120_1 (see 3.1.3) with a bonded window frame had a failure load of 6,8 kN. The mean value of series 2 (see 3.2.2) with the same geometry and the same openings without frame was only 3,96 kN. Due to little variations of the material properties the results have to be adjusted. After adjusting the results the panel with frame still carries 155 % of the load of the panel without frame. The calculation model of Böttcher (see chapter 2.1) gives conservatives results – compared to the results of test series 2. The mean value of the failure load in the test series was 3,96 kN (self weight included), the calculation model gives 2,78 kN.

-140

-120

-100

-80

-60

-40

-20

0

0 200 400 600 800 1000

No

rma

l st

ress

in N

/m

m²

y-coordinate in mm

Comparison of the stress distribution close to the opening with and

without frame

without

frame, load

level 1 kN

frame, load

level 1 kN

without

frame, load

level 3 kN

frame, load

level 3 kN


3.3 Experimental investigations with large openings (TKS

3.3.1 Test set-up

Alike to the investigations with reinforced small openings also a test series with large openings (width of the opening equates to width of the panel)been tested in a six point bending test. In figure 3.6 the test set up is shown.

3.3.2 Results

Mode and level of failure: All the panels failed by an overstressing of the longitudinal joint anthe complete system including wrinkling of the outer panels. In some cases the window frames slipped out of the joint. The slipping of the frames did not lead to an immediate collapse of the system, but certainly had an influence question of an exact fabrication of the window it can be avoided. Probably according to the inexactnesses of the windows sizes, the failure load levels were different for each system.

Experimental investigations with large openings (TKS – FSI)

Alike to the investigations with reinforced small openings also a test series with large openings (width of the opening equates to width of the panel) with a window at midspan has been tested in a six point bending test. In figure 3.6 the test set up is shown.

Figure 3.6: Experimental set-up

All the panels failed by an overstressing of the longitudinal joint and a following collapse of the complete system including wrinkling of the outer panels. In some cases the window frames slipped out of the joint. The slipping of the frames did not lead to an immediate collapse of the system, but certainly had an influence on the failure load. As the slipping is a question of an exact fabrication of the window it can be avoided. Probably according to the inexactnesses of the windows sizes, the failure load levels were different for each system.

Figure 3.7: Collapse of the system

34

Alike to the investigations with reinforced small openings also a test series with large with a window at midspan has

been tested in a six point bending test. In figure 3.6 the test set up is shown.

d a following collapse of the complete system including wrinkling of the outer panels. In some cases the window frames slipped out of the joint. The slipping of the frames did not lead to an immediate

on the failure load. As the slipping is a question of an exact fabrication of the window it can be avoided. Probably according to the inexactnesses of the windows sizes, the failure load levels were different for each system.


Table 3.6: Comparison of failure loads with and without window frame

Test Thickness

of the panel Failure load

in kN

Calculated failure load

of the complete panel in kN

Deviation in %

Mode of failure

1 60 9,30 15,94 41,66 Complete collapse 2 60 8,5 15,94 46,68 Complete collapse

3 60 6,7 12,91 48,10 Slipping out of the

window, then collapse

4 60 4,5 12,91 65,14 Complete collapse 5 120 11,9 22,59 47,32 Complete collapse

6 120 8,0 18,05 55,68 Slipping out of the

window, then collapse

3.3.3 Comparison with existing methods of calculation

In Böttcher (2005) a proposal exists for calculating a 3 panel system with an opening. According to this proposal, there are three possible failure modes: Shear failure in the outer panel, wrinkling of the outer panel and failure of the longitudinal joint. By recalculating the tests according to the paper of Böttcher, one asserts that the longitudinal joint is always the critical failure mode. For the bearing strength of the joint, in Böttcher (2005) only a rough estimate is given. This is one of the reasons for significant deviations between some of the test results and the recalculation according to Böttcher, like shown in table 3.7.

Table 3.7: Comparison between tests and calculations

Failure load per panel in kN 60_1 60_2 60_3 60_4 120_1 120_2

Test result 9,3 8,5 6,7 4,5 11,9 8 Calculation result

10,0 10,0 7,9 7,9 7,5 6,0

Deviation -7 % -15 % -16 % - 40 % + 59 % + 33 %

Within EASIE also tests on the load capacity of joints were performed. After recalculating the test 120_1 with these results, the deviation of 59 % decreased to about 10 %.


