Shear Failure Characteristics Of Steel Plate Girders - Edi-info.ir
ARTICLE IN PRESSThin-Walled Structures 47 (2009) 1498–1506Contents lists available at ScienceDirectThin-Walled Structuresjournal homepage: www.elsevier.com/locate/twsShear failure characteristics of steel plate girdersM.M. Alinia , Maryam Shakiba, H.R. HabashiDepartment of Civil Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15875-4413, Irana r t i c l e in f oa b s t r a c tArticle history:Received 28 November 2008Received in revised form30 April 2009Accepted 14 June 2009Available online 16 July 2009A number of full-scale plate girders are modeled and analyzed to determine their shear failuremechanism characteristics. An objective of this numerical nonlinear large deflection elastoplastic finiteelement study is to clarify how, when, and why plastic hinges that emerge in experimental tests actuallyform. It is observed that shear-induced plastic hinges only develop in the end panels. These hinges arecaused by the shear deformations near supports and not due to bending stresses arising from tensionfields. Also, a comparison between the ultimate capacity of various plate girders and different codes andtheories is presented. Finally, it is shown that simple shear panels, in the form of detached plates, do notaccurately represent the failure mechanism of web plates.& 2009 Elsevier Ltd. All rights reserved.Keywords:Steel plate girdersShear failure mechanismPlastic hingeUltimate capacity1. IntroductionPlate girders are designed to support heavy loads over longspans such as building floors, bridges and cranes; where standardrolled sections or compound girders are not answerable. Modernplate girders are, in general, fabricated by welding together twoflanges, a web and a series of transverse stiffeners. Flanges resistapplied moment, while web plates maintain the relative distancebetween flanges and resist shear. In most practical ranges, theinduced shearing force is relatively lower than the normal flangeforces. Therefore, to obtain a high strength to weight ratio, it iscommon to choose deep girders. This entails a deep web whoseweight is minimized by reducing its thickness. Various forms ofinstabilities, such as shear buckling of web plates, lateral-torsionalbuckling of girders, compression buckling of webs, flange-inducedbuckling of webs, and local buckling and crippling of webs areconsidered in design procedures.Due to the slenderness of web plates, they buckle at earlystages of loading. Therefore, one important design aspect of plategirders is the shear buckling and failure of web elements. Websare often reinforced with transverse and in some cases withlongitudinal stiffeners [1–3] to increase their buckling strength. Aproper web design involves finding a combination of optimumplate thickness and stiffener spacing that renders economy interms of material and fabrication cost. The design process of plategirder webs are commonly carried out within two categories: (i)allowable stress design based on elastic buckling as a limitingcondition; and (ii) strength design based on ultimate strength, Corresponding author. Tel.: 98 21 66418008; fax: 98 21 6454 3268.E-mail addresses: m.alinia@aut.ac.ir, alinia aut@yahoo.com (M.M. Alinia).0263-8231/ - see front matter & 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.tws.2009.06.002including postbuckling as a limit state. Till 1960s, the elasticbuckling concept was basically used in the design of plate girdersand the postbuckling strength was only indirectly accounted forby means of lowering safety factors.Wilson [4] first discovered the postbuckling behavior in 1886,and Wagner [5] developed the theory of uniform diagonal tensionfor aircraft structures with very thin panels and rigid flanges in1931. In late 1950s, Basler and Thurliman [6] took a differentapproach and carried out extensive studies on the postbucklingbehavior of plate girder web panels. They assumed that tensionfield develops only in parts of the web and that flanges are tooflexible to support normal stresses induced by the inclinedtension field. In other words, yield zones form away from flangesand merely transverse stiffeners act as anchors. Their allegedassumption was in contrast to the Wagner’s [5]; but later otherresearchers like Fujji [7] showed that the Basler’s formula wasgiven for complete tension field instead of limited band. Furtherresearch works by Basler [8–10] paved the way for the AmericanInstitute of Steel Construction (AISC) [11] and the AmericanAssociation of Steel Highway and Transportation Officials (AASHTO)[12] to adopt the postbuckling strength of plates into theirspecifications. By moving towards applying the limit state designconcept in the design of steel structures, SSRC [13] introduced anumber of modified failure concepts to achieve a better correlation between theories and test results.On the other side, the Cardiff model developed by Porter et al.[14] was adopted into the British Standards [15]. They alsoassumed that inclined tension fields only develop in a limitedportion, but that flanges do contribute to the postbucklingstrength by absorbing normal stresses from tension fields; andthat as a result, girders collapse when plastic hinges form in theirflanges.
