˘ ˇˆmarket regarding the long-term behaviour and resistance of polyurethane and polystyrene foam...

��

��

�� !�"��"��#��$�%��&��

�� !��'()��$�%��

�� !�� "�#� ��$��%� �$��!&� ��$ !��'��"��

��

ECCS TC7 TWG 7.9 Sandwich panels and Related structures

CIB Working Commission

W056 Sandwich Panels

ECCS/CIB Joint Committee

Preliminary European Recommendations for the Testing and Design of Fastenings for Sandwich

Panels

1st Edition, 2009

Preliminary European Recommendations for the Testing and Design of Fastenings for Sandwich Panels Nº127, 1st edition, 2009 Published by: ECCS – European Convention for Constructional Steelwork [email protected] www.steelconstruct.com All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner ECCS assumes no liability regarding the use for any application of the material and information contained in this publication. Copyright © 2009 ECCS – European Convention for Constructional Steelwork ISBN: 92-9147-000-93 Printed in Multicomp, Lda - Mem Martins, Portugal Photo cover credits: Simo Heikkilä

Preface

3

PREFACE

The European product standard for sandwich panels, EN 14509, covers the requirements and verification methods for the essential properties of factory made sandwich panel products. Fastenings are typically made at a building site outside the factory. Thus, fastenings are not a subject for a European product standard. The European Recommendations, CIB Publication No. 257 and ECCS Publication No. 115, published in 2000 and 2001, give loading arrangements and procudures with which to determine the tensile and shear resistance of both direct and concealed fastenings. These new recommendations update the previously published procedures for fastenings and extend the concept to include also fastenings fixed in a face layer.

The sources of information taken into account in the writing of these recommendations have included the previously published recommendations, relevant new research results and the current practice with regard to the available screw fastenings and concealed fastenings. The resulting recommendations are believed to be particularly applicable to the typical metal sheet-faced sandwich panels with cores of polyurethane or polystyrene foam or mineral wool which are on the market today. However, the rules and methods can be applied to other and new types of fastenings and sandwich panel products. When applying these recommendations, the user shall take into account the mechanical behaviour of the fastening in practice and shall take care to ensure the correspondence of the observed behaviour and resistance of the fastening in the tests and the actual behaviour in practice.

The recommendations are published as “Preliminary European Recommendations for the Testing and Design of Fastenings for Sandwich Panels”. There are two reasons for the prefix “preliminary”. The status of full-scale tests, when compared to tests using small-size specimens requires clearer definition. The rules for the adjustment of test results to nomimal values of the essential properties of the face and core materials require more detailed study in order to cover more reliably all types of core materals. Research anticipated in near future may provide the required information and make possible the publication of this document as “European Recommendations”.

The following individual members of ECCS TWG 7.9 and CIB W56 have taken part in the drafting of this document: Wim Bakens (NED), Klaus Berner (GER), Gianni Bottega (ITA), Sebastien Charton (FRA), Neus Comas (SPA), J.M. Davies (GBR), Stéphane Gilliot (FRA), Johan Gustafsson (SWE), Paavo Hassinen (FIN, chairman of ECCS TWG 7.9 and CIB W56), Antti Helenius (FIN), Lars Heselius (FIN), David Izabel (FRA), Karsten Kathage (GER), Maciej Kubanek (POL), Martin Lamers (NED), Jörg Lange (GER), Thomas Misiek (GER), Jan-Christer Mäki (SWE), Lars Pfeiffer (GER), Ralf Podleschny (GER), Helmut Saal (GER), Johan Schedin (BEL), Ton Tomá (NED) and Danijel Zupancic (SVN).

Preliminary European Recommendations for the Testing and Design of Fastenings for Sandwich Panels

4

The technology of structural sandwich panels continues to advance, and this requires that the guidelines for the design, testing and use of sandwich structures and their fastenings will continue to develop. ECCS TC7 and CIB W56 will, therefore, welcome critical comments and proposals to improve this document. Jörg Lange Chairman of ECCS TC 7

Paavo Hassinen Chairman of ECCS TWG 7.9 and Coordinator of CIB W56

Contents

5

CONTENTS

PREFACE ................................................................................................................................. 3

1. INTRODUCTION ...................................................................................................... 7

1.1 General ......................................................................................................................... 7

1.2 Symbols and notations ................................................................................................. 8

1.3 Definitions ................................................................................................................... 9

2. TESTING OF FASTENINGS USED TO FIX THE PANELS TO THE FRAMES OF BUILDINGS ................................................................................................... 11

2.1 General remarks ......................................................................................................... 11

2.2 Tensile resistance of fastenings ................................................................................. 14

2.2.1 Tensile failure modes .......................................................................................... 14

2.2.2 Testing of screw fastenings based on small sandwich panel specimens ............. 15

2.2.3 Testing of concealed fastenings based on small sandwich panel specimens ...... 18

2.2.4 Full-scale tests ..................................................................................................... 22

2.3 Shear resistance of fastenings .................................................................................... 25

2.4 Resistance of a screw to imposed deflection ............................................................. 28

3. TESTING OF FASTENINGS INSTALLED TO A FACE LAYER ................... 31

3.1 Tensile resistance ....................................................................................................... 31

3.2 Shear resistance ......................................................................................................... 32

4. ADDITIONAL TESTS ............................................................................................ 33

5. EVALUATION OF THE TEST RESULTS .......................................................... 35

5.1 Adjustment of the test results to nominal values ....................................................... 35

5.2 Characteristic tensile and shear resistance of fastenings ........................................... 36

6. DESIGN OF FASTENINGS ................................................................................... 39

6.1 Material factors of fastenings .................................................................................... 39

6.2 Effects of actions on fastenings ................................................................................. 39

6.3 Design for failure modes involving tensile and shear interaction ............................. 40

6.4 Interaction between the fastening and the sandwich panel ........................................ 40

REFERENCES ....................................................................................................................... 43


6

ANNEX A SMALL-SCALE TENSILE TEST BASED ON STEEL SHEET STRIP ..... 45

ANNEX B (INFORMATIVE), DESCRIPTION OF THE TEST SERIES FOR FASTENINGS, A PROPOSAL BASED ON NEEDS OF THE INDUSTRY ................... 49

ANNEX C DESIGN EXAMPLE ......................................................................................... 51

C.1 Analysis of the test results for a direct screw fastening ................................................ 51

C.2 Load-span table for a single-span wall panel ................................................................ 52

C.3 Design of the fastenings for a two-span wall panel ..................................................... 56

ANNEX D RELATIVE DISPLACEMENT BETWEEN THE INTERNAL AND EXTERNAL FACE ................................................................................................................ 59

D.1 Mechanisms which cause deflections .......................................................................... 59

D.2 Calculation procedures for γ and γ1 ............................................................................. 60

D.2.1 Sandwich panels with flat faces ........................................................................... 61

D.2.1.1 Simply supported panel with uniformly distributed load qo ....................... 61

D.2.1.2 Simply supported panel with a line load parallel to the supports .............. 61

D.2.1.3 Simply supported panel with a temperature difference between the faces. 61

D.2.1.4 Continuous panels ...................................................................................... 62

D.2.2 Sandwich panels with profiled faces .................................................................... 62

D.2.2.1 Simply supported panel with uniformly distributed load qo ....................... 62

D.2.2.2 Simply supported panel with a line load parallel to supports .................... 62

D.2.2.3 Simply supported panel with a temperature difference between the faces. 62

D.2.2.4 Continuous panels ...................................................................................... 63

D.2.3 Approximate calculation for single or multi-span panels with flat or profiled faces .................................................................................................................... 63

Introduction

7

1. INTRODUCTION

1.1 General

The European product standard for sandwich panels, EN 145091, provides the essential requirements for sandwich panels used to cover the walls and roofs of buildings and to isolate spaces inside buildings. Furthermore, the standard gives detailed test methods for the experimental determination of the properties relevant to the Construction Products Directive. The standard, therefore, covers the basic properties of the factory made panels but does not give information about the fastenings, which are made on a construction site. These Recommendations, together with the standard, provide complete guidance for the testing and design of sandwich panels systems. The Recommendations describe the testing and design of the fastenings used to fix sandwich panels to the frames or to the supporting beams of a building. They introduce, for the first time, the testing and design of fastenings fixed to one face layer of a sandwich panel only. Full-scale tests are introduced in order to provide a testing and verification method for complete sandwich panels systems including the fastenings. Such testing programmes should not be limited to the fastenings alone. Additional testing is also required to identify the properties of the core and face layers of the test specimens.

Testing methods for fastenings have previously been introduced in European

Recommendations for Sandwich panels published by CIB in 2000 and ECCS in 2001. These Recommendations update the earlier rules and expand the area of application to include concealed fastenings and fastenings fixed to a face layer, only. The Recommendations introduce methods to verify the mechanical resistance of fastenings used in typical wall and roof covering applications. They do not cover the testing and design of more advanced applications such as the fastening systems of shear walls, axially loaded panels, or fastenings subject to seismic actions. Other important issues in practice are the durability and the material compatibility of the fastenings in the long term. These items are outside of the scope of the Recommendations.

Common types of fasteners used to fix sandwich panels to the frames or to the supporting

beams are screws drilled through the panels or concealed fastenings placed in the longitudinal or transverse joints of the panels. The screws may have different sizes of washers, different diameters of the screw head and shaft, different geometries and dimensions of the threads in the shaft and finally different structures of the screw ends in order to make it possible to drill through different materials and material thicknesses of the sub-structure. The structure of concealed fastenings is less standardised and, in general, they are product-specific systems developed to be compatible with a specific joint geometry in a specific panel. However, the testing arrangements, analysis of the test results and the principles of design are similar in all of these fastening systems. 1 EN14509:2006-11: Self-supporting double skin metal faced insulating panels – Factory made products – Specifications


8

The need may arise to mount items such as skylights or coverings made of alternative

sheet materials or glass panes to a face of a sandwich panel. If the weight of the additional elements is relatively small, the fixing is readily made to the face layer only in order to avoid holes passing through the complete sandwich panel. The fasteners may be screws or rivets made of steel or aluminium. The Recommendations provide test arrangements to determine the tensile and shear resistance of the fastenings together with guidance for the design the fastenings. It is emphasized that, in the design of the screws fixed to a single face layer, the real effects of actions caused by the items to be mounted in a face shall be carefully be studied together with any possible additional mechanical loads to which these items may be exposed.

