F V interaction of girders with trapezoidally corrugated webs

Transcription

1 F V interaction of girders with trapezoidally corrugated webs Balázs Kövesdi PhD Student Supervisors: Prof. Dr.-Ing. László Dunai Prof. Dr.-Ing. Ulrike Kuhlmann

2 Introduction Previous research activities Investigation of the patch loading resistance Development of FE based design method Development of analytical design method Problem statement and research aims (F-V interaction) Literature overview Numerical modelling and structural behaviour Development of an F-V interaction curve Summary of the research work and possible further subjects

3 Literature overview Previous research activities Experimental program Numerical model development Numerical parametric study (determination of the geometric parameters which have influence on the patch loading resistance) FE based design method (Uni Budapest) -Proposals for possible imperfection shapes and applicable magnitudes. Analytical design method (Uni Stuttgart) = ρ ss t w w + f yw f = k α M plf ρ t w f yw

4 esearch aim 1. Design method of Kähönen d = ) k ( d1 + d 2 + d 3 d1 d 2 = k σ w f yw t w wep o a yw kr γ = 2 t k σ k σ M f yf t wep b f - Developed for building structures. - Does not follow the steps of the EC3 stability analysis (design methods with reduction factors). d 3 = 0.07 σ f b f t f - Possible interactions are considered in the design method. k o ; k w ; k r ; d3 2. Enhanced design method Based on design method of Kähönen+ numerical calculations + own experiments λ p = f σ yw cr 2 2 k 2 12 (1 ) σ π tw E υ ai = w + f = ρ ss t w f yw k α σ cr = M plf ρ t w f Pure patch loading resistance without interactions. yw esearch aim: Development of interaction equations. (F+V ; F+M)

5 Problem statement In the practice during launching of a bridge structure large shear (V) and transverse force (F) can be introduced at the same cross section. Mainly the web plate is loaded by both actions. Interaction should be considered in the design. 1. There are no recommendations in the EN for the F-V interaction (neither for flat web nor for corrugated web girders). 2. In the literature only a limited numer of investigations are available dealing with this topic, especially for corrugated web girders. Aim: New (F+V) interaction curve for trapezoidally corrugated webs.

6 esearch strategy - Literature overview and experimental background - Numerical model development - Analysis of the structural behaviour - Numerical parametric study - Developement of the F-V interaction curve

7 Literature overview 1. Analysis of the combined loading subdivided into two basic load cases Basis of the separation is that the shear stresses due to pure transverse force are already included in the patch loading resistance model and a reduction of the load carrying capacity is caused only by the additional shear stresses coming from pure shear force. 2. Analysis of Elgaaly and Seshadri Based on experiments 20 numerical calculations (V-0,5F) / VNum.. 1,1 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 V 0.5 F V 1.25 F + F Elgaaly & Seshadri numerical results 0,2 Elgaaly & Seshadri (for corrugated web girders) 0,1 F/F Num ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

8 Numerical modelling Test specimen Numerical model Numerical simulation Investigation of combined F+V Modell verification stiffener Numerical parametric study by different geometries and loading conditions.

9 Numerical modelling Modelling of the half girder 1. educed model. 2. By defining the parameter x, many shear force distributions can be analysed. Analysed parameter range: h w /t w : a 1 /t w : a: ss/h w : V 1 /V 2 : between -1 ; 1

10 Structural behaviour V 1 /V 2 =-1 V 1 /V 2 =0 V 1 /V 2 =0.5 V 1 /V 2 =1 Lateral displacements along a parallel fold: local buckling 875 hw [mm]. V1/V2=-1 V1/V2= interaction V1/V2=0.5 V1/V2=0.86 V1/V2= shear buckling (tension band) 125 e [mm] 0-0,8-0,6-0,4-0,2 0 0,2 0,4 0,6 0,8 1 1,2 1,4

11 1,1 1 Analysis of the interaction Evaluation of the numerical calculations (using the separation methodology) 0,9 0,8 (V-0,5F) / V,num. 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 numerical calculations numerical results of Elgaaly et al Elgaaly et al current proposal (lower limit) F/F,num 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1. Proposed interaction equation: V 0.5 F V F F

12 Analysis of the interaction Evaluation of the numerical calculations (without the separation methodology) 1,4 large scatter 1,2 1 V2 / V,num.. 0,8 0,6 0,4 0,2 numerical calculations current proposal 0 F/F,num. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 Proposed interaction equation: V V max F F 4 1.0

13 Analysis of the geometric parameters Effect of the web ratio: h w /t w 1,1 1 0,9 0,8 (V-0,5F)/V,num.. 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 hw/tw=200 hw/tw=150 hw/tw=125 hw/tw=100 Kuhlmann & Braun Elgaaly & Seshadri F/F,num. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 large h w /t w small h w /t w

14 Analysis of the geometric parameters Effect of the corrugation angle: 1,1 1 0,9 0,8 (V-0,5F)/V,num.. 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 alpha=60 alpha=40 alpha=30 alpha=20 Kuhlmann & Braun Elgaaly & Seshadri F/F,num. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 Influence is quite small. larger corrugation angle stronger interaction criterion

15 Analysis of the geometric parameters Effect of the fold ratio: a 1 /t w 1,1 1 0,9 0,8 (V-0,5F)/V,num.. 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 a1/tw=35 a1/tw=30 a1/tw=25 a1/tw=20 a1/tw=15 Kuhlmann & Braun Elgaaly & Seshadri F/F,num. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 Influence is negligible.

16 Analysis of the geometric parameters Effect of the loading length: ss/h w 1,1 1 0,9 0,8 (V-0,5F)/V,num.. 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 ss/hw=0,2 ss/hw=0,5 ss/hw=0,8 Kuhlmann & Braun Elgaaly & Seshadri F/F,num. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 larger loading length stronger interaction criterion

17 Interaction of shear and transverse forces Shear resistance Patch loading resistance Mainly depending on the web plate. - esistance of the web - esistance of the flange Flange contribution can be dominant If the flange is dominant web carries only a smaller part of the applied load Conclusion: Interaction criterion can be expressed by the ratio of flange and web contributions in the patch loading resistance. Shear resistance can be larger. Interaction criteria can be weaker.

18 Interaction of shear and transverse forces 1,1 1 0,9 (V-0,5F) / V,Ansys. 0,8 0,7 0,6 0,5 0,4 0,3 F,w / F,fl=1,00 F,w / F,fl=2,0 F,w / F,fl=2,6 F,w / F,fl=3,2 F,w / F,fl=3,75 Kövesdi et al (a=1.6) Proposed interaction equation: V 0.5 F V a + F F a 1.0 0,2 Kövesdi et al (a=1.4) Kövesdi et al (a=1.3) 0,1 0 Kövesdi et al (a=1.25) Kövesdi et al (a=1.2) F/F,Ansys 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 2,0 Determination of the index: F 0.25, w F, fl a = e but a > 1. 2 index of the interaction equation 1,9 1,8 1,7 1,6 1,5 numerical calculations 1,4 developed approximation 1,3 1,2 1,1 F,w / F,fl 1,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

19 Summary 1. Literature overview 2. Numerical model development 3. Analysis of the structural behaviour 4. Numerical parametric study 5. Parameters which have influence on the structural behaviour 6. Development of interaction curve Further research subject Interaction of bending and patch loading (F+M).

20 Thank you for your attention!