3.4 Experimental investigations with Fech - windows

3.4.1 Test set-up

Four tests (see table 3.8) with two different sizes of openings (width of the opening 0,7 respectively 1,9 m) with a window at midspan have been tested in a six point bending test. In figure 3.8 the test set ups are shown. It has been distinguished between bonded and not-bonded window-frames.

Figure 3.8: Experimental set-ups

3.4.2 Results

Mode and level of failure: All the panels failed by wrinkling of the upper face in the corner regions of the window frame. In case of the large windows this led directly to the collapse of the whole system. In the tests with small windows a further load increase was possible up to an overstressing of the longitudinal joint and a following collapse of the complete system.


Figure 3.9: Collapse of the system


Table 3.8: Failure loads

Test

Thickness of panel in

mm

Size of window

in mm

Window -Frames

Failure load wrinkling

(Load per panel)

failure load collapse

(Load per panel) Mode of failure

1 120 700 x 1900 bonded 4,7 kN - wrinkling

2 120

700 x 1900 not

bonded 4,5 kN* - wrinkling

3 60

700 x 700 bonded 5,9 kN /3,4 kN** 6,9 kN wrinkling, followed

by joint failure

4 60

700 x 700 not

bonded 4,7 kN /3,0 kN** 6,8 kN

wrinkling, followed by joint failure

* failure during loading of a outer panel (unsymmetrical loading) ** mean value/load of middle panel

The results show that the bonding of the frames does not have a great influence on the failure loads because of weak bond between face and window frame as shown in 3.2.1. Tests with complete panels with 6 m length and a thickness of 120 mm had failure moments of 13,5 kNm. The tests 1 and 2 lead to failure moments of approx. 2,8 kNm, which is 21 % of the loading of a complete panel. For the small windows (test 3 and 4) the wrinkling of the middle panel took place at 3,0 respectively 3,4 kN. Tests with the same panels and window sizes without neighbouring panels (see chapter 3.1.2) failed also at 3,4 kN. So the neighbouring panels do not have an influence on the failure load for wrinkling of the middle panel, but allow a load increase afterwards again.


3.5 Calculation models for large openings

3.5.1 Types of large openings

At the moment, there are different types of large openings on the market. For windows, one can differentiate three categories:

• Ribbon windows with adapter profiles (Figure 3.10a)• Ribbon windows with punctual fixing (Figure 3.10b)• Windows with bonded frames

Figure 3.10a

The load transfer of these systems is very different so the calculations model has to be adapted for each type. All the models are based on the existing beam model of Böttcher (2005) which is described in chapter 2.2.2. 3.5.2 Ribbon windows with adapter profiles

Based on the beam model of bearing and deflection behavior of sandwich panel systems with ribbon windowsprofiles within the joint. The ribbon window itself is not able to transfer the load to the substructure, so the whole load has to be transferredadjacent panels. In the figure an example of an adapter profile with and wstructure is shown.

Calculation models for large openings

Types of large openings

re are different types of large openings on the market. For windows, one can differentiate three categories:

Ribbon windows with adapter profiles (Figure 3.10a) Ribbon windows with punctual fixing (Figure 3.10b) Windows with bonded frames (Figure 3.10c)

Figure 3.10b Figure 3.

The load transfer of these systems is very different so the calculations model has to be adapted for each type. All the models are based on the existing beam model of Böttcher

ed in chapter 2.2.2.

Ribbon windows with adapter profiles

Based on the beam model of Böttcher (2005) a possibility is presented, to calculate the load bearing and deflection behavior of sandwich panel systems with ribbon windows

in the joint. The ribbon window itself is not able to transfer the load to the load has to be transferred by the adapter profile

In the figure an example of an adapter profile with and without the

39

re are different types of large openings on the market. For windows, one

Figure 3.10c

The load transfer of these systems is very different so the calculations model has to be adapted for each type. All the models are based on the existing beam model of Böttcher

(2005) a possibility is presented, to calculate the load bearing and deflection behavior of sandwich panel systems with ribbon windows and adapter

in the joint. The ribbon window itself is not able to transfer the load to the by the adapter profile and to the

ithout the sandwich


Figure 3.