European product standard EN 14509 covers metal faced sandwich panels with a core

made of any of the following: rigid polyurethane foam, expanded or extruded polystyrene foam, phenolic foam, cellular glass or mineral wool. There is adequate experience in the market regarding the long-term behaviour and resistance of polyurethane and polystyrene foam and mineral wool cored sandwich panels including the performance of the fastenings. The properties of panels and fastenings with phenolic foam and foam glass cores are, at the time of writing these Recommendations, less well known. For the lesser known products, full-scale tests with fastenings are recommended and, possibly, specific tests should be developed in order to establish the potential modes of failure.

The properties and resistance of fastenings have influence on the behaviour of complete

sandwich panels. The flexibility of the fastenings changes the deflection of the sandwich panels and has an influence on the bending moment and shear force diagrams of continuous multi-span sandwich panels. The number and location of fastenings at intermediate supports has a direct influence on the bending moment resistance at an intermediate support. The interactions between the fastenings and the panels are briefly introduced in these Recommendations.

1.2 Symbols and notations B overall width of the panel Bs bending rigidity of the sandwich part of a cross-section d diameter of a screw, washer e base of natural logarithm (e = 2.718282) eC effective depth of the sandwich panel e1, e2, e3, e4 distance f1, f2, f3 adjustment factors fCc, fCv, fCt compressive, shear and tensile strength of the core layer fy yield stress of a metal sheet F load, force k coefficient to determine the level of repeated loads kσ fractile factor L span length

Introduction

9

n number of tests Rp0.2 stress at a non-proportional extension of 0.2% ReH upper yield strength of metal material Rm tensile strength of metal material S shear rigidity of a sandwich panel t, tnom, tobs design thickness and nominal and observed thickness of the face sheet t1 thickness of the substructure u displacement w deflection ΔT change of temperature, thermal gradient γM material factor γM2 material factor for fastenings for ultimate limit state verification γM.SER material factor for fastenings for serviceability limit state verification Subscripts C core layer of the sandwich panel F face layer of the sandwich panel R resistance d design value k characteristic value nom nominal value obs measured value in a test rep repeated load t tension u ultimate v shear

1.3 Definitions Core layer of material, which is bonded between the internal

and external faces extended applications applicability of the test results when extended to a larger

group of panels and fastenings face layer flat, lightly profiled or profiled thin metal sheet firmly

bonded to the core family of sandwich panel products

group of products, for which the test results for one or more charactristics of one product in the family are valid for all other products within the family. In testing the principle of “worst case” shall apply

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

full-scale test test in which the dimensions and loading correspond to the real installation in practice


10

concealed fastening hidden fastening placed typically in a longitudinal joint between two panels

nominal thickness thickness given in the product information table pull-over failure mode, in which the head and washer of the screw

penetrates through the face layer of the panel pull-out failure mode, in which the end of the screw becomes

unfastened from the substructure rivet fastener nail or bolt, the ends of which are pressed to form heads

against the surfaces of the sheets to be fastened sandwich panel building product consisting of two metal faces

positioned on either side of a core and firmly bonded to each other so as to act compositely under load

screw fastener metal pin with a spiral ridge along its shaft that is fastened to the substructure by turning

small-scale test test based on a representative part of the structure, which shows the real failure mode and describes in an acceptable way the load – deformation behaviour of the actual assembly

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

Testing of fastenings used to fix the panels to the frames of buildings

11

2. TESTING OF FASTENINGS USED TO FIX THE PANELS TO THE

FRAMES OF BUILDINGS 2.1 General remarks

The procedures given in this chapter can be used to determine the load-carrying resistance of fastenings in order to transfer local tensile and/or shear loads to a panel. The fastenings may be based on screws drilled through the panel or on other similar types of fastening. The test arrangements have previously been described in Refs. /CIB 2000/ and /ECCS 2001/. These Recommendations update the arrangements and expand the areas of application to cover also concealed fastenings. When applying the results in practice, particular attention should be given to:

• type and combination of loading • thickness, material and strength of the supporting member • type and dimensions of the fastener including the head and washer etc. • stiffness and strength of the core • thickness and strength of the face materials • end and edge distances of the fastenings and • geometric details of a concealed fastening

It is a good practice to include a minimum of ten similar static tests and five similar

dynamic tests in any test series on fastenings. However, the number of individual tests in a series may be less if the influence of several parameters are studied in related series of tests.

The test arrangements given in the Recommendations are primarily used to determine the ultimate resistance and the stiffness of the fastening. There may be the requirement to limit the capacity of a fastening because of increased deformations due to the repeated loading, because of visual damage or loss of water tightness or because of other effects at the serviceability limit state. At the present time, there are no definitions for the serviceability limit state failures of fastenings. Thus, there are no direct test methods and requirements for the determination of the resistance of fastenings limited by failure or unacceptable performance at the serviceability limit state. A technical limit can possibly be derived from the load level at which the load-deformation curve first becomes non-linear (sections 2.2.3 and 2.2.4).

Test series include both static tests and tests with repeated load. The repeated loading history used in the tests depends on the action that is simulated in the test. Fastenings are loaded by repeated wind load with or without additional effects caused by vibrations. Repeated wind load without additional vibrations is covered by approximately 5000 cycles in the tests. Fastenings are loaded also by other environmental loads such as changes and differences in the temperature. The loading history in the full-scale tests (section 2.2.4) and in the bending test on an individual fastener (section 2.4) include the temperature effects and require a larger number of load cycles.


12

NOTE: National application documents may require other load histories and other number of cycles to be used in the tests.

The Recommendations provide alternative tests to study the tensile resistance of the

fastenings of sandwich panels. Table 1 gives guidance regarding the choice of the appropriate test method in each case. The application of shear tests and the tests for fastenings fixed in a face sheet are also briefly introduced.

Table 1: Application of the test methods for fastenings.

Property of the fastening

Type of test When to apply the test Section

Tensile resistance of direct and concealed fastenings

Full-scale test static loading tests

- a general procedure to test the complete sandwich panel system with fastenings

- for a more accurate determination of the resistance

- if a scale effect has a large influence on the behaviour

2.2.4

Test based on small sandwich panel specimen

- for known core materials * - when the scale-effect of the

panel and fastenings is known

2.2.2 2.2.3

Pull-over resistance of screw fastening based on metal sheet strips

- to have a quick estimate (conservative approach) for the pull-over resistance

Annex A

Shear resistance of the fastening

Shear resistance of the internal face

- normal use of sandwich panels as covering elements

2.3

Shear resistance of a sandwich wall

Full-scale shear test including several panels and fastenings

- to study the diaphragm action and resistance of a shear wall

tests arrangements case by case

Resistance of a screw fastener to deflection of screw shaft

Test with repeated loading history

- for all screw fasteners 2.4

Full-scale test repeated loading tests

- in the case of a scale effect - if basic values cannot be

applied

2.2.4

Tensile resistance of fastenings in one face


- when the action effect on the fastening is known

3.1


13

Shear resistance of fastenings in one face


- when the action effect on the fastening is known

3.2

* known core materials and sandwich panel products at the time of writing the Recommendations are rigid polyurethane foams, expanded and extruded polystyrene foams and mineral wools

The test series may cover a family of sandwich panel products. In a family, the panels

shall have similar profiling in the faces, the same core material though with varying depths combined with similar fasteners whose length will vary according to the depth of the core material. Typically, panels with the smallest and the largest depth in the production are chosen for the test series. If there is a large variation between the test results with the smallest and largest panel depths, the tests may be completed with tests on a panel of average depth. The test results for panel depths between the depths used in the tests, may be estimated by linear interpolation. Similar face profiling in a product family may cover, for instance, all the panels classified to be thin faced panels, i.e., flat, microprofiled and slightly profiled faces of the panel, the other properties of which are similar. However, the metal sheet thickness shall remain the same, usually corresponding the thinnest face thickness used in the production of the panels in the family. The term ‘similar fastener’ means the same screw or special fastener with the same washer type and diameter. However, the end distance may vary in the test series, which shall then be taken into account in the analysis of the test results.

A change of a parameter in the fastening may cause a small or a large effect in the resistance of the fastening. The analysis in Table 2 evaluates the effect of a change of a parameter in the tensile resistance of fastening and thus gives indicative advice regarding the need for a further test series. Because of the large number of combinations of types of fasteners and sandwich panels, the analysis in Table 2 is schematic without numerical requirements.

Table 2: Extended applications of fastenings tested in tensile tests. Indicative advice regarding the need for further tests because of a change of a parameter in a screw fastening.

Parameter in the fastening Change (increase or decrease) of the parameter Action

Diameter of the washer increase use available test results decrease retest

Diameter of the drill-point or Pre-drilled hole

increase retest decrease use available test results

Head style or diameter of the head

increase use available test results decrease retest

Sheet thickness (in contact to washer and head)



14

Depth of profiling of a flat or lightly profiled face against the head of a fastener (d ≤

3mm)

increase use available test results

decrease retest *

Depth of lining of a profiled face

(d > 3mm) increase/decrease retest

Test results for end support to use for intermediate support use available test results Test results for intermediate

support to use for end support retest

Edge distance at an end support


* it is a good practice to test a flat-faced panel, in which the flat face is against the head of the screw, and to then apply the results to panels with slightly profiled faces 2.2 Tensile resistance of fastenings 2.2.1 Tensile failure modes

The tensile failure modes to be taken into account in the testing and design are pull-over

failure through the external face layer of a sandwich panel, pull-out failure of the fastener from the sub-structure and failure of the fastener itself (Fig. 1). Other failure modes, such as shear failure of the panel around the fasteners or distorsion of the longitudinal joint as well as the combined modes consisting of failure at the fastening and of the global buckling, shear or compression failure of the cross-section, may also take place.

