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Microsoft-Excel® based program determining internal forces and stresses in sandwich panels

Part 1

Raabe, Oliver

Abstract This report introduces a Microsoft-EXCEL® based program determining internal forces and stresses in sandwich panels on the base of ECCS-Recommendations [1]. The program consists of two parts which can be downloaded from the Institute for Sandwich Technology – Mainz homepage at www.fh-mainz.de/sandwich. Additional program parts will be provided with following reports. Zusammenfassung In diesem ersten Bericht wird eine Lösung zur Ermittlung der Schnittgrößen und Spannungen bei Sandwichbautei-len mit Hilfe eines „kleinen“ EDV-Programms auf der Basis der Tabellenkalkulation EXCEL® von Microsoft® und auf Grundlage der ECCS-Richtlinien [1] vorgestellt. Die Pro-gramme (2 Teilprogramme) können kostenfrei als Freeware über die Homepage des Instituts für Sandwichtechnik-Mainz (iS-Mainz) unter www.fh-mainz.de/sandwich bezo-gen werden. Im Rahmen dieser Berichtsreihe werden noch weitere kleinere EXCEL®-basierte Programmteile folgen. 1. Problem Sandwich panels consisting of two thin faces (e.g. tin steel) and a rigid core (PUR, PIR, EPS, Mineral Wool, etc.) are today used in a wide range of applications varying from roof coverings to wall finishes, making use of their construction relevant practical advan-tages. These advantages are increased stability as well as superior heat-, sound- and moisture-insulation. Apart from these well-known advantages an inte-grated construction shows, it is very often the rela-tively complicated design procedures that are named as disadvantages. Literature such as [1], [2] and [3] describe different solutions for mathematical design procedures. These are generally based on linear sandwich theory with respect to yielding bond between core and faces. They are valid for both, flat and profiled faces. Furthermore in sandwich panel design not only wind, snow and self-weight loads need to be considered, but also temperature differences between upper and lower face as well creep under dead loads (see [4], [5] [6].)

2. Bases of Calculation For general use of sandwich theory, approximate so-lutions such as differentiation method [3] or adjusted method of consistent deformations [8] are available. These methods however can reasonably used in com-puter programs only. Apart from these general solu-tions, closed solutions for the differential equations presented in [3] are available (so called exact solution in [1].) Being still quite complex, these solutions are not very convenient for calculation by hand. For certain conditions an EXCEL based program was build, calculating internal forces and stresses. The program is based on the ECCS recommendations [1]. It allows for calculating internal forces and stresses for single- and two-span panels with equal span lengths, allowing to enter both, flat or as if flat and profiled fa-ces. Results are calculated separately for all common load cases. The program and the whole report can be download-ed from www.fh-mainz.de/sandwich. When applying the program, the following points need to be consid-ered: • Inner and outer face is either flat, as if flat, trapezi-

um shaped or wave shaped. • System is single- or two-span system with equal

span length • Loading in uniform from e.g. self weight, snow or

wind (constantly distributed) • Temperature difference between upper and lower

face (constant over panel length) • It is possibility to enter creep effects Further features are: • Menu prompts and printout optional in English

and German • Denotation in accordance with ECCS recommen-

dations Derivation and presentation of the formulas is ab-stained at this point, but can be found under [1]. Mis-prints in [1] however make it necessary to mention some corrections. Under chapter 3.5.2 in the ECCS recommendations the solutions of a differential equa-

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tion for a two-span panel under temperature load is given. Here the interim values 5 and 6 need to be fac-torized with “-1” to get correct results. The corrected formula then is:

( ) ( )( )( )

λλ

−β+α+

λλ−λ

−α+−=ε

tanh131

cosh1cosh

2113 2

5 (Gl. 1)

25

6ε

+=ε (Gl. 2)

3. Application Advice In principle the program can be used in two ways. 3.1 Proof of single load case For a given static system (single- or two-span panel where l1 = l2) it is possible to calculate internal forces and stresses as well as deformations for individual predetermined load cases such as self-weight, snow-, and wind-load, temperature differences between faces or creep effects. Based on the determined internal forces, stresses and deformation, it is then possible to determine the de-gree of exploitation through comparison with allow-able values. Praxis relevant design which implements load case combination and safety concepts is not im-plemented in the program. 3.2 Evaluation of full scale panel testing Based on full scale panel testing design values such as wrinkling strength need to be determined. With given span length and maximum loads derived from testing it is possible to calculate the relevant stresses for sin-gle- and two-span beams. These results then after normalisation and statistical evaluation give the de-sign value for allowable wrinkling strength. 4. Example In this chapter two available programs (resp. EXCEL sheets) are presented. • ECCS – flat

EXCEL program following the regulations given in ECCS recommendations for sandwich panels with flat or lightly profiled inner and outer face.

• ECCS – profiled EXCEL program following the regulations given in ECCS recommendations for sandwich panels with one or two profiled faces.

For a better understanding and to allow for compari-son of results the input data is taken as presented in [10], Chapter 7.7. The input (highlighted in yellow) as well as the results (printed in bold) can also be found in the annex. 4.1 Determination of internal forces and stresses

for a sandwich element with as if flat faces under wind- and temperature load.

Given: Sandwich element with lightly profiled faces, its associated geometry and material properties (cross section area, distance between centroids of faces, shear modulus of core, etc.). The panel is loaded with a uniformly distributed load of q = 0,50 kN/m2 and a temperature difference of ∆T = 55° - 25° = 30° K (summer). The static sys-tem is as follows:

Wanted:

Internal forces, stresses and deflections Input and results are presented in annex 1. A good correlation of results with [10] can be found. The oc-curing differences are smaller than 1% and are primar-ily due to rounding errors. 4.2 Determination of internal forces and stresses

for a sandwich element with profiled faces under area- and temperature load.