ARTICLE IN PRESSM.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506NotationsAabfcEefyhwkarea of end-post/stiffenerpanel widthflange widthposition of flange plastic hingeelastic moduluswidth of end stiffenermaterial yield stressweb heightshear buckling coefficientBasler [10], Porter et al. [14], Takeuchi [16] and Herzog [17]assumed that the diagonal tension field develops in a limitedportion of the web. In contrast, Fujji [18], Komatsu [19], Chern andOstapenko [20] and Sharp and Clark [21] assumed that diagonaltension spreads all over the panel, but with different intensity. TheSteinhardt and Schroter’s [22] assumption, lies half way betweenthe two previous assumptions. Hoglund [23–25] developed atheory for transversely stiffened and unstiffened plate girders. Heused the system of diagonal tension and compression bars tomodel web plates. His theory later became the basis for Eurocode3 [26].Although these classical failure theories assumed differentyield zone patterns, the fundamental assumption that ‘‘compressive stresses that develop in the direction perpendicular to thetension diagonal do not increase any further once elastic bucklinghas taken place’’ was common in all of them. The application ofthis fundamental assumption to the whole web panel led to thewell-known theory that the tension field action in plate girderswith transverse stiffeners needs to be anchored by flanges andstiffeners in order for the webs to develop their full postbucklingstrength.Takeuchi [16] was the first to make an allowance for the effectof flange stiffness on the yield zone of web plates. Among theprevious researchers, Fujji [18], Komatsu [19], Porter et al. [14] andHoglund [25] assumed that the normal stresses induced by thetension fields are anchored by the top and bottom flanges and/orthe combination of transverse stiffeners and adjacent panels.These normal stresses, thus, produce a beam mechanism inflanges and the ultimate capacity of plate girder is accompaniedby the formation of plastic hinges in flanges. Their proposedtheories, it seems, were invented to justify the formation of plastichinges that had materialized in extensive experiments.In other series of analytical and experimental works, Lee andYoo [27–31] showed that flanges and transverse stiffeners do notnecessarily behave as anchors. Their studies confirmed thatintermediate transverse stiffeners are not subjected to compressive forces and that flanges are not subjected to lateral loadings.They further introduced an approach that was referred to as theshear cell analogy to resolve the discrepancy between theirprevious understandings and new findings. However, on reexamining, they noticed that the shear cell analogy does in factcontain a serious flaw. An important stress component wasinadvertently omitted during the transformation process from atwo-dimensional stress to an assembly of one-dimensional barelement.Ever since Wagner [5] proposed the pre-mentioned fundamental assumption, no one has examined it critically. AlthoughMarsh et al. [32] found that the diagonal compression at thetension corners of the web increased after buckling, they stillconcluded that flanges contribute to the shear capacity of panelsdue to their bending strength, which permits the development ofsome diagonal tension.LtftstsetwDdusx, sytcrtxy1499girder spanflange thicknessthickness of intermediate stiffenersthickness of end stiffenersweb plate thicknessin-plane deflection of girderout-of-plane displacement of web panelsPoisson’s rationormal stressescritical shear stressshear stressThe assumed failure mechanisms in Basler, Cardiff and othermentioned models probably do not accurately represent theultimate shear behavior of web panels, since they are significantlyaffected by bending stresses when panels undergo large postbuckling deformations and the pattern of yield zones at one face isdifferent from the other [33]. In short, although the classicaltheories underestimate the buckling strength due to the negligence of torsional rigidity of boundary members, they give highervalues for the ultimate shear strength, because of their overestimation in the postbuckling strength [31,34,35].The nonlinear shear stress and normal stress interaction thattakes place from the onset of elastic shear buckling to the ultimatestrength state is so complex that any attempt to address thisphenomenon using classical closed form