( )koutpullRtkfailurefastenerRtkoverpullRtRtk FFFF ...... ,,min= (2.1)

All types of failure mode may occur in the tests described in this chapter. The particular failure modes, which occur only in the fastenings of sandwich panels, are pull-over failure of the head of the fastener through the face supported by the core layer and bending failure of the fastener. Test methods to study the tensile resistance in the case of these particular failures are introduced in these Recommendations. Pull-out failure and tensile failure of the fastener itself may also occur in structures consisting entirely of steel elements. General guidelines for testing and design with regard to pull-out failure and failure of the fastener itself can be found in EN 1993-1-3. Test arrangements to study the pull-out failure are given in ECCS publication No. 124.

Small-scale tests make it possible to study the influence of a large number of parameters easily. The arrangements for appropriate small-scale tests are given in sections 2.2.2 and 2.2.3. If the failure mode appearing in a small-scale test is not a tensile failure of the fastening system, but is a shear or wrinkling failure of the specimen, either the test


15

arrangements shall be modfied in order to obtain a failure of the fastening or, alternatively, full-scale tests shall be considered.

Full-scale tests show the complete behaviour, failure modes and the resistance of the panels including the failure of the panel and/or the failure of fastenings. Full-scale tests therefore give a complete picture and full information regarding the response and progress of the failure. Arrangements for full-scale tests, based on the ref [UEATC], are given in section 2.2.4.

pull-over failure,

test arrangements in section 2.2 failure of fastener, shall be studied by the manufacturer of the fastener

pull-out failure, see refs.

Fig. 1: Failure modes of a screw fastening between the sandwich panel and a sub-structure.

2.2.2 Testing of screw fastenings based on small sandwich panel specimens

Screw fastenings based on long screws drilled through the sandwich panel to the sub-structure are also termed “direct fastenings” in order to make a distinction with concealed fastenings, which are normally also based on screws but may also include other elements. An alternative term for concealed fastening is “indirect fastening”.

Separate tests shall be carried out for screw fastenings at the end support of a panel and for fastenings at an intermediate support as shown in Fig. 2. In tests carried out in order to determine the tensile resistance at an end support, the minimum distance between the fastener and the end of the panel (e1) shall be used. The distances (e2, e3, e4) shall be sufficiently large that the failure mode of the fastening is not influenced by the supports or edges. However, these distances shall not be so large that they allow global failure of the cross-section of the specimen by buckling, shear or compression to dominate the test.

The load or displacement shall be increased monotonically up to the ultimate load. The use of a displacement-controlled testing machine is to be preferred. The loading rate shall be such as to result in a failure between 3 and 5 minutes after the commencement of the test. The local displacement at the fastening may be measured during the course of the test up to a point close to the maximum load as shown in Fig. 3. The local tensile displacement in the


16

fastening is defined as w = w1 - w2 (see Fig. 2). Load versus displacement values may be used when determining the stiffness of the fastening in the depth direction of the panel in order to model the stiffness of the supports in the static analysis of the sandwich panels. The displacement close to the maximum load may be needed in the classification of the failure.

The ultimate failure load and the mode of failure (pull through, pull out, failure of fastener itself or any other mode of failure) shall be recorded.

If the fastening is exposed to repeated loading, such as a wall panel loaded by a wind load, repeated loading tests shall be carried out in order to determine the resistance of the fastening after a repeated loading history. The repeated loading history consisting of 5000 loading cycles (see section 2.1) is appropriate for the wind loading of normal wall panels. Loading histories for other cases, in which other action effects such as vibrations cause repeated loading, have to be defined on a case by case basis. In each cycle, the minimum and maximum loads are 0.1 k FRt and k FRt, in which FRt is the mean tensile resistance determined in the static loading tests. A value of k = 0,5 is recommended at the commencement of the tests, but may be adjusted if failure occurs at an early stage.

At least five repeated load tests shall be performed. The cyclic loading frequency in the test shall not exceed 5 Hz. After the application of the repeated loads, the specimen shall be loaded up to the ultimate limit state by a monotonically increasing static load.

The mean of the maximum loads under static loading, FRt,residual, shall be equal to or higher than 1.3 k FRt. If this requirement is not fulfilled, k shall be decreased. The tensile resistance of the fastening for repeated loading FRtk.rep is taken to be the minimum value of (2 k FRtk) and FRtk, where FRtk is the characteristic value of the results of the static tests preceding the repeated loading tests.

( )RtkRtkrepRtk FFkF ,2min. = (2.2)


17

a) end support

b) intermediate support

e1 corresponds to the minimum edge distance defined by the manufacturer e2 ≥ max{eC, 100 mm} e3 ≥ B/4 where B is the overall width of the panel e4 ≥ 400 mm Fig. 2: Testing of the tensile resistance of a fastening at an end and at an intermediate support. The fastening is

typically a screw drilled through the sandwich panel to the supporting structure. The distances (e2, e3 and e4) are recommendations and shall be studied separately in each case taking into account the minimum and maximum

edge distances used in practice. NOTES: Tests with a larger span should be made in order to assess the influence of the span. If the diameter of the washer of the screw fastener is equal to or greater than 19 mm, the characteristic tensile resistance of the fastening with respect to repeated loading may be taken to be FRtk.rep = 0.66 FRtk and no repeated loading tests are required. If the deviation of the load-displacement curve from the linear estimate of the initial slope takes place at load less than 0.5 Fu, a limit for the load at the serviceability limit state may be required.

w 1

Fw 2

eC

e 1 e 2

direction of span

w1

Fw2

eC

e4 e4

e3

e3


18

0

1

2

3

4

5

0 10 20 30 40 50

Displacement [mm]

Load

[kN

]

experimentallinear estimate

ultimate load Fu

Fig. 3: Example illustrating the tensile load – displacement curve of a direct screw fastening and the

determination of the ultimate load. 2.2.3 Testing of concealed fastenings based on small sandwich panel specimens

Concealed fastenings can be placed in either the longitudinal or the transverse joints between two sandwich panels. Fig 4 illustrates some common concealed fastening systems fixed to the external face of the sandwich panel. Concealed fixings typically include special profiles and plates and one or more screws. The test arrangements shall correspond the real combination and installation with respect to any additional profiles, parts and screws.

Concealed fastenings may also be based on fixing the internal face only. However, this system is not recommended, because the local transverse tensile stresses in the core may cause brittle failure of the complete fastening.

In general, the same principles of testing can be applied to hidden fastenings in both longitudinal and transverse joints. The difference is in the support system of the specimens (see Figs. 5 and 6).

The test specimen shall consist of two pieces of the sandwich panel, one with tongue geometry and the other with groove geometry, that are jointed to incorporate the concealed fastening. The pieces are fixed together using two cross beams which also serve to prevent the separation of the pieces during the test. The test arrangement shall simulate the real joint configuration. The distance between the fastening and the edge of the support (e2 or e4) shall be chosen such that the edge does not have primary influence on the failure mode of the fastening. In principle, the test configuration described for concealed fastenings at an intermediate support can also be utilised for testing at an end support (Fig. 5).


19

The loading arrangement for a concealed fastening placed in the transverse joint is shown in Fig. 6. Two pieces of sandwich panels are both supported at two points. The cantilever with the concealed fastening is loaded in order to simulate the loading on the fastening.

Fig. 4: Examples of concealed fastenings placed in the longitudinal joints (a…e) and in the transverse joints

(f…h) of sandwich panels.

The concealed fastening is loaded in increments. The speed of the cross head needs to be chosen so that a failure occurs within three to five minutes after the commencement of the testing. The load applied to the fastening should be recorded continuously with an adequate accuracy. In order to determine the flexibility of the fastening, the movement between the moving head and the sandwich panel should be measured. This can be achieved in one of two ways:

a)

b)

c)

d)

e)

f)

g)

h)

load distributor

sealing strip distributor


concealed fixing


saddle washercover plate

transverse joint with cover plate

load distributor sealing strip distributor


insulation

transverse joint with cover plate

insulation

insulation

clamb


20

1. a displacement transducer may be mounted on the moving cross head 2. the displacement may be measured at at least two points close to the fixing and the

average displacement is subtracted from the cross head movement (Fig. 7)

The measured movement shall represent the local displacement of the fastening. Thus, the global displacements of the specimen have to be subtracted from the measurements.

a) end support

e3

e3

b) intermediate support

e1 corresponds to the minimum edge distance defined by the manufacturer e2 ≥ max{eC, 100 mm} e3 ≥ B/4 where B is the overall width of the panel e4 ≥ 400 mm Fig. 5: Testing of the tensile resistance of a concealed fastening placed in the longitudinal joint at an end and

intermediate support. The distances (e2, e3 and e4) are recommendations and shall be determined separately for each case.

eC

w2

w1 e 1 e2

F direction of span

w2

w1 F

eC

e4 e 4

e3

e3


21

e1 ≥ max{eC, 100 mm} e2 ≥ B/4 where B is the overall width of the panel

Fig. 6: Testing of the tensile resistance of a concealed fastening placed in the transverse joint between two panels. The distances (e1 and e2) are recommendations and shall be determined separately for each case taking

into account the real distances used in practice.

For the determination of plastic deformations one test shall be carried out by unloading and re-loading the specimen at a minimum of 5 intervals. The load-deflection curve shall be drawn.

If the concealed fastening is exposed to the action effects of repeated loading, repeated loading tests shall be carried out in order to verify the tensile resistance of the concealed fastening. The guidelines given in 2.2.2 for repeated loading tests shall be applied.

