Duerr, M.

Saal, H.

English

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold-Formed Steel Structures (2004) - 17th International Specialty Conference on Cold-Formed Steel Structures Oct 26th, 12:00 AM Influence of Profile Distortion on the Shear Flexibility of Profiled Steel Sheeting Diaphragms M. Duerr H. Saal Follow this and additional works at: https://scholarsmine.mst.edu/isccss  Part of the Structural Engineering Commons Recommended Citation Duerr, M. and Saal, H., "Influence of Profile Distortion on the Shear Flexibility of Profiled Steel Sheeting Diaphragms" (2006). International Specialty Conference on Cold-Formed Steel Structures. 5. https://scholarsmine.mst.edu/isccss/17iccfss/17iccfss-session8/5 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in International Specialty Conference on Cold-Formed Steel Structures by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. Seventeenth International Specialty Conference on Cold-Formed Steel Structures Orlando, Florida, U.S.A, November 4-5,2004 Influence of profile distortion on the shear flexibility of pro-filed steel sheeting diaphragms Duerr, M.I and Saal, H.2 Abstract The shear flexibility of diaphragms consisting of profiled steel sheeting can be calculated by means of the ECCS-Recommendations TC7 TWG 7.5. The main component of the shear flexibility accounts for sheet deformation, which consists of profile distortion Cl,l and shear strain cJ,2. The dominant part cl,l is propor-tional to Ki. The factor Ki=KJ applies with fasteners in every trough and Ki=K2 applies with fasteners in alternate troughs. Both KJ and K2 depend on the ratios lid and hid of the cross section dimensions d=pitch of the corrugations, h=height of the sheeting profile and l=width of the top flange. For vertical webs KJ is larger than K2. This means that larger profile distortion is predicted with fastening in every trough than with fastening in alternate troughs. This is in contradiction to reality. Finite-Element calculations show that the Krvalues given in ECCS-Recommendations TC7 TWG 7.5 are wrong. The correct values for K2 are given as result of this investigation. 1. Introduction In the past decades new perceptions and improvements as well as continuative optimization led to a huge boom and a rapid world-wide extension of light-weight constructions. The constant quest for optimization resulted in the possi-bility to stabilize steel-framed building constructions especially for typical in-dustrial buildings by means of the shear capacity of elements like trapezoidal sheets. U ser-friendly rules for dimensioning und calculation of shear diaphragms consisting of trapezoidal sheets furthered this development. One of the most I Scientific Assistant, Versuchsanstalt fur Stahl, Holz und Steine, Universitat Karlsruhe (TH), D-76128 Karlsruhe, Germany 2 Full Professor, idem. 617 618 popular publications are the European Recommendations for the Application of Metal Sheeting acting as a Diaphragm [4], which is among other things based on investigations of Bryan and Davies [2] [3]. 2. Basic pr~nciples of calculating the shear flexibility of diaphragms Formulae to calculate the total shear flexibility v of a diaphragm under shear load V are given in [4]. The total shear flexibility v of a shear panel is the sum of components due to different influences. Figure 1: shear load V and shear flexibility v The dominant part of this shear flexibility - in addition to slip in the fastenings of the diaphragm - is the sheet deformation c). c) consists of profile distortion c),) and shear strain C),2. Both parts are shown in figure 2. -t-- Q---t -rD--~----- Lt ----- _v_J t C1.2 tv=l Figure 2: illustration of profile distortion c),) and shear strain C),2 619 Cl,l and Cl,2 are obtained from equations (1) and (2). a·d 2.5 .K. c = I 1,1 E.(2.5 .b2 c = _2a_'--,C_1 +_V...:.)_· [::....1_+...:..C2_h_l_d)'-".l 1,2 E 'f.b with and E V modulus of elasticity Poisson's Ratio (1) (2) The profile distortion Cl,l is proportional to Ki. The factor Ki is given in table form in [4]. Kl applies for fastening in every trough and K2 applies for fasteners in alternate troughs. Both K\ and K2 depend on the ratios lid and hid of the cross section dimensions d=pitch of the corrugations, h=height of the sheeting profile and l=width of the top flange (see figure 3). I --h d Figure 3: defmition of the cross section dimensions 3. Inconsistencies with K2 In case of vertical webs (9=0) the tables in [4] give larger values for Kl than for K2. This means that larger profile distortion is predicted with fastening in every trough than with fastening in alternate troughs. The following diagrams demonstrate this inconsistency of the Kz-values taken from [4]. 620 5,----------------------------------------; : K. (hld=O.3) 4,5 -t-------------------j---.------i 4r------------------------4--~: /~i 3,5 +--------------------/----1-1 ...... 6=5 H 6=10 i 3 6=ffi~ 10 ...... 6=20 ; 2,5 +-----------£-,6,/' -6=25---j 2 ~ ~;~ 1,5 ~ .... __ ./ ~ ../ 0,50 !==:::;~;=~====~:=~::::===3 I/di o 0,2 0,4 0,6 0,8 Diagram 1: vari~tion ofK2 with lid and 9 for h/d=O.3 :: '~~: ... ~~~:;;'''''-'''-'---------''----'''-''''--''''---''''-''''''---''-''-'''-'''-'--''''''------'-''''-'-'''''''1 14~--------~~~~-----------~ 12+------~-~~~-------~ 10+-----~~~~~~~------~ _6=0 ....... 6=20 8 +---""""""7~--r:----,,;:.