solutions appear to beunsuccessful. The fact that there have been many theories forexplaining this occurrence is evidence to the complexity oftension field action. The objective of this nonlinear largedeflection elastoplastic finite element (FE) study is to clarify themechanism of shear failure in steel plate girders; and to answerwhy, how, when, and where plastic hinges form. Other aspects ofshear plate behaviors, such as their deformability and rigidity andstrength degradation due to fatigue-induced cracks have previously been reported by the present first author and hiscolleagues [34–38].2. Method of study2.1. GeneralA detached web panel simulation model, a simply supportedweb plate in shear, or even single-panel experimental tests cannottruly represent the behavior of plate girder web plates, since:(a) A web plate is bound to have some bending moments due tolateral loadings.(b) The torsional rigidity of girder flanges must be accounted forin the rotational stiffness of panel boundary conditions. Thetrue behavior of flange–web junction is neither simplysupported nor clamped.(c) In reality, flanges are allowed to move towards or apart fromeach other, and their weak axis second moment of areabecomes an important factor in this regard. A free orrestrained in-plane movement of panel edges cannot represent the real behavior of web plates.(d) The number of sub-plates created by intermediate transversestiffeners and conditions of end-posts (end stiffeners) haveconsiderable effects on the behavior of plate girders.Therefore, in order to investigate the explicit shear failuremechanism of plate girders, complete girders with appropriateboundary restraints must be simulated. In this research, simple
ARTICLE IN PRESSM.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506girder beam models subjected to point loads at their mid-spansare considered. The loading and end support conditions guaranteeconstant shear and a relatively small flexure throughout webpanels. The FE modeling and the corresponding boundaryconditions are illustrated in Fig. 1.The mild steel material properties, with the elastic modulusE ¼ 210 GPa, normal yield stress fy ¼ 345 MPa and the Poisson’sratio u ¼ 0.3 are used throughout the work. The material isassumed to be elastic perfectly plastic with no strain hardening.2.2. FE modeling and validationsFig. 2 shows the variation of percentage errors obtained bycomparing the finite element analysis results to the theoretical valuefor different numbers of incorporated mesh elements. Based on thisfigure, the model with a mesh refinement of 30 30 elementsproduced results which had good agreement with the theory andwas, therefore, taken as the minimum requirement in the analyses.To validate the overall modeling, boundary conditions andloading procedure, test results reported by Real et al. [40] wereremodeled and analyzed. Fig. 3 presents the comparison betweenthe mid-span in-plane deflections of a typical experimental dataand the current FEA procedures.2.3. ModelsSeveral transversely stiffened plate girders having identicaldepth and panel width of 1000 mm in spans of 2, 4 and 6 m, suchas the one given in Fig. 4, were considered and parametric studiesregarding web thickness, flange dimensions and end-posts werecarried out. Initial comparative analyses on the 2-, 4- and 6-panel1y2xz1uxuyuz x y76543The four-noded-reduced-integrated element S4R of the ABAQUSsoftware [39] is selected for all Eigenvalue and incrementalnonlinear analysis. For convergence studies on mesh numbering,simple-detached panels were meshed into sufficient number ofelements to allow the development of shear buckling modes anddisplacements. The elastic shear buckling stress values obtainedvia numerical analyses were compared to those obtained from thetheoretical formula (1). 2kp2 Etwtcr ¼ð1Þ12ð1 u2 Þ hwRestraintpoints8% Error1500 z1 free2 restrainedFig. 1. FE modeling of a typical plate girder.210050010001500200025003000Number of elementsFig. 