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120Displacement [mm]

Load

[kN

]

specimencrosshead

displacement in fastening

ultimate load Fu

Fig. 7: Load – deflection curve and determination of the ultimate load for a concealed fastening.

direction of span e1

wF

e2


22

2.2.4 Full-scale tests

Specimens for full-scale tests consist of single- and two-span panels fixed to supports

with the appropriate fastenings. Tests with panels continuous over two-spans are required only when continuous multi-span panels are included in the practical applications of the panel. A full-scale sandwich panel loaded with negative distributed load or equivalent line loads simulates the real behaviour of the panel and the fastenings simultaneously. A full-scale test allows possible failures in the fastening as well as in the face and core to be observed and recorded. It reveals the behaviour of the panels and the dominant mode of failure including failure of the fastening and local and global failures of the panel. Thus, a full-scale test shows the detailed behaviour at the serviceability limit state and the progress of failure up to the ultimte limit state. Full-scale tests make it possible to study and to optimize the performance of the sandwich panel system including the fastenings. The modes of failure and failure loads in full-scale tests depend on the depth and the span of the panel. Thus, tests with several panels depths and span lengths are usually required.

Full-scale test arrangements are shown in the UEAtc guidelines2. The results of a full-

scale test are directly applicable to the specimen (span, depth etc) and the loading case used in the test. The application of the test results can be extended by interpolating between the test spans or between the other parameters used in the tests for otherwise identical structural systems.

Full-scale tests are an alternative approach to tests with small-scale specimens. Full-scale

tests can also be used as verification tests in order to check the fulfilment of the predicted response and resistance in special cases.

In general, a set of full-scale tests consist of the following static tests - based on single-span loading arrangements, a test on a small, an intermediate and a

large span with panels having a small, an intermediate and a large panel depth: that is a total of 3 x 3 = 9 tests and

- where required, based on continuous two-span loading arrangements, a test on a small, an intermediate and a large span with panels having a small, an intermediate and a large panel depth: that is a total of 3 x 3 = 9 tests

Thus, the test series includes a total of 9 + 9 = 18 tests. Where the face thicknesses also vary, the minimum face thicknesses are generally used in the tests.

In principle, full-scale tests are serviceability limit state tests using the following the

procedure; - determine the failure of the fastening in static tests

2 UEAtc Technical Report for Assessment of Installations using Sandwich Panels with a CFC-free polyurethane foam, 1996


23

- define the serviceability limit load F1 based on the results of the static tests. Generally, F1 is chosen as a value between Fstatic.u/3 and Fstatic.u/2, taking into account the deflection limit of L/200 where Fstatic.u is the ultimate load in a static test.

- carry out the required tests with repeated loading - carry out the static tests that are required after the repeated loading tests - compare the ultimate load reached in the static tests to the load F1 and make

conclusions regarding the characteristic resistance of the panel The test panel is mounted on two or three supports using the specific type, number and

distribution of the fastenings which are to be studied in the test. The span lengths of the specimens represent the maximal, minimum and an intermediate span for the maximum load applied during the service life of the panel (Fig. 8).

0.1 L 0.1 L 0.3 L 0.3 L 0.2 L

0.25 F 0.25 F 0.25 F 0.25 F support support

displacement transducer

single-span specimen

0.25 F 0.25 F 0.25 F 0.25 F

0.125 L 0.125 L 0.525 L 0.35 L 0.35 L 0.525 L

support support support

displacement transducer

two-span specimen

Fig. 8: Loading arrangements in the full-scale test based on equivalent line loads.

The loading may also be based on distributed loads. The direction of the loading is negative causing tensile loading of the fastenings.

The given load level in a full-scale test is denoted by F1 which generally represents the

highest unfactored load caused by the mechanical and environmental loads on the structure. The test shall be executed with a single-span and, where required, with a continuous two-span arrangement (Fig. 8).

The full-scale test specimen shall be loaded with a repeated loading history including - a loading of 50000 cycles between F1/4 and 3F1/4, - a loading of 20000 cycles between F1/2 and F1 and - a loading of 8000 cycles between F1/2 and 3F1/2.


24

The maximum frequency of the loading is 20 cycles per minute. The displacements and deformations of the panel and the possible failures in the faces and in the core and finally, the local deformations close to the fastenings shall be controlled and recorded

NOTE: The load cycles in the loading history have the following background.

- 50 000 cycles represent the effects of the normal wind on the panels during the service life of the panel in the building and - 8000 cycles the effects of the extreme wind on the panels during the service life of the panels in the building

After the cyclic loading phase, the specimen shall be loaded with static load up to failure.

It is required that the ultimate load in the static test shall be at least 2 F1. If this requirement is fulfilled, the characteristic ultimate load of the panel to be used in design shall be taken as 1.5 F1. If the requirement for the ultimate load of 2 F1 is not fulfilled in the static test, a new load F1 shall be defined and the repeated loading test series shall be repeated. The characteristic value of the tensile resistance of the system, incorporating the sandwich panel and the specific fastenings used in the tests is

15.1 FFRtk = (2.3)

The design value of the tensile resistance of the system to be used in the design

calculations is

2

1

2

5.1

MM

RtkRtd

FFF

γγ== (2.4)

in which γM2 is the material factor for the failure of the sandwich panel and the fastening.

NOTE: A safe, approximate value for the resistance of fastenings to typical repeated wind loading may be derived by multiplying the 5% fractile value of the results of the static tests by 0.66. An alternative solution is to expose the full set of test specimens to 5000 cycles of repeated loading to simulate typical wind load (see 2.2.2). For non-typical repeated or dynamic loading cases, an appropriate loading history shall be determined on a case by case basis.

screwfastener

washer

saddlewasher

Fig. 9: Typical structure of the special strengthening washer plate, termed a ‘saddle washer’, which is placed on the outer flange of the external face of a sandwich panel.


25

NOTE: The basic design values for the fastenings used in France to take into account the fatigue of the fastening for the normal wind load are given in Tables 3a and 3b. These values are based on the results obtained from a large number of fatigue tests (Ref UEAtc 1996). The diameter of the washer of the screws is 19 mm and the yield strength of the steel face is 320 N/mm2. FUR and FER represent the resistance at the ultimate and at the serviceability limit state respectively corresponding to the pull-over failure mode.

Table 3.a Basic design values of FR without a saddle washer (see Fig. 9.).

Nominal thickness of the steel sheet of the external face, mm

FUR kN

FER kN

0.50 1.5 0.75 0.60 or 0.63 3.0 1.65 0.75 or 0.80 3.6 1.8

Table 3.b Basic design values of FR with a saddle washer (see Fig. 9.).

Nominal thickness of the steel steel of the external face, mm

FUR kN

FER kN

0.50 3.3 1.65 0.60 or 0.63 4.0 2.0 0.75 or 0.80 5.2 2.6

2.3 Shear resistance of fastenings

The fastenings used to fix the sandwich panels to a sub-structure or to a frame of a building, may be loaded by shear forces caused by self-weight, live loads or diaphragm action. The shear resistance of a single fastening for normal applications is considered in this section. The distribution of the shear forces, the shear failure mechanisms in shear diaphragms and the resistance to repeated shear loads are outside of the scope of this chapter.

The shear resistance of a fastening may be determined by failure of the metal face, failure at the point of connection to the sub-structure or failure of the fastener itself. Here, testing for the shear resistance is based on small sandwich panel specimens (Fig. 10). Because, in normal applications, the shear loads are carried primarily by the inner face of a sandwich panel, an alternative testing arrangement shown in Fig. 11 has been developed and may be used in the shear tests.


26

The width of the specimen shall be chosen such that the longitudinal edges do not influence the test results. In general, a series of fastenings placed in line at uniform spacing across the full width of the panel are tested.

If the distance between the end of the panel and the fastener is less than 30 mm, it is recommended to carry out separate tests for fastenings at the end of a panel and those at a larger distance from the end of the panel, i.e., at an intermediate support. It is good practice to carry out shear tests using the minimum end distance.

For each screw type or for each type of the hidden fastening, the tests shall be carried out for the largest panel depth to be used in practice.

a) direct screw fastening

b) special fastenings in longitudinal joints

For shear loads at an end of the panel, e1 corresponds the minimum end distance. A larger distance simulates the behaviour at an intermediate support. t1 is the thickness of the sub-structure. Fig, 10: Testing of the shear resistance of fastenings: a) direct screw fastening passed through the panel and b)

special fastenings placed in longitudinal joints between the panels. The displacement u at the and of the fastener represents the shear deformation.

F

eC u

t1

direction of span

e1 F

eCu

t 1direction of span

e1


27

Fig. 11: Alternative arrangement for shear tests

The load or displacement shall be increased monotonically up to the ultimate load. The use of a displacement-controlled testing machine is to be preferred. The shear displacement at the fastening shall be measured in order to determine the shear stiffness. The shear displacement corresponding to the maximum load in the fastening shall also be measured. The loading rate shall be such as to result in a failure between three and five minutes after the commencement of the test.

The ultimate load is defined to be the smallest of (Fig. 12): • the maximum load recorded during the test • the load at which the first decrease in load is observed in the load - deflection curve • the load corresponding to a displacement of 3 mm, if this occurs on the rising part

of the load - deflection curve.

The maximum load, the corresponding displacement (hole elongation, misalignment of the screw) and the mode of failure (pull out, failure of fastener itself, elongation of the hole, misalignment of the screw etc.) shall be recorded.

The ductility of a fastening loaded in shear may be determined on the basis of a certain decrease in the load. A fall of 10% after the attainment of the ultimate load would represent a typical measurement point. Because of the possibility of local maximum and minimum loads in the typical load-deformation curve, only the global decrease in the load should be taken into account (curve a in Fig. 12).


28

Shear test of a fastening

0

1

2

3

4

0 2 4 6 8 10Displacement [mm]

Loa

d [k

N]

a) maximum loadb) load corresponding the displacement of 3 mmc) load at first fall of loadS j 7

Fig. 12. Examples of shear load – displacement curves and definition of the ultimate load. A displacement

controlled testing machine is assumed. 2.4 Resistance of a screw to imposed deflection

In addition to tensile and shear forces, screw fasteners may also be loaded by the bending moment induced by thermal movement of the sandwich panel. The changing temperatures cause repeated imposed deflections and thus repeated bending stresses in the shaft of the screw. This is a load case that is peculiar to the screws fixing sandwich panels. The bending of the shaft may cause deformations in the thread of the screw in the sub-structure which, in turn, may result in a reduction in the pull-out strength of the fastening.

