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Unformatted text preview: MECHANICS OF DIAGONAL TENSION FIELD ACTION TENSION Chai H. “Jay” Yoo, Ph.D., P.E., F. ASCE Professor Emeritus Department of Civil Engineering Auburn University CIVL 7690 July 14, 2009 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/ Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Functions of Webs in Plate Girders? Girders? 1. Maintain the relative distance between two flanges. 2. Carry the induced shear. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Bending Moment & Shear Bending Bending Moment =αwl Shear = βwl Auburn University 2 MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS AASHTO LRFD (2007) Article 6.10.2 AASHTO Cross-Section Proportion D / tw £ 300 with longitudinal stiffeners D / tw £ 150 without longitudinal stiffeners b f / ( 2t f ) £ 12 bf ³ D / 6 t f ³ 11tw . Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS 28" 28" 1 2" 2 1 2" 2 5 " 8 84" y = 42176" . 27" 3" M y = 18 ,717 k-ft Auburn University 27" 3" M y flg = 0.95 M y MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Minimum Steel Thickness? Minimum 5/16 (0.3125) in. for all main members per AASHTO LRFD Article 6.7.3 - corrosive environment - weldability Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Background 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 Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Shear Strength Curve Shear C Elastic buckling curve AASHTO LRFD (2007) 1.0 T1 T2 Yield zone 0 Auburn University Transition Elastic buckling zone zone 1.12 1.40 λ= D tw Ek Fyw MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Postbuckling is a very complex nonlinear response. 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Incorrect Tension Field Models Incorrect Plastic Hinge (a) Basler (1963) (b) Fujii (1968, 1971) Plastic Hinge (c) Porter et al. (1975) (d) Steinhardt and Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Free body diagram (Basler 1963) Free B A b/2 C V V b/2 C φ A do B Fs Fw Ff Auburn University Cφ V/2 tσt O C V/2 Fw Ff +ΔFf MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Ultimate Strength vs. Flange Size Ultimate Shear Force (kN) 900 600 Simply Supported Panel Light Flange Moderate Flange Heavy Flange 300 0 0 10 20 Out-of-plane displacement at center of web panel (mm) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Stress Development at Prebuckling Stage at τ τ τ σ σ τ (a) Shear stress Auburn University τ (b) Diagonal tension (c) Diagonal compression MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Incomplete Stress State after Buckling after σ2 σ2 τ -τ cr σ1 τ -τ cr σ1 σt (a) Diagonal tension Auburn University (b) No diagonal compression MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Out-of-plane Displacement Out-of-plane Shear Force (kN) 900 Phase3 Phase4 600 Phase2 Phase1 300 0 Vertical and horizontal strips Auburn University 0 5 10 15 20 Displacement (mm) at the center of the panel 25 MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Normal Stresses in Vertical Strip Normal Horizontal direction Vertical direction Phase1 -0.50 -0.25 Phase2 Wep Depth Wep Depth Phase1 Phase2 Phase3 Phase4 0.00 0.25 0.50 σ1 /Fyw Auburn University Phase3 Phase4 -0.50 -0.25 0.00 0.25 0.50 σ2 /Fyw MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Normal Stresses in Horizontal Strip Normal Horizontal direction Vertical direction 0.50 0.50 0.25 0.25 σ 1 0.00 σ 2 0.00 Fy w -0.25 Phase1 Phase2 Phase3 Phase4 Fy w -0.25 Phase1 Phase2 Phase3 Phase4 -0.50 -0.50 Web width Auburn University Web width MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Principal Stresses under Pure Shear Principal Buckling stage Ultimate stage ↔ Tension Compression Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Diagonal Stress Diagram at Ultimate Stage at Diagonal tension Vu/2 Diagonal compression Vu/2 Vu Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Lateral Deflection along Compression Diagonal along 2 Phase1 Phase2 1 Phase3 Phase4 w0 tw -1 -2 -3 Compression diagonal of web panel Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Tension-Field in Plate Girder Tension-Field Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Effect of Transverse Stiffener Effect 0.50 0.25 S. S. Simple Support Transverse Stiffener S. S. S. S. S. S. Transverse Stiffener Left Edge σ2 0.00 Fyw -0.25 1I=Is 4Is Is I=4 6 I=6Is -0.50 Web Width (Left Panel) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS 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 MECHANICS 28" 28" 1 2" 2 1 2" 2 5 " 8 84" y = 42176" . 27" 3" M y = 18 ,717 k-ft Auburn University 27" 3" M y flg = 0.95 M y MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Conclusions 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). Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Incorrect Tension Field Models Incorrect Plastic Hinge (a) Basler (1963) (b) Fujii (1968, 1971) Plastic Hinge (c) Porter et al. (1975) (d) Steinhardt and Schroter (1971) Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Conclusions (continued) Conclusions 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. Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS Questions? Questions? Samford Hall, Auburn University Auburn University MECHANICS OF DIAGONAL TENSION FIELD ACTION MECHANICS ...
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