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MECHANICS OF DIAGONAL TENSION FIELD ACTION

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, 200 9. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION.

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MECHANICS OF DIAGONAL TENSION FIELD ACTION

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  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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION • 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 • A pdf file of the paper can be downloaded from • http://www.asce.org/

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

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

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

  6. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

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

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

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

  10. C Elastic buckling curve AASHTO LRFD (2007) 1.0 T1 T2 Yield zone Elastic buckling zone Transition zone 0 1.12 1.40 Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Shear Strength Curve

  11. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION • There were no reliable analytical tools available to examine nonlinear behavior in the 1960s and 1970s. • Postbuckling is a very complex nonlinear response. • 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. Plastic Hinge Plastic Hinge (a) Basler (1963) (b) Fujii (1968, 1971) (d) Steinhardt and Schroter (1971) (c) Porter et al. (1975) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Incorrect Tension Field Models

  13. B A b/2 V V C C b/2 φ do A B Fs tσt φ C C O V/2 Fw Fw V/2 Ff +ΔFf Ff Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Free body diagram (Basler 1963)

  14. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION • Both Basler and Rockey theories were calibrated with extensive test data. “Calibration=Finagling?” • 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. Out-of-plane displacement at center of web panel (mm) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Ultimate Strength vs. Flange Size

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

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

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

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

  20. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION 1 Fyw 2 Fyw Normal Stresses in Horizontal Strip Horizontal direction Vertical direction

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

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

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

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

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

  26. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION • 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.

  27. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION

  28. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION 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. • 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. • There is no truss action that takes place as suggested by Basler (American model).

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

  30. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Conclusions (continued) • There is no need to have sturdy flanges present in order to develop tension field action as suggested by Rockey (British model ). • 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. Samford Hall, Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION Questions?

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