The resistance of the fastener to such an imposed deflection shall be determined using the test arrangement shown in Fig. 13. The fastener is fixed as a cantilever of length ‘l’, where ‘l’ is equal to the depth of the panel (eC) at the point of the connection. The details of the test arrangement shall correspond as closely as possible to those in the actual structure. In particular, the fastener shall be fixed into material of the same thickness ‘t’ as in the supporting member in the actual sub-structure. The head of the fastener (detail A in Fig. 13) shall not be restrained during the test.

The fastener shall be tested in a displacement-controlled testing machine and shall be subjected to the following unilateral displacement spectrum where ‘u’ is the maximum lateral displacement calculated at the point of the attachment

(1) 20000 cycles at 4/7 u (2) 2000 cycles at 6/7 u (3) 100 cycles at u

The frequency shall not exceed 5 Hz. The procedure for the determination of the

displacement u is given in Annex D.


29

For a given fastener, the test procedure shall include the following tests - ten static tensile tests using the loading arrangement shown in ECCS Publication

No.124. The mean of the tensile resistance of the specimens so obtained is denoted by FRt.mean .

- ten tests with repeated bending loading in which the specimens are exposed to the deflection spectrum described above

- after the application of the above displacement spectrum, each specimen shall be tested to failure in a static tensile test

Evaluation of the test results shall be based on the mean of the initial static tests, FRt.mean,

together with the results of the static tests carried out after the repeated bending tests. The tensile resistance of each specimen in the final static test shall be at least 80% of the mean of the tensile resistance prior to cyclic loading.

Fig. 13: Test arrangement for the repeated bending test of a fastener. The restraint to the screw at the point

shown in the detail A shall allow freedom of rotation. The drilling of the screw into the sub-structure shall be made in a manner corresponding to the usual practice.

e

130

Detail A

d 45°

45°

+ u A

screw fastener

t1 l


30

NOTES:

1. The arrangement shown in Fig. 13 represents a suitable arrangement for testing of an individual fastener subject to imposed bending. By varying the length ‘l’ and the displacement ‘u’, this test can be used to determine the maximum allowable value of ‘u’ for different panel thicknesses. In the systematic testing of a particular fastener, the thickness ‘t1’ of the sub-structure material shall also be varied because a larger thickness results in an increased bending restraint and therefore a reduced deformation capacity. Further details of the interpretation of this test are given in Appendix D.

2. The recommended displacement spectrum is based on a procedure that is

accepted in Germany. This, in turn, is based on the following temperature variations during a 50 year working life:

number of cycles ΔT 20000 40°C 2000 60°C 100 70°C.

3. Detail A is designed to allow the head of the screw to rotate freely during the test.

If this detail does in practice not allow free rotation, thus putting the screw into double curvature, detail A may require a modification.

Testing of fastenings installed to a face layer

31

3. TESTING OF FASTENINGS INSTALLED TO A FACE LAYER

Fasteners used to fix additional elements to the external or internal face layer only, are typically rivets or self-drilling screws. The resistance of the fastening is based on the face layer supported by the core. For design, the resistance and the flexibility of the fastening with respect to both tensile and shear loads are required. In this chapter, test arrangements for screw and rivet fastenings in one face layer are described.

3.1 Tensile resistance

The typical failure modes of screw and rivet fastenings fixed into a face layer are: - pull-out failure from the face sheet at the point of fastening, - tensile failure of the core layer of the panel at the point of fastening, especially if the

fastening is located close to an end of a panel and - failure of the fastener itself, which is more typical of rivets. The test arrangements described in 2.2.2 can be used to study the tensile resistance and

the flexibility of fasteners fixed in a face layer only (Fig. 14). The distance between the end of the panel and the fastening has an influence on the test results. Repeated loading may have a negative influence on the adhesion between the core and face layers, leading to a reduction of the tensile resistance of the connection due to delamination.

Tensile test of a screw fastenings fixed to a face layer, only

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10Displacement [mm]

Load

[kN

]

ultimate load

Fig. 14: Example of tensile load – displacement curve and determination of the ultimate load. The load –

deflection curve is typically approximately linear unless the fastenings are fixed close to an end of the panel.


32

3.2 Shear resistance

The typical shear failure modes of the screw and rivet fastenings fixed in a face layer are: - yielding and crippling and finally pull-out failure from the face layer, - shear failure of the fastener especially in the case of rivet fasteners The test arrangements described in section 2.3 can be used to study the shear resistance

and flexibility of fastenings fixed to a face layer only (Fig. 15). If the fastening is placed close to an end of the panel, the distance between the fastening and the end of the panel has an influence on the shear resistance.

Fig. 15: Example of a shear load – displacement curve and the determination of the ultimate load.

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14

Displacement u [mm]

Load [kN]

a) first decrease in the load

b) load corresponding the displacement of 3 mm

Fu

Fu

Additional Tests

33

4. ADDITIONAL TESTS

The tests introduced in Chapters 2 and 3 give experimental information about the properties and resistance of the fastenings. In order to analyse and to adjust the test results to the nominal values of the properties of the constituent elements of the product, information about the properties of the core and faces as well as of the fastener itself is required. The additional tests described in this section are intended to determine these properies. They may be classified as follows

- external and internal face layers - metal core thickness (tobs) , yield stress (Rp0.2 , ReH) and ultimate tensile strength (Rm), in all cases

- core layer - cross panel tensile strength (fCt), in all cases - cross panel compressive strength (fCc), in all cases - shear strength (fCv), in the case of concealed fastenings

- fastener, washer and additional parts in concealed fastening - dimensions and material properties, where required

- dimensions of the test specimen, in all cases

The relevant tests on the core layer and on the sandwich panel itself are given in detail in EN 14509, the tests on the metal sheet face layers in EN 10002-1 and the test on the fasteners themselves in ECCS Publication No. 42.


34

Evaluation of test results

35

5. EVALUATION OF THE TEST RESULTS 5.1 Adjustment of the test results to nominal values

In general, the thickness and strength of the face of the sandwich panel in a test do not

correspond exactly with the nominal thickness and strength used in design. Therefore, the results of the tests have to be modified in order to adjust the results to the values used in design. Because the core of the sandwich panel has an important influence on the resistance of the fastening, the results shall also be adusted to the nominal strength of the core. Exceptions are the results of the tests based on a metal sheet strip (Annex A), in which case only the adjustment to the nominal values of the properties of the face is required.

The tensile test results of direct screw fastenings shall be adjusted using the expression:

iobsiadj RffR ,21, ),min(= (5.1)

and the tensile test results of indirect screw fastenings, and the results of full-scale tests, using the expression:

iobsiadj RfffR ,321, ),,min(= (5.2)

The results of shear tests on fastenings shall be adjusted using the expression:

iobsiadj RfR ,1, = (5.3)

In the expressions (5.1) to (5.3),

1,

1 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

obsobsm

u

tt

Rf

f (5.4)

121

,2 ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛=

obsCc

Cck

ff

f and 121

,3 ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛=

obsCv

Cvk

ff

f (5.5, 5.6)

where the factor f1 takes into account the influene of the face and the factors f2 and f3 the

influence of the core. The smallest of these factors shall be taken into account in the analysis.

In the above expressions: Robs,i = result of test number i Radj,i = result of test i modified to correspond to the nominal values of the face and

the core used in the design fu = nominal value of the ultimate tensile strength of the face sheet, used in

design


36

Rm,obs = mean ultimate tensile strength of the face sheet measured in the test specimen

t = design thickness of the metal face sheet tobs = mean thickness of the metal core of the face sheet measured in the test

specimen fCck = characteristic value of the compression strength of the core used in design fCc,obs = mean value of the compression strength of the core measured in the test

specimens fCvk = characteristic value of the shear strength of the core used in design fCv,obs = mean value of the shear strength of the core measured in the test

specimens NOTE:

Nominal values of the basic yield strength and ultimate tensile strength of typical steel sheets used in sandwich panels are, according to EN10326:

Steel grade ReH , R0,2 , fy [N/mm2]

Rm , fu [N/mm2]

S220GD 220 300 S250GD 250 330 S280GD 280 360 S320GD 320 390 S350GD 350 420

5.2 Characteristic tensile and shear resistance of fastenings

Characteristic values of the tensile and shear resistance of a fastening are evaluated on the basis of the log-normal distribution of the adjusted test results using the expression:

( )yky

p ex σσ−= (5.7) where

)( ini xLy = is natural logarithm of an adjusted test result xi

∑=

=n

iin xL

ny

1

)(1 mean value of yi

kσ fractile factor (see the Table below)

( )( )∑=

−−

=n

iiny yxL

n 1

2

11σ standard deviation of yi

n number of test results

Evaluation of the test results

37

Assuming a confidence level of 75%, the fractile values according to EN 14509 are: number of specimens

3 4 5 6 7 8 9 10 15 20 30 60 ∞

k σ 3.15 2.68 2.46 2.34 2.25 2.19 2.14 2.10 1.99 1.93 1.87 1.80 1.76


38

Design of fastenings

39

6. DESIGN OF FASTENINGS 6.1 Material factors of fastenings

The determination of the material factors to correspond with the failure modes of sandwich panels is given in EN 14509. The same procedure can be applied in order to determine the material factors for the tensile and shear resistance of fastenings at the ultimate limit state:

yy eeM

σσγ 115.2)645.17.48.0(2 05.105.1 == −⋅ (6.1) and at the serviceability limit state:

yy eeSERMσσγ 755.0)645.10.38.0(

. 0.10.1 == −⋅ (6.2) where σy is the variance of Ln(xi) of the test results. The recommended minimum value of the material factor for fastenings at the ultimate

and at the serviceability limit state verifications is γM2 = 1.33 and γM.SER = 1.0. The design values of the tensile and shear resistance are calculated as:

2M

RtkRtd

FF

γ= and

2M

RvkRvd

FF

γ= (6.3), (6.4)

NOTE: In principal, the safety factors are determined at the national level. In absence of national values, the material factors derived in Section 6.1 are recommended.

