1. MECHANICS OF DIAGONAL TENSION FIELD ACTION Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE Professor Emeritus Department of Civil Engineering Auburn University CIVL 7690 July 14, 2009

2. Yoo, C.H., and Lee, S.C., “Mechanics of Web Panel Postbuckling Behavior in Shear,” Journal of Structural Engineering, ASCE, Vol. 132, No. 10, October, 2006 Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION A pdf file of the paper can be downloaded from http://www.asce.org/

3. Functions of Webs in Plate Girders? 1. Maintain the relative distance between two flanges. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION 2. Carry the induced shear.

4. Bending Moment & Shear Bending Moment Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Shear

5. AASHTO LRFD (2007) Article 6.10.2 Cross-Section Proportion Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

7. Minimum Steel Thickness? 5/16 (0.3125) in. for all main members per AASHTO LRFD Article 6.7.3 Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION - corrosive environment - weldability

8. Background It is desired to use as thin a web panel as you can get by  elastic buckling becomes a major concern Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION In 1886, Wilson considered the possibility of utilizing postbuckling strength In 1931, Wagner demonstrated the tension field action

9. A postbuckling mode shape of a super thin high strength wire is shown. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Although a considerable postbuckling strength is available at this stage of deformation, it is highly impractical to use in practical design.

10. Shear Strength Curve 1.121.40 1.0 0 C Yield zone Transition zone Elastic buckling zone T1T2 Elastic buckling curve AASHTO LRFD (2007) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

11. Postbuckling is a very complex nonlinear response. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION There were no reliable analytical tools available to examine nonlinear behavior in the 1960s and 1970s. More than a dozen simplified and linearized models and their derivatives for the postbuckling behavior of web panels subjected to shear were a futile exercise. The analysis of web panels has remained elusive for nearly 50 years and various researchers have agreed to disagree.

12. Incorrect Tension Field Models (a) Basler (1963) (c) Porter et al. (1975) Plastic Hinge (b) Fujii (1968, 1971) Plastic Hinge (d) Steinhardt and Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

13. Free body diagram (Basler 1963) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

14. Both Basler and Rockey theories were calibrated with extensive test data. “Calibration=Finagling?” Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION The aspect ratio of those specimens were mostly equal to one. The steel industry wants to increase the aspect ratio for economic reasons. As the test data cannot be extrapolated, old design provisions stuck.

15. Ultimate Strength vs. Flange Size Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Out-of-plane displacement at center of web panel (mm )

16. Stress Development at Prebuckling Stage (a) Shear stress (b) Diagonal tension       (c) Diagonal compression  Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

17. Incomplete Stress State after Buckling (a) Diagonal tension  -  cr tt (b) No diagonal compression 22 11 11 22 Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

18. Out-of-plane Displacement Vertical and horizontal strips Displacement (mm) at the center of the panel Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

19. Normal Stresses in Vertical Strip Horizontal directionVertical direction Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION  1 /F yw  2 /F yw

20. Normal Stresses in Horizontal Strip  1 F yw  2 F yw Horizontal directionVertical direction Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

21. Principal Stresses under Pure Shear Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Buckling stageUltimate stage   Tension  Compression

22. Diagonal Stress Diagram at Ultimate Stage Diagonal tension Diagonal compression V u /2 VuVu Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

23. Lateral Deflection along Compression Diagonal Compression diagonal of web panel wtwwtw Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

24. Tension-Field in Plate Girder Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

25. Effect of Transverse Stiffener Transverse Stiffener Simple Support S. I=I s I=4I s I=6I s  2 F yw Web Width (Left Panel) Transverse Stiffener Left Edge Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

26. Since the moment of inertia of the transverse stiffener is proportional to the cube of the width of the stiffener, the width only needs to be increased to 1.8 times the old width [6^(1/3)=1.8]. The placement of transverse stiffeners helps shipping and handling of the slender girders by making the girder torsionally stiff. Wider transverse stiffeners are beneficial to this concern. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

28. Conclusions All previous tension field (postbuckling) models including those by Basler and Rockey were incorrect. All forces developed during postbuckling are in a self-equilibrating force system. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION There is no truss action that takes place as suggested by Basler (American model). There is no net axial compressive force developed in an intermediate transverse stiffener. Hence, the current area requirement for a transverse stiffener is irrelevant. There is no need to distinguish the end panel from the interior panel. Tension field action can take place in the end panel.

29. Incorrect Tension Field Models (a) Basler (1963) (c) Porter et al. (1975) Plastic Hinge (b) Fujii (1968, 1971) Plastic Hinge (d) Steinhardt and Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

30. Conclusions (continued) There is no need to have sturdy flanges present in order to develop tension field action as suggested by Rockey (British model ). Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Transverse stiffeners need to have sufficient stiffnesses (moment of inertia) in order to form and maintain nodal lines during the history of postbuckling. All design specifications regarding the tension field action, AISC, AASHTO, BS 5400, Eurocode 3, must be revised. All current steel design textbooks in the world incorporating erroneous theories must be revised.

31. Questions? Samford Hall, Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION