1. ADVANCES ON SHEAR STRENGTH AND BEHAVIOR OF BRIDGE GIRDERS WITH STEEL CORRUGATED WEBS Dr. MOSTAFA FAHMI HASSANEIN Associate Professor Department of Structural Engineering; Faculty of Engineering; Tanta University, Tanta; Egypt HONDANI BRIDGE Tuesday – 17 Nov., 2015

2. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

3. Introduction 1. Advantages of corrugated web plates  They have much higher buckling strengths.  The own significant out-of-plane stiffness.  They act as continuous stiffeners, so no need to use stiffeners.  Their thickness is significantly reduced. Hamada et al. (1984) Chan et al. (2002) 9-13% 10.6%

4. Introduction 1. Advantages of corrugated web plates  They have much higher buckling strengths.  The own significant out-of-plane stiffness.  They act as continuous stiffeners, so no need to use stiffeners.  Their thickness is significantly reduced. Maupré BridgeHondani Bridge  Structural efficiency  Aesthetical appearance

5. Introduction 2. Interaction between shear and flexural behaviors  Corrugated webs do not carry significant longitudinal stresses from the primary flexure of the girders and, consequently, the bending moment can reasonably be assumed to be carried totally by the flanges. Hamilton (1993) and Driver et al (2006)  This is called the “accordion effect” and it is characterized by negligible axial stiffness.  Therefore, the shear is carried entirely by the webs.

6. Introduction 3. Elastic shear buckling Local bucklingGlobal buckling Interactive buckling Orthotropic-plate buckling theoryClassical plate buckling theory Lindner and Aschinger (1988)

7. Introduction 4. Interactive shear buckling stresses Several researches were conducted to find the best exponent

8. Introduction 5. Types of tapered web panels I 1 2345 6 III II Direction of Tension Field Compression on tapered flange Tension on tapered flange B.M.D. S.F.D.

9. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

10. Objectives 1. Research objectives is to provide additional data to engineers and the scientific community about the shear strength and behavior of:  Prismatic bridge girders with corrugated webs.  Tapered bridge girders with corrugated webs. In detail, to  find the real behavior at the juncture between the corrugated web and the flanges of Prismatic girders. Never been studied  provide new critical stress formula.  suggest a more suitable strength than those available in literature.

11. Objectives 1. Research objectives: Continue is to provide additional data to engineers and the scientific community about the shear strength and behavior of:  Prismatic bridge girders with corrugated webs.  Tapered bridge girders with corrugated webs. In detail, to  Investigate the effect of different junctures between the corrugated web and the flanges of Tapered girders.  provide new critical stress formulas for different tapered typologies.  get the appropriate design strengths of Tapered girders.

12. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

13. Validation of FEM 1. Flat web plates Simple juncture Fixed juncture

14. Validation of FEM 2. Prismatic girders with corrugated webs τ FE / τ y Deflection (mm) G7A: Driver et al. (2006) Deflection (mm) Τ [Mpa] M12: Moon et al. (2009)

15. Validation of FEM 3. Tapered girders with flat webs Deflection (mm) Τ [Mpa] Bedynek et al. (2013)

16. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

17. Prismatic Prismatic Parametric study Tapered Tapered Plates Panels Girders Bridge name b [mm] d [mm] c [mm] h r [mm] t w [mm] h w [mm] α [º] Shinkai2502002501509118336.9 Matsnoki30026030015010221030.0 Hondani3302703362009331536.5 Cognac3533193531508177125.2 Maupre2842412841508265031.9 Dole43037043022010254630.7 IIsun330 38620018229231.2 Average32528433417410228132 bdbd c hrhr α twtw

18. Prismatic Parametric study Tapered Tapered Plates Girders bdbd c hrhr α twtw Bridge name b [mm] d [mm] c [mm] h r [mm] t w [mm] h w [mm] α [º] Shinkai2502002501509118336.9 Matsnoki30026030015010221030.0 Hondani3302703362009331536.5 Cognac3533193531508177125.2 Maupre2842412841508265031.9 Dole43037043022010254630.7 IIsun330 38620018229231.2 Average32528433417410228132

19. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

20. Results and discussion 1. Effect of simple and fixed boundary conditions No. [mm] Buckling mode [N/mm 2 ] [10]/[11] SFSF [1][2][3][8][9][10][11][12] 110006LL3663770.97 210008II6126360.96 3100010II8899320.95 4100012II118412550.94 5100014II148915790.94 6100016II178219040.94 7100018II208522350.93 1514006II3513540.99 1614008II5785900.98 17140010II8188530.96 18140012GI107011190.96 19140014GI132913910.96 20140016GI159416730.95 21140018GI186419620.95 Ave0.96 COV0.014 Prismatic - Plates