6.2 Effects of actions on fastenings The fastenings used to fix the panels to a sub-structure or to a frame of a building are

loaded by tensile loads caused mainly by the wind suction load and by the temperature difference between the faces. These fastenings may also be loaded by shear loads caused by the self-weight of a wall panel, by the self-weight of roof panels and by the snow load on inclined roofs, by the weight of any covering elements or additional items mounted on panels and, further, by any loads resulting from diaphragm (stressed skin) action.

Fastenings fixed in one face layer only may be loaded by the weight of any additional

covering elements and additional items fixed to the panel. An additional covering may cause


40

further shear loads in fastenings because of the static interaction between the covering and the sandwich panel.

The tensile and shear load on a single fastening is determined in the static design

calculations. The tensile and shear loads in fastenings at both the serviceability and the ultimate limit states shall be calculated using the theory of elasticity. If the design is based on full-scale testing, the ultimate resistance determined in the test can be used without making a distinction between the failure of the fastening and the failure of the sandwich panel (chapter 2.2.4). However, the material factor determined at the national level or derived using the expressions given in Section 6.1, shall be applied.

Load factors and combination factors for loads on fastenings and, in addition, the rules

for combinations are given in EN 14509.

6.3 Design for failure modes involving tensile and shear interaction Fastenings used to fix the panels to a sub-structure or to a frame of a building are

designed separately for the tensile and shear loads. If the failure mode is a pull-over failure, interaction studies in typical direct screw fastenings are not normally required, because the tensile mode of failure in the outer face and the shear failure mode in the inner face do not influence each other. However, if failure in tension and shear take place at the same point, i.e., in the connection to substructure or in the shaft of the fastener, an interaction study is required. The expression (6.5) can then be applied.

Fasteners fixed to a face layer only are designed separately for tensile load and shear

load. Because the tensile and shear failure modes develop at the same point in the face sheet, interaction studies between tensile and shear failures are required. In the verification for the combined failure mode, expression (6.5) taken from EN1993-1-3 can be applied.

1≤+Rvd

vd

Rtd

td

FF

FF

(6.5)

6.4 Interaction between the fastening and the sandwich panel

Deformations in the fastenings cause additional flexibility at the connection points of sandwich panels in walls and roofs. The flexibility of the fastenings therefore changes the deflected shape of both single-span and multi-span sandwich panels. Thus, if the deflection is an important design criterion, the influence of the flexibility of the fastenings should be taken into account.

The flexibility of the fastenings causes changes in the bending moment and shear force diagrams of continuous multi-span sandwich panels. Typically, the flexibility reduces the absolute values of the bending moments and shear forces at intermediate supports, caused by

Design of fastenings

41

distributed loads and/or the difference of the temperature between the faces. On the other hand, the flexibility increases the bending moments in the spans caused by distributed loads. Thus, the infuence of the flexibility of the fastenings may be favourable in the verification for the serviceability limit state.

The deformations and stresses at the points of fastenings cause imperfections in the sandwich panels. This is especially the case in direct fastenings, in which the srews are drilled through the faces and the core. The imperfections due to the fastenings reduce the resistance of the faces to compressive stresses and the resistance of the core to shear stresses. These considerations shall be taken into account in the design of sandwich panels and fastenings. EN 14509 gives test arrangements to study the resistance of the sandwich panels at intermediate supports for interaction failure modes. In EN 14509, the interaction is directly taken into account in the full-scale tests and in the proposed clauses for design made by testing [EN 14509 Annex F (Draft)].


42

References

43

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.

Proposed Annex F of EN 14509, (Draft May 2007). Design by testing. Paris.

EN1990, (2002) (European standard). Basis of Structural Design. Published by CEN (Comité Européen de Normalisation), Brussels.

EN1991, (2004) (European standard). Eurocode 1: Actions on structures. Part 1-3: General actions. Snow loads. Published by CEN (Comité Européen de Normalisation), Brussels.

EN1991, (2005) (European standard). Eurocode 1: Actions on structures. Part 1-4: General actions - Wind actions. Published by CEN (Comité Européen de Normalisation), Brussels.

EN1993-1-3, (2006) (European standard). Eurocode 3: Design of steel structures. Part 1-3: General rules, Supplementary rules for cold-formed thin gauge members and sheeting. Published by CEN (Comité Européen de Normalisation), Brussels.

CIB W56 (2000). European Recommendations for Sandwich Panels, Part I: Design. CIB/ECCS Report Publication 257.

ECCS TWG 7.9 (2001). European Recommendations for Sandwich Panels, Part I: Design. ECCS Publication No 115, Brussels.

ECCS TWG 7.10 (2008). The Testing of Connections with Mechanical Fasteners in Steel Sheeting and Section. ECCS Publication No 124, Brussels.

ECCS TWG 7.2 (1983). Mechanical fasteners for use in steel sheeting and sections. ECCS Publication No 42, Brussels.

UEAtc (1996). UEAtc Technical Report for assessment of installations using sandwich panels with a CFC-free polyurethane foam core. MOAT56. Paris.


44

Annex A - Small-scale tensile test based on steel sheet strip

45

ANNEX A SMALL-SCALE TENSILE TEST BASED ON STEEL SHEET STRIP

The tensile resistance of screw fastenings drilled through a sandwich panel may be determined by applying the test arrangements given in the report (ECCS TWG 7.10, 2008) (Fig. A1). The test procedure is based on a steel sheet strip which is bent into the form of a folded plate. A screw fastener is drilled through the flange of this profile and tested by the application of a tensile load. This test was originally developed for fastenings in trapezoidally profiled sheeting and the application of the same test procedure to fastenings in sandwich panels is possible. However, this is not recommended for general use because the interpretation of the test results may be complicated.

Fig. A1. Test arrangements based on steel sheet strip.

The formed sheet of the test specimen, with its fixed dimensions and the rigid clamping of the webs to the test set-up, serves as a model of a profiled sheeting. This test arrangement will give satisfactory results for many sheeting profiles. For sandwich panels with PU-cores, the test results (5%-fractile values, F5%) have to be adjusted using the factors given in Table A1 to take into account the geometry of the faces and the influence of the core material (fgeo) and, in addition, the influence of repeated loading (fcyc).

The characteristic value FRtk of the tensile resistance for static loading is:

%5FfF staticRtk = (A1) and the characteristic value FRt,ch,rep for repeated (dynamic) loading is:

%5. FfF dynamicrepRtk = (A2)

In these expressions F5% is the characteristic value of the test results based on steel sheet

strip specimens and fstatic and fdynamic are factors given in Table A.1.

75 °

Ft

strip offace sheet

screw

pull -overfailure mode

clamping device

50 mm


46

For core materials other than PU-foam, no adjustment values exist and no

recommendations are possible. For edge distances within the range 20mm ≤ e1 ≤ 45mm, the pull-over resistance derived

from the test results based on the metal sheet strip has to be reduced additionally by multiplying the results given by the expressions (A1, A2) with the factor fel given by equation (A3) /2/

⎩⎨⎧≥≤

⋅−=9,00,1

03,04,11 Se df (A3)

in which the diameter of the washer dS is given in mm. For edge distances e1 smaller

than 20 mm, no statement is possible.

Table A1. Reduction factors fstatic and fdynamic for test results based on tests with steel sheet strips.

shape of the face and location of the fastener fstatic = fgeo fdynamic = fgeo x fcyc

1

0,70 0,70

2

no saddle washer*

0,50 0,30

3

(symmetric)

0,70 0,70

4

e

bF

(asymmetric)

bF ≤150

mm

≤250

mm

>250

mm

bF ≤150

mm

≤250

mm

>250

mm e/bF e/bF

≤ 0,25 0,7 0,5 0,35 ≤ 0,25 0,7 0,35 0,25

> 0,25 0,7 0,5 0,35 > 0,25 0,6 0,35 0,25

Annex A - Small-scale tensile test based on steel sheet strip

47

5

a

bF

(symmetric)

0.7 0.5

* a saddle washer is a specially profiled washer that distributes the load over the flange of the face profile

Because of the influence of the geometry of the specimen, repeated loading tests using

arrangements based on metal sheet strips have no significance for the use with sandwich panels and shall not be performed. In general, the application of the adjustment factors given in Table A1 should be sufficient. REFERENCES FOR ANNEX A

ECCS TWG 7.10 (2008), The Testing of Connections with Mechanical Fasteners in Steel Sheeting and Sections. Chapter 3.3.2 in ECCS Publication No 124, Brussels.

Saal H, Misiek T, (2008). Durchknöpftragfähigkeit der Befestigungsmittel von Sandwichelementen bei direkter Befestigung. Frauenhofer IRB Verlag. (in German)


48

Annex B - Description of the test series for fastenings a proposal based on needs of the industry

49

ANNEX B (INFORMATIVE) DESCRIPTION OF THE TEST SERIES FOR FASTENINGS A PROPOSAL BASED ON NEEDS OF THE INDUSTRY

The following examples illustrate the application of the test methods for the fasteners and fastenings of sandwich panels introduced in the Recommendations.

1. The pull out test of a screw fastener should be carried out by the manufacturer of the fastener by testing of each type of the screw

2. The resistance of a screw fastener to the head deflection should be determined by the manufacturer of the fastener. Use the test arrangements given in chapter 2.4.

3. The tensile resistance of a direct screw fastening should be determined using the test arrangements given in chapter 2.2.2. A test series should include ten static tests and three repeated loading test with 5000 loading cycles for fastening at an end and intermediate support. The tests should include fastenings fixed to the panel with the minimum and maximum core depths, such as 60 and 200 mm. Thus, a test series should include 10 x 2 (end and intermediate support) x 2 (min and max depth) = 40 static tests and 3 x 2 x 2 = 12 tests with repeated loading for each fastening.

4. The tensile resistance of a concealed fastening without any load distributing plate below the head of the screw should be determined using the test arrangements given in chapter 2.2.3. A test series should include ten static tests and three repeated loading tests with 5000 loading cycles for fastenings at an end and intermediate support. The tests should include fastenings fixed to the panel with the minimum and maximum core depths such as 100 and 200 mm. Thus, a typical test series should include 10 x 2 (end and intermediate support) x 2 (min and max depth) = 40 static tests and 3 x 2 x 2 = 12 tests with repeated loading for each fastening.

5. The tensile resistance of a concealed fastening with a load distributing plate such as a saddle washer below the head of the screw does not require any additional testing if the end distances and other critical details are at least equal to those used in the tests under point 4 above.

6. The tensile resistance of all kind of fastenings can be studied using the full-scale tests given in chapter 2.2.5. The test series should include single-span and, if required, two-span panels with the minimum and maximum core depths such as 60 and 200 mm. The specimens shall be subjected to static loading and 5000 cycles of repeated loading. Typically, the span of a single-span specimen should be between 4 and 6 m and the span of a two-span specimen between 2 m and 3 m. The test series should include five static tests and three tests with repeated loading for each type of specimen. Thus, a typical test series includes 5 x 2 (single-span and two-span tests) x 2 (min and max depth) = 20 static tests and 3 x 2 x 2 = 12 tests with repeated loading.

7. The shear resistance of fastenings should be determined using the test arrangements given in chapter 2.3. The tests should be carried out using the largest depth of panel. A typical test series should include ten static tests.

8. Tests needed to characterize the test specimens are defined in chapter 4.


50

NOTE: In general, and in all cases, 3 repeated loading tests are sufficient to cover the need for information regarding sandwich panels and their fastenings exposed to the dynamic effect of wind load. 5000 cycles of load are sufficient to simulate the action effect of typical wind loads.

Annex C - Design Example

51

ANNEX C DESIGN EXAMPLE C.1 Analysis of the test results for a direct screw fastening

The results of ten tensile tests using the load arrangements in section 2.2.2, are given in Table C.1 and in graph C.1. The test results are adjusted to correspond to the the nominal values of the face and core. On the basis of the adjusted values, the mean value, the standard deviation and the characteristic value of the results based on the normal and log-normal distributions are determined. The characteristic value of the resistance to be used in design is chosen on the basis of the calculated values.

The nominal and measured mean ultimate tensile strengths of the face steel are 390 and 430 N/mm2, and the nominal and measured mean steel core thicknesses of the face sheet are 0.56 and 0.585 mm, respectively. In addition, the nominal and measured mean compression strengths of the core layer are 0.1 and 0.124 N/mm2. The corresponding adjustment factors are calculated as follows:

869.0582.056.0

432390

1 =⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=f and 898.0

124.01.0 ½

2 =⎟⎠⎞

⎜⎝⎛=f , ( ) obsobsadj RRffR 869.0,min 21 ==

Table C.1: Test results and adjusted test results of a tensile test series, calculated mean value, standard deviation

and characteristic value based on normal and log-normal distribution. Choice of the characteristic tensile resistance to be used in design.

Specimen Test result Robs, kN

Adjusted test result, Radj, kN

Ln(Radj)

1 2 3 4 5 6 7 8 9 10

3.96 4.22 4.28 4.02 3.88 4.15 4.05 4.25 3.92 3.98

3.44 3.67 3.72 3.49 3.37 3.60 3.52 3.69 3.41 3.46

1.235 1.299 1.313 1.250 1.215 1.282 1.258 1.306 1.225 1.240

Mean value 3.54 1.263 Standard deviation 0.125 0.0353 Fractile factor, kσ 2.1 2.1 Characteristic value, FRtk.test 3.27 3.28 Characteristic value for design, FRtk 3.2


52

Fig. C.1: Test results and adjusted results of a tensile test series, mean and characteristic resistance values.

Evaluation of the material factor for the ultimate limit state verifications: - exponent of the expression 6.1; 0747.00353.0)645.17.48.0( =−⋅ - material factor, expression 6.1 ; 131.105.1 0747.0

. == etestMγ Selection of the material factor; 33.1)33.1,max( .2 == testMM γγ Design (factored) value of the tensile resistance; kNkNFF MRtkRtd 4.233.12.32 === γ C.2 Load-span table for a single-span wall panel

This section describes a procedure for the determination of the characteristic load-span table for a single-span, thin-faced, symmetric wall panel fixed with three direct screw fastenings at each end support. The panel is loaded by wind suction load and a Summer temperature difference of CTTT °−=−=−=Δ 40652512 between the internal and external faces. The mechanical properties of the panel are given in Table C.2.

3.0

3.5

4.0

4.5

0 1 2 3 4 5 6 7 8 9 10 Test

Tens

ile re

sist

ance

[kN

]

mean value

characteristic value

test result

adjusted test result


53

Table C.2: Mechanical properties and design criteria for a single-span wall panel loaded by wind suction load. The buckling strength of the face, shear strength of the core and tensile resistance of the fastening are design

values.

Total width B, mm 1200 Effective depth of panel eC, mm 100 Steel core thickness of face tFd, mm 0.56 Modulus of elasticity of face EF, N/mm2 210000 Coefficient of thermal elongation of face αF, 1/°C 0.000012 Support width Ls, mm 80 Shear modulus of core GC, N/mm2 3 Allowable deflection L/100 Load factor γF 1.5 Combination coefficient ψ0 0.6 Combination coefficient ψ1 0.75 Buckling strength of face fFcd, N/mm2 140 Shear strength of core fCvd, N/mm2 0.08 Tensile resistance of fastening FRtd, kN 2.4 Number of fastenings at each support, nf 3

The bending rigidity and shear rigidity of the panel are calculated as follows:

mNmmetEB CFdFs2122 10588.05.0 ⋅== , mNeGS CCC

6103.0 ⋅==

The design criteria and expressions for the characteristic load are given in Table C.3. The verification for the buckling and shear strength and for the resistance of the fastenings is made for the wind suction load with the load factor for the ultimate limit state. Deflections are calculated at the serviceability limit state with the corresponding combination factors for the frequent combination of the action effects.

Table C.3: Design criteria and expressions to determinate the characteristic load-span table.

Buckling strength of internal face

FcdFdC

FckFF f

teLq

≡=8

2.γ

σ FcdF

FdCFck f

Lte

q 2.8γ

=

Shear strength of core Cvd

E

kCvFC f

eLq

≡=2

γτ Cvd

F

CCvk f

Le

qγ2

. =

Tensile resistance of fastenings

( ) RtdfsRtkF FnBLLqF 2.1 ≡+= γ ( )BLL

Fnq

sF

RtdfRtk +

=γ

2.


54

Allowable deflection, frequent combination of action effects at serviceability limit state

10081

3845 2

1..4

1.. LS

LqB

Lqw

C

wk

s

wk ≡+=

100883845 2

1024

2..1L

eLT

SL

BLqw

C

F

Cswk ≡

Δ+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

αψψψ

100883845 2

124

3..10L

eLT

SL

BLqw

C

F

Cswk ≡

Δ+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

αψψψ

( )3..2..1... ,,min wkwkwkwk qqqq = Characteristic load

( )wkRtkCvkFckk qqqqq .... ,,,min=

Based on the given mechanical values and the expressions in Table C.3, the characteristic

load corresponding to each design criterion is determined and, finally, the envelope curve representing the characteristic wind suction load can be calculated (Fig. C.2). In practice, the fastenings should be placed symmetrically at the same distance from the end of the panel as in the tests.

0

1

2

3

4

5

3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2Span length [m]

Cha

ract

erist

ic lo

ad q

[kN

/m2] wrinkling

shearfasteningdeflectioncharacteristic load

Fig. C.2: Characteristic wind suction load for a single-span thin-faced wall panel fixed with three screw fasteners

at each end support. In addition to the wind load, there is a difference of temperature between the faces.

Screw fastenings provide supports to the panel which have a certain flexibility. This flexibility has an influence on the deflections of single-span, simply supported wall panels and this may be taken into account by replacing the flexible supports by elastic springs, the spring coefficient of which has been determined in the fastening tests. The adjusted spring coefficient of a direct screw fastening in the tests in this example is k1 = 250 N/mm. The screws at each support are springs which act in parallel. Thus, the total spring coefficient of the fastenings at both end support to the panel width and to a unit width is


55

mmNmmNkk fas /750/25033 1 =⋅=⋅= mmmNmmmNBkk fas //625//2.125033 1 =⋅=⋅=

Expressions for the deflections, including the flexibility of the fastenings, are given in

Table C4. There are no changes in expressions for the compression stress of the face, shear stress of the core and tensile force of the fastening, which remain as in Table C3. The characteristic load including the influence of the flexibility of the fastenings is shown in Figure C.3. Table C.4: Determination of the characteristic load-span table where the expressions for deflections include the

flexibility of the fastenings.

Allowable deflection, frequent combination of action effects at the serviceability limit state

100281

3845 1..

21..

41.. L

kLq

SLq

BLq

wfas

wk

C

wk

s

wk ≡++=

1008283845 2

1024

2..1L

eLT

kL

SL

BLqw

C

F

fasCswk ≡

Δ+⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

αψψψ

1008283845 2

124

3..10L

eLT

kL

SL

BLqw

C

F

fasCswk ≡

Δ+⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

αψψψ

( )3..2..1... ,,min wkwkwkwk qqqq = Characteristic load

( )wkRtkCvkFckk qqqqq .... ,,,min= *

* values for qk.Fc, qk.Cv and qk.Rt from Table C.3

0

1

2

3

4

5

3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2Span length [m]

Cha

ract

erist

ic lo

ad q

[kN

/m2]

wrinklingshearfasteningdeflection, inc. flexibility of fasteningscharacteristic load

Figure C.3: Characteristic wind suction load of a single-span, thin-faced wall panel fixed with three screw

fasteners at each end support. In addition to the wind load, there is a difference of temperature between the faces. The flexibility of the fastenings has been taken into account in the determination of the deflection values.


56

C.3 Design of the fastenings for a two-span wall panel

Here, the sandwich panel introduced in section C.2 is supported on three supports and has two equal spans of 4.2 + 4.2 m. The panel is loaded by a wind suction load of qk = 1 kN/m2. In addition, there is a difference of the temperature of CTTTS °−=−=−=Δ 40652512 in Summer and CTTTW °=−−=−=Δ 50)30(2012 in Winter between the internal and external faces. The mechanical properties of the panel are given in Table C.2.