Beam 1 represents the complete related torsional rigidity IT and the bending stiffness behavior in cross direction (EIrepresent the stiffness of the jointwith its bending stiffness EIAdapter

The following stiffnesses and material properties have to be applied: Beam 1: E= ED= 21000 kN/cm² G = GK,L

11

11,

FF

FF

LytB

tBI

+⋅

⋅⋅=

Figure 3.11 Adapter profiles and beam model

Beam 1 represents the complete adjacent sandwich panel in longitudinal direction with the and the bending stiffness EIL. The cross-beams (2) represent the (EIQ, GQ). They have a distance of lQ. The vertical elements

represent the stiffness of the joint kF and the horizontal beam 4 represents the adapter profile

Adapter. following stiffnesses and material properties have to be applied:

= 21000 kN/cm² E-modulus of the face

G-modulus of the core in longitudinal direction

2

22

22c

FF

FF etB

tB⋅

⋅+

⋅⋅

Moment of inertia in longitudinal direction

40

longitudinal direction with the beams (2) represent the

. The vertical elements (3) and the horizontal beam 4 represents the adapter profile

modulus of the core in longitudinal direction

Moment of inertia in longitudinal direction


λ � ()*,+), ∙ ��-./��∙��-∙�� Coefficient for the torsional stiffness according to

Stamm/Witte

I1 � 4 ∙ e�# ∙ B ∙ ��-��-∙�� ∙ 51 7��89:;∙<�=

;∙<�> ),)*,+

Torsional rigidity of the complete panel, standardized to GD

AL = B . ec Area of the core Beam 2: E= EV E-modulus of the face in cross direction G = GK,Q G-modulus of the core in cross direction

I?,@ � l@∙ ��-∙��-�� ∙ e�² Moment of inertia in cross direction

lQ= distance of the joint elements A Q = lQ . ec Area of the core in cross direction Beam 3: E= ED E-modulus of the face (definition)

A � ��∙�D∙E�F, Back-calculated area for the stiffness of the joint

kF= spring rate for the joint lF= length of beam 3 in the model Beam 4: EI y,Adapter Bending stiffness of the adapter profile

(from tests) G � ∞ I 1 ∙ 10KL An assumption for this model is the fact that the adapter profiles are supported by the substructure. The adapter profile is loaded by half of the area load of the window. Depending on the stiffness of adapter profile, joint and sandwich panel the loads will be divided on the adapter profile and the adjacent sandwich panel. The panel is loaded eccentrically which leads to additional stresses in the face and the core material. These stresses have to be added to the stresses caused by the bending moment.


The beam model brings the following results for the particular beams: Longitudinal beam: My,L, MT, Qz,L Cross-beam: My,Q und Qz Joint elements: N Adapter profile: My und Qz After the determination of the stress resultants and deflections using the beam model the structural analyses for the different failure modes can be implemented. The following failure modes are possible:

1) Wrinkling of the face in the adjacent panel 2) Shear failure of the core in the adjacent panel 3) Joint failure 4) Failure of the adapter profile – This case will not be investigated in this report, the

producer of the adapter profiles are responsible for the load bearing capacity of the profiles.

1) Wrinkling of the face: The normal stress in the adjacent panel can be determined by addition of the normal stress due to bending and the normal stress caused by the eccentric load. The following two ratios of normal stress in the face exist:

σM � �NON,+ ∙ :7 ��

# = Existing normal stress due to bending (33)

(Independent from the window)

σ# � kQ ∙ M?,E ∙ K��#∙ON,+ Normal stress due to eccentric loading (34)

The complete stress results in: σ� RMy&kσ ∙ My,LU ∙ 7ec2∙Iy,L (35)

The factor kϬ can be taken from diagrams (see the parametric study, figure 2.8). The confirmation is then:

γ� ∙ RM? & kQ ∙ M?,EU ∙ K��#∙ON,+ Y Z��[

\] (36)