Given: Sandwich element with profiled outer and lightly-profiled inner face, its associated geometry and material properties (cross section area, moments of inertia, distance between centroids of faces, shear modulus of core, etc.). The panel is loaded with a uniformly distributed load of q = 0,75 kN/m2 and a temperature difference of ∆T = 55° - 25° = 30° K. The static system is as fol-lows:

l = 6,80 m

Taußen = 55°C Tinnen = 25°C

q = 0,50 kN/m2

l1 = 3,30 m

Taußen = 55°C Tinnen = 25°C

q = 0,75 kN/m2

l2 = 3,30 m

Taußen = 55°C Tinnen = 25°C

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Wanted: Internal forces, stresses and deflections

Input and results are presented in appendix 1. A good correlation of results with [10] can be found. The found differences are smaller than 2%. For roof panels it is also possible to account for long term creep of core by entering the long-term shear modulus. The shear modulus of the core GS then changes to:

t

St,S 1

GG

Φ+= (Gl. 3)

mit GS,t = long-term shear modulus GS = shear modulus (short-term) Φt = creep factor 4.3 Determination of wrinkling strength from full

scale panel test Given:

The same sandwich panel as described in example 1 is now loaded in a two span test as indicated be-low. The panel was loaded until failure (wrinkling of lower face at intermediate support). The ulti-mate load was found to be qU = 2,17 kN/m.

Wanted:

Wrinkling strength of inner face at intermediate support.

Input and results for unit load q=1 kN/m2 can be taken from Annex 3. The wrinkling strength in this test is then:

ncalculatio

testncalculatio,Ktest,K q

q⋅σ=σ (Gl. 4)

2test,K mm/N67,112

00,117,2

92,51 =⋅=σ (Gl. 5)

Following [10], Chapter 7.7.1.2 the design value for wrinkling strength at serviceability limit state of the inner face is 103,82 N/mm2. This however is a 5% fractal value based on a test series after statistical analysis.

Here it is pointed out that the wrinkling strength for single- and two-span panels with profiled faces can be determined accordingly, if the panel shows linear elastic behaviour until failure. 5. Supply of EXCEL sheets The presented EXCEL data sheets can be down-loaded as freeware from the homepage of the Insti-tute for Sandwich Technology – Mainz (iS-mainz) at www.fh-mainz.de/sandwich. Alternatively they can be obtained from Ingenieurbüro Berner & Gruber. 6. Final remarks The use of two EXCEL data sheets for determination of internal forces, stresses and deformations based on the ECCS recommendations were presented. These sheets can be used for both, design procedures and evaluation of test results. Furthermore they can be used to validate results ob-tained from other design programs such as SandStat [11]. The series of EXCEL data sheets will be continued. It is planned to present sheets for evaluation of short beam shear test and determination of 5% fractal val-ues from test results before long. 7. Literary reference [1] ECCS/CIB:

European Recommendations for Sandwich Pan-els, Part I: Design ECCS TWG 7.9 (Sandwich panels and related structures)/CIB-Report W056 (Lightweight con-structions) - Publication 257, 2000

[2] Stamm, K., Witte, H.: Sandwichkonstruktionen – Berechnung, Ferti-gung, Ausführung Springer Verlag, Wien – New York, 1974

[3] Jungbluth, O., Berner, K.: Verbund- und Sandwichtragwerke Springer Verlag, Berlin/Heidelberg/New York/ Tokyo, 1986

[4] prEN 14509: Selbsttragende Sandwich-Dämmelemente mit beidseitiger Metalldeckschicht Entwurf vom März 2002

[5] Davies, J. M. (Editor): Lightweight sandwich constructions Blackwell Science Ltd., 2001

[6] DIBt: Allgemein bauaufsichtliche Zulassungen für Sandwichbauteile Nr. Z-10.4-XXX

qU = 2,17 kN/m

l2 = 4,00 m l1 = 4,00 m

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[7] Berner, K.: Erarbeitung vollständiger Bemessungsunterlagen im Rahmen bautechnischer Zulassungen für Sandwichbauteile Research for DIBt, Berlin 1995

[8] Stamm, K.: Sandwichelemente mit metallischen Deckschich-ten als Dachbautafeln im Bauwesen Ernst & Sohn Verlag, Berlin, Der Stahlbau, Heft 8 (1984) S. 231-236

[9] Berner, K.: Praxisgerechte Nachweise zur Trag- und Ge-brauchsfähigkeit von Sandwichbauteilen Ernst & Sohn Verlag, Berlin, Der Stahlbau, Heft 12 (1998) S. 910-925

[10] Koschade, R. (Statik: Berner, K.): Die Sandwichbauweise Ernst & Sohn Verlag, Berlin, 2000

[11] Manual of program SandStat 3 Berner & Gruber GmbH, since 1997

8. Author Raabe, Oliver, Dipl.-Ing. (FH): employed with Ingen-ieurbüro Berner & Gruber GmbH, Elisabethen-straße 62, 64283 Darmstadt, Germany and freelancer at iS-mainz

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Annex 1

Example 1: Single span wall panel with lightly profiled faces

Annex 1 Page 1/2

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Annex 2

Example 2: Two-span panel with profiled faces

Annex 2 Page 1/3

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Annex 2 Page 2/3

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Annex 2 Page 3/3

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Annex 3

Example 3: Two-span panel with lightly profiled faces Determination of the wrinkling stress at intermediate support on the lower face

Annex 3 Page 1/2

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Annex 3 Page 2/2