Negative support reactions are calculated using the expressions given in Annex E of EN14509 (Table C.5). These expressions are based on the linear theory of elasticity of thin-faced sandwich beams. The combination of support reactions is carried out at the ultimate limit state using the corresponding load and combination factors given in Annex E of EN14509. Finally, the number of fastenings is determined using the design value of the tensile resistance derived in the example in section C.1. This example studies the design of fastenings to resist tensile loads only and does not cover the design of the panel itself. In practice, the resistance of the fastenings to shear loads should also be considered.

The combination of the support reactions with thermal effects based on the theory of elasticity at the ultimate limit state results in conservative design values for the support reactions and therefore gives an overestimate of the number of fastenings required at the supports. Table C.5: Support reactions at the end and central supports of a continuous two-span wall panel. Combination

of design values of the support reactions and the number of fastenings required at each support.

End support Central support Parameter k

3333.0103.02.410588.033

32

3

2 =⋅⋅⋅⋅

=⋅

=SL

Bk S

Wind suction load (negative for suction load)

( )

( )

mkN

mkN

kLq

F kkq

706.1

3333.01411

22.4)1(

1411

2..1

−

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−⋅−

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

( )

( )

mkN

mkN

kLqF kkq

988.4

3333.014112.4)1(

1411..2

−

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

+⋅−

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

+=

Temperature difference in Winter (end) and Summer (central support)

mkN

keT

LB

FC

WFSkT

945.0

3333.011

100.0501012

2.4210588.03

11

23

63

..1

−

=+

⋅⋅

⋅⋅−

=+

Δ⋅

⋅−=

−

α

( )

mkN

keT

LB

FC

SFSkT

512.1

3333.011

100.0401012

2.410588.03

113

63

..2

−

=+

−⋅⋅⋅

=+

Δ⋅=

−

α


57

Combination at the ultimate limit state

mkN

FFF kTFkqFd

41.3945.06.05.1706.15.1

..10..1.1

−=⋅⋅−⋅−

=+= ψγγ

mkN

FFF kTFkqFd

843.8512.16.05.1988.45.1

..20..2.2

−=⋅⋅−⋅−

=+= ψγγ

Number of fastenings 4.1

4.241.3.1

1. =−

==Rtd

dscrew F

Fn 7.3

4.2843.8.2

2. =−

==Rtd

dscrew F

Fn

Number of fastenings in practice

at least two fastenings at each end support

at least four fastenings at central support

Screw fastenings provide flexible supports to the panel. This flexibility has influence on

the support reactions of continuous multi-span sandwich beams. The flexibility may be modelled using elastic spring coefficients based on the displacements measured in the fastening tests. The adjusted spring coefficient of a direct screw fastening in the example is k1 = 250 N/mm. The screws at supports act as springs in parallel. Thus, the total spring coefficients of the fastenings at end support and central support to the width and to a unit width are

mmNmmNkk fas /500/25022 11. =⋅=⋅= (two screws at both end support, to the panel width)

mmNmmmNBkk fas /417//2.1/25022 11. =⋅=⋅= (to a unit width)

mmNmmNkk fas /1000/25044 12. =⋅=⋅= (four screws at central support, to the panel width)

mmNmmNBkk fas /833/2.1/2504/4 12. =⋅=⋅= (to a unit width)

The expressions for the support reactions in Table C.6 have been derived on the basis of the theory of elasticity of thin-faced sandwich beams. The numerical results show the difference in the support reactions caused by the flexibility of the support (Tables C.5 and C.6).


58

Table C.6: Support reactions at the end and central supports of the continuous two-span wall panel with elastic

supports taking account of the flexibility of the fastenings. Combination of the design values of the support reactions.

Parameter k 3333.0

103.02.410588.033

32

3

2 =⋅⋅⋅⋅

=⋅

=SL

Bk S

Support reaction at the central support Wind suction load (negative for suction load)

mkN

mkN

kLS

kLS

k

kLS

kLqF

fasfas

faskkq

925.4

833.02.4103.02

417.02.4103.0

3333.011

417.02.4103.02

3333.0451

2.4)1(

211

2451

33

3

2.1.

1...2

−=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⋅⋅⋅

+⋅⋅

++

⋅⋅+

⋅+

⋅−

=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+++

++

=

Temperature difference in Summer (central support) ( )

mkN

kLS

kLS

k

LSe

TF

fasfas

C

SFkT

393.1

833.02.4103.02

41.02.4103.0

3333.011

2.4103.01.0

40000012.0

211

33

3

2.1.

..2

−=

⋅⋅⋅

+⋅⋅

++

⋅⋅−⋅

=+++

Δ=

α


mkNFFF kTFkqFd 641.8393.16.05.1925.45.1..20..2.2 −=⋅⋅−⋅−=+= ψγγ

Support reaction at the end support Wind suction load ( ) ( )

mkNFLqF kqkkq 737.12925.42.412..2...1 −=−−−=−=

Temperature difference in Winter (end support)

( )mkN

kLS

kLS

k

LSe

TF

fasfas

C

WFkT

870.0

833.02.4103.02

41.02.4103.0

3333.011

2.4103.01.02

50000012.0

2112

33

3

2.1.

..1

−=

⋅⋅⋅

+⋅⋅

++

⋅⋅⋅

⋅

=+++

Δ=

α


mkNFFF kTFkqFd 39.3870.06.05.1737.15.1..10..1.1 −=⋅⋅−⋅−=+= ψγγ

Annex D - Relative displacement between the internal and external face

59

ANNEX D RELATIVE DISPLACEMENT BETWEEN THE INTERNAL AND EXTERNAL FACE D.1 Mechanisms which cause deflections

Shear-strain γ due to elastic shear deformation in the core

γτ

=G C

γ

Bending rotation at the support

γ 1 =dwdx

x

w

γ 1

γ 1

u = imposed deflection of the fastener, being the relative displacement between the

internal and the external skins at the head of the fastener. u is related to reference point A in figure D.1.

u = u (γ1) - u (γ) (D1)

The calculated deflection u shall be less than the deflection u used in the test in accordance to Section 2.4.

The displacement u of the head of the fasteners can be evaluated on the basis of the superposition of displacements u (γ) and u (γ1) as shown in figure D1.

Celu ⋅−′⋅= γγ 1 (D2)


60

In the following, calculation methods are given to determine γ and γ1 for different static systems and load cases.

Fig. D.1. Displacements at the end of sandwich panel.

D.2 Calculation procedures for γ and γ1

The parameters and symbols which are used in these procedures are given in Section 1.2. In addition:

CC GBeS = (D3)

α =+B BB

F F

S

1 2

(D4)

2LSBS=β

(D5)

A

l'

B u (γ)

γ

γ 1 γ1

head of fastener u

shaft of fastener

eC

u(γ1)


61

λα

αβ2 1

=+

(D6)

21 FFStot BBBB ++= (D7) where S is the shear rigidity of the sandwich panel, BF1 and BF1 the bending rigidity of the profiled external and internal face layers and Bs the bending rigidity of the sandwich part of the cross-section. D.2.1 Sandwich panels with flat faces D.2.1.1 Simply supported panel with uniformly distributed load qo

Qq Lo=

2

SQ

=γ

SLq

BLq o

S

o

224

3

1 +=γ

q0

L

D.2.1.2 Simply supported panel with a line load parallel to the supports At the support A

LaLFQ −

=

γ =QS

[ ] ( )εεεεγ −++−= 1326

322

1 SF

BFL

S

D.2.1.3 Simply supported panel with a temperature difference between the faces γ = 0

[ ]C

FF

eLTT

21122

1αα

γ−

=

where αF1 and αF2 are the coefficients of thermal expansion of faces 1 and 2, respectively.

T1 (°C)

T2 (°C)

FA

a

L

ε = aL

a L<2

eC


62

D.2.1.4 Continuous panels These are solved by the superposition of the simply supported system and the statically indeterminate forces as shown below.

A B CL1 L2

A CL = L1 + L2

A B CL1 L2

+ =

D.2.2 Sandwich panels with profiled faces D.2.2.1 Simply supported panel with uniformly distributed load qo

⎥⎦⎤

⎢⎣⎡ −=

2tan1

213 λ

λβ

γtot

o

BLq

⎥⎦⎤

⎢⎣⎡ −+=

2tanh1

21

241

32

3

1λ

αλαλγ

tot

o

BLq

D.2.2.2 Simply supported panel with a line load parallel to supports At the support A

( )⎥⎦⎤

⎢⎣⎡ −

−−=λ

ελεβγsinh

1sinh12

totBFL

[ ] ( ) ( )⎥⎦

⎤⎢⎣

⎡⎥⎦⎤

⎢⎣⎡ −

−−++−=λ

ελελα

εεεγsinh

1sinh113261

232

2

1totB

FL

D.2.2.3 Simply supported panel with a temperature difference between the faces

C

FF

eTT 1122 αα

θ−

=

2tanh λ

λθγ L

−=

γθ

α λλ

1 112

12

=+

−⎡⎣⎢

⎤⎦⎥

Ltanh

T1 (°C)

T 2 (°C)

eC

FA

a

L

ε = aL

a L<2


63

D.2.2.4 Continuous panels

The same procedure shall be followed as described for the panels with flat faces (see D.2.1.4) D.2.3 Approximate calculation for single or multi-span panels with flat or profiled faces

[ ]tot

Coo B

eLqqu

24

3

=

[ ]2

CeLTu

θ=Δ

L

L1 = L L2 = L

The limits of application of the above formulae are given by L L L L1 2 3= = = =L

5.2>SB

SL

REFERENCE FOR ANNEX D

Toma A.W. 1984, Proposal for chapter 4 of the European Recommendations for sandwich panels: Design of fastenings for sandwich panels. TNO Report BI-84-012. Delft.


64

��

��

˘ ˇˆmarket regarding the long-term behaviour and resistance of polyurethane and polystyrene foam...

Documents