-~~--,-. ~"=:--------1--6=25 -+-6=30 6 -6~ >~ 4 ~-----=::.c=~=--------~~""""~-=------i 2+----------------------~ ot-__ ~·~==~·==~::==~·===:·====~==:·====·~==:·--~I'~d o 0,2 0,4 0,6 0,8 Diagram 2: variation ofK2IKt with lid and 9 for h/d=O.3 Both diagrams show that the values for 9=0 do not match with the other results. Diagram 2 even shows that the ratios for 9=0 are less than 1 for small values of lid. This means that profile distortion for fastening in every trough is larger than for fasteners in alternate troughs. 4. Numerical Analysis 621 Numerical analyses were performed with the Finite-Element program ANSYS 7.1 to find the correct solution to this problem. Shear diaphragms were modeled with alb-ratios varying from 0.5 to 2.0. The model, which is related to the assumptions in [1] to [4] is depicted in figures 4a and 4b. nAA ~Sl! .t.1'r. 4 ~Uj "'·,)~lJ!> Figure 4a: FE-model with single load and "",m"''',"" conditions Figure 4b: detail of FE-model Different types of geometry with 0.1.:::Jld::;0.9, 0.1::;hld::;0.8 and 8=0 were investigated in a parametric study. This investigation was restricted to 8=0 because it was expected from diagrams 1 and 2 that the error was only with the values for this slope. Figure 5 shows the example of a deformed finite element model with lId=OA and hld=OA together with the applied loading at the edge rib. 622 Figure 5: deformation of a loaded shear diaphragm with a/b=0.75 For the evaluation of the numerical analysis the displacement CPEM of the dia-phragm was determined. Subtracting the displacement due to the shear strain according to [4] gives the displacement due to profile distortion with the factor K j included. Thus the fac-tor K j is obtained from the results CFEM of the Finite Element analysis with K. = . c oE ot ob-2a o(1+v)o[1+-] b·t1.5 { 2h } I aod2.5 FEM d (3) The factors Kz resulting from the numerical analysis are shown in table 1. ,< " 1I~ " 'P hid . Q,1 Jt.70 00,3 O,A 0,5 . 0,6 0,7 0,8 1~ . Q,9_ 0,1 0,1 0,13 0,18 0,23 0,25 0,27 0,32 0,40 0,61 0,2 0,25 0,42 0,53 0,66 0,74 0,83 1,04 1,29 2,05 ~ 0,3 0,46 0,80 1,12 1,23 1,39 1,56 1,75 2,25 2,86 0,4 0,74 1,19 1,77 2,15 2,39 2,63 2,94 3,76 5,31 0,5 1,44 2,16 2,58 2,93 3,48 3,70 4,09 5,06 8,38 0,6 2,75 3,54 4,51 4,99 5,98 6,35 6,60 7,93 11,63 0,7 4,49 5,33 6,54 7,35 8,07 8,56 9,36 11,06 15,36 t o,8 6,44 7,28 9,06 10,40 10,35 11 ,33 12,61 14,46 20,44 Table 1: factors K2 623 5. Comparison and review of the calculated results To classify the results, which resulted from the numerical ~nalysis, it is neces-sary to compare them to results from other sources existing on this subject mat-ter. K-factors for calculating the shear flexibility of diaphragms are also given by Baehre in [1]. These factors were verified with test results of shear diaphragms. The following diagram shows the Kz-factors of [1] and [4] in comparison to the results of table 1. Diagram 3: comparison of different K2- factors for 8=0 and hid of 0.3 3,00 -,-----------------------------------, Kz (h/d;;O.3) 2,50 t-------------------r'--------i 2,00 -f----------------r--j 1,50 t-----------------::::--:::=;;:.~-----------i 1,00 -f-------:7":;...--=-------------,''----------' 0,50 -f---.P"=-------------------,,,,..-=---------i lid .. ---_ .. --_._ .... ------_ .. _ ..... --0,00 +-----~='---_._---_._---__,_---~-------i a 0,2 0,4 0,6 0,8 It is obvious that the factors from our numerical analysis agree with the values of [1]. If the BCeS-values for 8=0, which are definitely shown to be incorrect, are substituted by our results or those from [1], it will be found that these values match much better with the Krfactors for sloping webs. Diagram 4 shows this. Diagram 4: Kz-values for hid-ratio of 0.3 with changed values for 8=0 4,5 K2(hfd::O.3) 4 ! 3,5 3 2,5 2 1,5 1 ~ 0,5 -~ ° ° 0,2 0,4 0,6 0,8 624 6. Conclusions • The present paper shows the inconsistency of the K2- values of [4] for calculating the profile distortion of shear loaded diaphragms consisting of trapezoidal sheet-ing. By means of Finite-Element calculations more realistic values for alternate fastening in combination with vertical webs were found and given in table 1 of chapter 4 for 0=0. The results of the study were verified by comparison to [1]. The values of[ 1] to [4] for 0>0 are confirmed by this analysis. The authors recommend to substitute the K2-factors, which are printed in ECCS-Recommendations TC7 TWG 7.5 for alternate fastenings and vertical webs, by table 1 of this present paper. 7. References [1] Baehre, R., Kaltgeformte, leichte Stahlprofile als Tragwerkskomponenten in bautechnischer Anwendung, Forschungsbericht zum Forschungsauftrag Nr. 111 der Studiengesellschaft von Eisen und Stahl e.V., 1985 [2] Bryan, E.R., The Stressed Skin Design of Steel Buildings, London, 1973 [3] Davies, J .M. and Bryan, E.R., Manual of stressed skin diaphragm design, Granada Publishing, 1982 [4] ECCS Recommendations for the Application of Metal Sheeting acting as a Diaphragm, European Convention for Constructional Steelwork TC7 TWG 7.5, Brussel, 1995, First Edition 

Influence of Profile Distortion on the Shear Flexibility of Profiled Steel Sheeting Diaphragms

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Influence of Profile Distortion on the Shear Flexibility of Profiled Steel Sheeting Diaphragms

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