21. Results and discussion 2. Comparison with the available interactive critical stress (n=1.0) No. [mm] [mm] SimpleFixed k G =36k G =31.6k G =68.4k G =59.2k G =68.4k G =59.2 [1][2][3][4][5][6][7][8][9] 1100061.121.130.680.690.830.85 2100081.081.090.660.670.850.87 31000101.041.050.640.650.850.87 41000120.991.010.610.630.840.87 51000140.950.970.590.600.820.86 61000160.900.920.560.570.800.84 71000180.860.890.540.550.780.82 15140061.131.140.670.680.880.90 16140081.101.120.660.670.900.94 171400101.051.080.640.650.910.95 181400121.011.040.610.630.900.94 191400140.981.020.590.610.890.93 201400160.951.000.570.600.880.93 211400180.940.980.560.590.870.92 Ave1.121.170.670.700.991.05 COV0.1300.1490.0660.0760.1310.150 Prismatic - Plates

22. Results and discussion 3. Limit of fixed juncture Prismatic - Panels t w [mm] t f /t w Relative critical stresses RF/SRF/FRF/SRF/FRF/SRF/FRF/SRF/FRF/SRF/F h w =1.6mh w =1.8mh w =2.0mh w =2.2mh w =2.4m 631.000.991.010.991.010.991.000.991.010.99 641.000.991.021.01 0.991.000.991.010.99 651.000.991.021.01 0.991.031.01 1.00 831.021.001.030.991.051.001.041.001.041.01 841.021.001.041.001.051.011.051.011.051.02 851.031.011.051.011.051.011.051.011.061.02 1031.041.001.041.001.041.001.041.001.041.01 1041.051.001.051.011.061.011.061.021.061.02 1051.061.011.071.021.071.021.071.031.071.04 Ave1.041.001.051.011.041.011.041.011.041.01 COV0.0240.0120.0180.0110.0200.0140.0180.0120.0190.013  when the flanges are rigid enough (tf / tw ≥ 3.0), shear failure mechanisms occurs.  if they are relatively rigid (tf / tw < 3.0), the strength becomes controlled by the deformation of flanges.  The realistic support condition at the juncture is nearly fixed for the case of (t f / t w ≥ 3.0). flange web

23. Embedded connections Hondani Bridge Results and discussion 4. Recommended validity limit of the proposed formula Prismatic - Panels  For cases of girders with steel flanges having ( t f / t w ≥ 3.0).  In composite girders with Embedded shear connections. Ikeda and Sakurada (2005) Kurobegawa Bridge

24. Results and discussion 5. Comparison with available shear strengths Prismatic - Girders Moon et al. Sause and Braxtan Driver et al. Design manual for PC bridges with corrugated steel webs

25. Results and discussion 5. Comparison with available shear strengths Prismatic - Girders Girder ( - ) Failure modes 1600-6I0.850.860.710.630.911.800.770.91 1600-8I0.921.000.710.631.002.860.790.85 1600-10I0.791.000.710.631.004.020.791.00 1600-12G0.851.000.710.631.005.270.790.93 1800-6I0.900.860.710.630.901.700.770.86 1800-8I0.910.970.710.630.992.660.790.87 1800-10I0.801.000.710.631.003.710.790.99 1800-12G1.011.000.710.631.004.810.790.78 Ave0.850.950.710.630.973.000.780.93 COV0.0770.0660.000 0.0511.1500.0120.090 Elgaaly et al. (1996)

26. Results and discussion 5. Comparison with available shear strengths Prismatic - Girders

27. Results and discussion 1. Effect tapered web typology on interactive critical stress Tapered - Plates Case ICase IICase IIICase IVCase ICase IICase IIICase IV Case ICase IICase IIICase IV

28. Results and discussion 2. Proposed interactive critical stress of tapered webs Tapered - Plates The recommendation of the current design code for plated structural elements EN 1993-1-5 (2007) to determine the ultimate shear resistance of tapered plate girders with flat web plates as prismatic ones CANNOT BE USED. Case ICase IICase III Case IV Applicable for different boundary conditions