2) Shear failure of the core: Also in the core the stresses caused by the centric shear force have to be superimposed with the stresses from the eccentric loading. For the eccentric load an effective width of the panel of 25 cm (panel width 100 to 120 cm) can be taken into account for conservative results. The following two ratios of shear stress in the core exist (all dimensions in N, mm and N/mm²):

Shear stress due to the existing shear force in the panel: τM � @^+ (37)

Shear stress due to the eccentric load: _# � `a,b#$%cc∙de (38)

The confirmation according to the technical approval is:

γ� ∙ : @^+ & @f,+#$%��∙��= Y Z�g

\] (39)

3) Failure of the joint: For the load transfer from the adapter profile to the adjacent panel the load bearing capacity of the joint has to be proved as well. The beam model provides the maximum load in the joint as normal force N in the joint elements. The load bearing capacity of the joint Fj has to be determined by tests (see chapter 2.2.4). The result from the beam model is:

Fijk8� � l�D (40)

The equation of approval is:

γ� ∙ l�D Y�m\] (41)


Calculation example Below an example for a ribbon window with adapter profiles is calculated. For all load capacities and stiffnesses realistic values derived from tests at TU Darmstadt are used.

Table 3.9 Input values for the calculation example

Geometry: Section properties: L = 5000 mm AL = 120000 mm² B = 1000 mm Iy,L = 3600000 mm4

ec = 120 mm IT = 1,816E+1

0 mm4

tF2 = 0,5 mm ED = 210000 N/mm² tF1 = 0,5 mm GD = 81000 N/mm² lQ = 250 mm EV = 76284 N/mm² lF = 100 mm GK,L = 3,4 N/mm² GK,Q = 2,82 N/mm² Values of the approval: fcv = 0,09 N/mm² Load: fFck/gm = -113 N/mm² wD = 0,8 kN/m²

Test results for the joint:

kF = 1,5 kN/m/mm Fj/gM = 4,063 kN/m

For the calculation of the beam model you get the following input values: Beam 1: E= ED= 210000 N/mm² G = GK,L=3,4 N/mm²

I?,E � ��-∙��-∙��∙��-∙��-��∙�� ∙ e�² � 3600000mmq

λ � ()*,+), ∙ ��-./��∙��-∙�� 1,183 ∙ 10Ks M

��

I1 � 4 ∙ e�# ∙ B ∙ ��-��-∙�� ∙ 51 7��89:;∙<�=

;∙<�> ),)*,+ � 3,51 ∙ 10M%mmq

AE � B ∙ e� � 120000mm²


Beam 2: E= EV= 76184 N/mm² G = GK,Q = 2,82 N/mm²

1

1,

t

ttlI

F

F

QQy+

⋅⋅=

AQ = lQ · ec = 30000 mm² Beam 3: E= ED=210000 N/mm²

E

LlkA

D

FQF ⋅⋅=

Beam 4: EIy,Adapter = 100 kNm² G = ∞ = 1 · 106

Belastung: qAdapter= 0,4 kN/m The calculation of the beam model brings the following results for beam 1:

0,000

1,093

2,075

0 100

76184 N/mm²

= 2,82 N/mm²

42

2

2 900000 mmet

tc

F

F =+

= 30000 mm²

=210000 N/mm²

²1785,0 mm=

= 100 kNm² (if the adapter profiles have a diffe

the profile with less stiffness has6

= 0,4 kN/m

The calculation of the beam model brings the following results for beam 1:

Figure 3.12 Static system

Figure 3.13 Deflection in mm

2,075

2,850

3,514

2,850

2,075

1,093

0,000

100 200 300 400 500

45

different stiffness, the profile with less stiffness has to be used)

0,000


Figure 3.14 Bending moment in kNm

Figure 3.15 Shear force in kN

Figure 3.16 Torsional moment in kNm

In the joint elements the following normal forces exist:

Figure 3.17 Normal forces in kN

With these results the analyses for the ultimate limit state can be made.