29. Results and discussion 3. Nonlinear strengths – Parametric study results Tapered - Girders Type [mm] [kN] Buckling mode Case I 60.683944I 80.5331318G 100.4451693G 120.3862144G 140.3462619G Case II 60.6961097I 80.5441619G 100.4532010G 120.3942147G 140.3522295F Case III 60.602652I 80.470917I 100.3921146G 120.3411450G 140.3051686G Case IV 60.624634I 80.487894I 100.4061136G 120.3531397G 140.3161666G 0.96 1.00 1.03 1.09 1.14 1.12 1.23 1.09 1.00 0.66 0.70 0.74 0.73 0.64 0.68 0.69 0.71 0.73 This means that neither the type of the axial force in the inclined flange (tension or compression) nor the direction of the developed tension field (short or on the long web diagonal) has any effect on the strength of these girders (Cases III and IV)

30. Results and discussion 4. Failure modes and stress distributions Tapered - Girders Case I Case II Case III Case IV

31. Moon et al. Sause and Braxtan Design manual for PC bridges with corrugated steel webs Results and discussion 5. Comparison with available shear strengths Tapered - Girders

32. Results and discussion 5. Comparison with available shear strengths Tapered - Girders Type [mm] [kN] Buckling mode Case I 60.683944I 80.5331318G 100.4451693G 120.3862144G 140.3462619G Case II 60.6961097I 80.5441619G 100.4532010G 120.3942147G 140.3522295F Case III 60.602652I 80.470917I 100.3921146G 120.3411450G 140.3051686G Case IV 60.624634I 80.487894I 100.4061136G 120.3531397G 140.3161666G 0.96 0.980.81 1.00 0.79 1.03 0.970.77 1.09 0.920.72 1.14 0.880.69 1.12 0.890.71 1.23 0.810.64 1.23 0.810.64 1.09 0.920.72 1.00 0.79 0.66 1.501.20 0.70 1.431.13 0.70 1.431.13 0.74 1.351.07 0.73 1.371.08 0.64 1.481.22 0.68 1.471.16 0.69 1.451.14 0.71 1.411.11 0.731.371.08 0.97 0.91 0.86 0.88 0.97 0.94 0.93 0.90 0.88

33. Results and discussion 6. Recommended design shear strengths Tapered - Girders Case ICase II Case IIICase IV

34. Contents Validation of finite element models Results and discussion Recommendations Objectives Introduction Parametric study

35. Recommendations  New experimental results on girders with corrugated webs with real bridge dimensions should be conducted.  New work should be made on checking the available buckling and design equations on all available bridge corrugated web profiles. An MSc is under preparation now by Elkawase, A.A. at Tanta University.  The real behaviour of continuous tapered girders with corrugated webs, containing different web typologies, should be carried out by means of experimental tests. A thesis is under preparation now by Hassanein and El Hadidy at Tanta University.  Concentration on the behaviour of tapered girders’ behaviour should be made. A paper is under review now by Zevallos et al. (Zevallos, E., Hassanein, M.F., Real, E. Mirambell, E.) as a collaboration between Tanta University and Universitat Politècnica de Catalunya, UPC of Spain.

36. Recommendations  Composite girders with corrugated webs in negative bending moment zones should be checked by using fibre reinforced polymers. An MSc is under preparation know by Elshinrawy, T. at Tanta University.

37. For more information:  Hassanein, M.F., Kharoob O.F., (2015), "Linearly Tapered Bridge Girder Panels with Steel Corrugated Webs near Intermediate Supports of Continuous Bridges", Thin-Walled Structures, Vol. 88, pp. 119-128.  Hassanein, M.F., Kharoob O.F., (2014), “Shear buckling Behavior of Tapered Bridge Girders with Steel Corrugated Webs”, Engineering Structures, Vol. 74, pp. 157-169, 2014.  Hassanein, M.F., Kharoob O.F., (2013), “Behavior of Bridge Girders with Corrugated Webs: (II) Shear Strength and Design”, Engineering Structures, Vol. 57, pp. 544-553.  Hassanein, M.F., Kharoob O.F., (2013), “Behavior of Bridge Girders with Corrugated Webs: (I) Real Boundary Conditions at the Juncture of the Web and Flanges”, Engineering Structures, Vol. 57, pp. 554-564.

38. Thank you for listening Contact details: Dr. MOSTAFA FAHMI HASSANEIN Department of Structural Engineering; Faculty of Engineering; Tanta University, Tanta; Egypt E-mail: mostafa.fahmi@yahoo.commostafa.fahmi@yahoo.com mostafa.fahmi@f-eng.tanta.edu.eg Mobile Tel: +201228898494 Fax: +20403315860