0,00

0,34

0,63

0,86

1,04

0,86

0,63

0,34

0,00

0 100 200 300 400 500

0,69 0,670,56

0,40

0,05

-0,32

-0,48-0,62

-0,69

0,00 100,00 200,00 300,00 400,00 500,00

0,35 0,330,28

0,20

0,02

-0,16

-0,24

-0,31-0,35

0,00 100,00 200,00 300,00 400,00 500,00

0,046

0,074

0,0860,091

0,086

0,074

0,046

0 125 250 375 500


1) Wrinkling of the face:

γ� ∙ RM? & kQ ∙ M?,EU ∙ K��#∙ON,+ Y Z��[

\] (42)

An interpolation between the diagrams (Figure 2.8) leads to a factor m of 1,33. For gF 1,85 is

used:

1,85 ∙ 50,8uv/x² ∙ 1x ∙ y5xz²8 & 1,33 ∙ 1,04uvx> ∙ 760xx

3600000xxq Y 113v/xx²

119,7 l�� } 113N/mm² (43)

In this case the proof against wrinkling cannot be provided!!! 2) Shear failure of the core material (gM = 1,2):

γ� ∙ : @^+ & @f,+#$%��∙��= Y Z�g

\] (44)

1,85 ∙ :%,$∙%,��l/�∙$�M#%%%%��² & L�%l#$%��∙M#%��= Y %,%�l/��²

M,# (45)

0,0734 l�� Y 0,075N/mm² (46)

3) Failure of the longitudinal joint:

γ� ∙ l�D Y�m\] (47)

1,85 ∙ %,%�M�l%,#$� Y 4,06kN/m (48)

0,673 �l� Y 4,06kN/m (49)


3.5.3 Ribbon windows with punctual fixing

Analog to the model described above, also sandwich facades with punctual fixed ribbon windows can be calculated. As the windows are not supported at the end, the whole load has to be transferred to the neighboring panels.

Figure 3.18 Test setup for a ribbon window with punctual fixing

The calculation and the analyses are the same as described before. Just the load is not applied on an adapter profile but punctual on the crossbeams. An example for the beam model is shown in figure 3.19.

Figure 3.19 Beam model for the calculation of a sandwich panel in neighborhood of a punctual

fixed ribbon window


Additional to the calculation of the panel, the punctual fixing has to be tested. An example is given in Figure 3.20. The load bearing capacity of this detail is very dependent on the kind of fixing, so the maximum load should be derived from tests.

Figure 3.20 Example for a punctual fixing

3.5.4 Windows with bonded frames

Sandwich facades with bonded window frames have a load bearing behavior which is a little bit different. In this case not the whole panel is replaced by a window (see Figure 3.21). Parts of the panel still participate in the load transfer.

Figure 3.21 Windows with bonded frames in a sandwich facade


Tests within EASIE showed that the frames improve the load bearing capacity of panels with openings clearly. Further the tests showed that the frames do not carry parts of the load by themselves but stabilise the faces in the high stressed regions around the opening. Therefore it is necessary that the frame stabilises the face in a region of at least 5 cm around the opening. Based on the test results of very few tests the existing equations (see equation 1a,b) can be used to calculate the load bearing capacity of single panels with small openings and bonded frames. The factor kF has to be adapted for the bonded frames to the factor kF,frame:

( )( )

≤<⋅−

≤≤⋅−⋅−=

8.04.06.016.0

4.00)6.01(1,

ββ

βββ

if

ifk frameF (50)

Figure 3.22 Load bearing capacity of panels with reinforced openings

The model above is based on only one test series, so further investigations are necessary to verify these proposals! If the bonding strength can be improved the effect of the frame could be even higher. For openings through longitudinal joints like shown in figure 3.23 the load bearing capacity is always the sum of the residual load bearing capacities of the outer panels. In case of a single span panel the inner panels do not contribute to the load transfer.

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8 1

rela

ted

load

be

ari

ng

ca

pa

city

related width of the opening

Existing model

Model with frame

Test with frame

Tests without frame


Figure 3.23 Geometries of large openings

The calculated load bearing capacity is very depending on the calculation model. If the panels are lateral supported, they are able to carrIn figure 3.24 the related load bearing capacity for a system of two panels with an opening (width of the opening 1 m, according to figure 3.23, left side) with different eccentricities is compared for lateral supported and lateral not supported panels.

Figure 3.24 Load bearing capacity for a system of two panels with one opening

b1

B B

b2

n = 2

Figure 3.23 Geometries of large openings

The calculated load bearing capacity is very depending on the calculation model. If the panels are lateral supported, they are able to carry much more load than lateral unsupported panels.

the related load bearing capacity for a system of two panels with an opening (width of the opening 1 m, according to figure 3.23, left side) with different eccentricities is

teral supported and lateral not supported panels.


(Width of the opening 1 m)

B B B

b1 b2

n = 4

51

The calculated load bearing capacity is very depending on the calculation model. If the panels y much more load than lateral unsupported panels.

the related load bearing capacity for a system of two panels with an opening (width of the opening 1 m, according to figure 3.23, left side) with different eccentricities is


B


Due to the neighboring panels and the bonding between the window frame and the panels a lateral support can be assumed. In this case the following equation can be used:

�� y�zde∙�∙�� Y u# ∙ ��-�� ∙ �� (51)

with

k�,k � �y1 7βkz#if0 Y βk Y 0,40,6 ∙ y1 7 βkzif0,4 � βk Y 0,8� (52)

The result for the system tested within EASIE (see chapter 3.4.2, Test 1, three panels and an opening with a width of 1,9 m) is shown in figure 3.25. For this test a good correlation between the test result and the calculation proposal can be stated.


(Width of the opening 1 m)

All the models above are based on very few tests, so further investigations are necessary to verify these proposals!

0,33

0,22

0,33

0,23

0,00

0,10

0,20

0,30

0,40

0,50

-500 -300 -100 100 300 500

rela

ted

load

be

ari

ng

ca

pa

city

eccentricity of the opening in mm

calculation, panels lateral supported test


4 Conclusions

The report is a state of the art report on the influence of openings on the behaviour and resistance of sandwich panels. It introduces the currently known calculation models for the design of sole sandwich panels and of complete sandwich panel walls, which have openings of different sizes and shapes placed in different locations of the spans of the panels. For profiled panels with small openings new calculation models – derived from test results at TU Darmstadt within EASIE - are presented. Test results from the EASIE project regarding openings with additional reinforcing are presented and calculation models have been developed for three types of reinforcement. For one case also a calculation example is presented.


REFERENCES

EN 14509, (November 2006) (European standard). Self-supporting double skin metal faced

insulating panels – Factory made products – Specifications. Published by CEN (Comité Européen de Normalisation), Brussels.

DIN EN ISO 6892-1 (2009) (European standard). Metallic materials – tensile testing- Part 1: method of tests at room temperature. Published by CEN (Comité Européen de Normalisation), Brussels. Berner, K. 2006, Openings in sandwich panels. IS Mainz Berner, K. 2006, Öffnungen in Sandwichbauteilen. Proceedings of LeichtBauen 16-17.3.2006 Technische Universität Darmstadt. pp 145-166. (in German) Böttcher, M. 2005, Berechnungsverfahren für Wand-Sandwichelemente mit Öffnungen. IFBS-Fachinformation 5.09 Statik, IFBS e.V, Düsseldorf (in German) Courage, W. & Toma T. 1994, Structural detailing of openings in sandwich panels. TNO report 94-CON-R0729-01 Davies JM. (ed) 2001, Lightweight Sandwich Construction. Blackwell Science. Heselius, L. 2004, Wrinkling analysis of flat faced sandwich panels with respect to bonding strength and core properties with mineral wool as core material. Dissertation. Darmstadt, ISBN 952-91-8639-8 Höglund, T. 1986, Load Bearing Strength of Sandwich Panel Walls with Window Openings. Proceedings of the IABSE Colloquium, Stockholm 1986, IABSE Report Vol. 49 Lange, J. & Böttcher, M. 2006, Theoretische und experimentelle Grundlagen für die Berechnung von Wand-Sandwichelementen mit Öffnungen. Bauingenieur (81), Springer VDI Verlag, Düsseldorf, 2006 (in German) Lange, J. et al. 2010, Stahlleichtbau mit Verbundelementen. Stahlbau 79 (2010), Ernst & Sohn Verlag, Berlin (in German) Stamm, K. & Witte, H. 1974, Sandwichkonstruktionen. Springer Verlag, Wien, 1974 (in German) Warmuth, F. & Lange, J. 2010, Openings in sandwich elements. International Conference on Steel & Composite Structures, Sydney 2010

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