2. Convergence study for the number of mesh elements.girders showed good correlation for both deflections and stresses.Fig. 5 compares the out-of-plane displacement of the center ofpanels 1 or 3 of the four-panel girder in Fig. 4 to the corresponding2- and 6-panel girders. The variation of the shear stress txy at thecentral horizontal axis of the beams at the ultimate load isdepicted in Fig. 6. The figure shows that the state of shear stressesis similar in the 2-, 4- and 6-panel girders.An important element in the behavior and design of plategirders is the end-posts and therefore, a considerable part of thisstudy is devoted to them. North American codes do not explicitlydefine end-posts; but in Eurocode 3 [26] three types of endstiffeners/posts, as shown in Fig. 7, are defined for steel plategirders. (a) Plate girders with no end-post, (b) plate girders withrigid end-posts and (c) plate girders with non-rigid end-posts.3. Discussion of results3.1. Shear vs. flexural plastic hingesThe FEM results of various plate girders indicate that theformation of plastic hinges in flanges may either have flexural orshear basis; as shown in Figs. 8 and 9. In the bending-initiatedmechanism, plastic hinges form at mid-spans (Fig. 8); while in theshear-initiated mechanism, plastic hinges only occur in the endpanels (Fig. 9).If flange plates are not rigid enough to withstand bendinginduced normal stresses, plastic hinges appear at the position ofmaximum-bending moment. In the typical model depicted in Fig.8, plastic hinges are formed at the center-span adjacent to thecentral transverse stiffener. On the other hand, if the flange platesare rigid enough, shear-initiated mechanism becomes apparent bythe formation of plastic hinges in the end panels next to the endstiffeners, as shown in Fig. 9. However, if both flange and webplates are strong enough to carry direct and shear stresses, othermechanisms such as local buckling and web crippling occur.3.2. Failure modesIn order to characterize failure modes, some four-panel girderswith non-rigid end-posts having various relative flange and web
ARTICLE IN PRESSM.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506800800700700600600500Load (kN)Load (kN)1501400300500400300200200100100000 1 2 3 4 5 6 7 8 9 10 11 121314Experimental testNumerical test0-2Deflection (mm)-4 -6 -8 -10 -12 -14Deflection (mm)Fig. 3. FE model validation: (a) Numerical analysis and (b) test results [40].Fig. 4. Directions, panels and loading.in Table 1. The results show that irrespective of the flange width toweb height ratio (bf/hw), when the ratio of flange to web thicknessis more than 3 (tf/twZ3), the failure mode is always in shear; andif tf/twr2, the flexure mode governs. In the intermediate range(2otf/two3), failure mode depends on the web slendernessparameter. Thicker webs (hw/two200) result in flexural failure,while more slender webs fail in shear. AASHTO [12] has classifiedflange dimensions into three categories, as given in Table 2. Tables1 and 2 deduce that girders made up with AASHTO’s light flangescollapse in flexural mode, whereas moderate and heavy flangegirders collapse in shear.Further elaboration of results implies that the minimumrequired flange thickness and width for girders not to collapse inflexure mode is in accordance with the simple beam theory bylimiting the maximum stress to the material yield stress (fy); as inEq. (2). Therefore, the control of flexural mechanism is a simpleprocedure and easily preventive. In the next sections, the rathercomplex shear failure mechanism is discussed.700600Applied Load (kN)5004 panel girder4006 panelgirder3002002 panel girder10000246810Out-of-plane displacement (mm)1214min¼IGirderMmax hw2fyð2ÞFig. 5. Maximum out-of-plane deflection of the 2-, 4- and 6-panel girders.dimensions were considered in a parametric study. The intermediate transverse stiffener thicknesses were presumed to betwice that of the web (ts ¼ 2tw). The geometrical properties ofselected plate girders and their predicted failure modes are given3.3. Shear-induced plastic hingesIn the shear failure mode, plastic hinges are formed in theflanges of end panels; after formation of web-inclined yield band.
ARTICLE IN PRESS1502M.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506Fig. 6. Comparison of shear stresses in the 2-, 4- and 6-panel girders.Fig. 7. Types of end stiffeners [26].Fig. 8. Flexural failure mechanism.Fig. 9. Shear failure mechanism.The in-plane vertical displacement of top and bottom flange platesin a typical girder near the end support is shown in Fig. 10. Thesedisplacement curves are extracted from the numerical analysis,and can be used as a guide to explain excessive sheardeformations in plate girder end panels. It also demonstrateshow end-posts act as clamped boundary conditions for top flangeplates, whilst lower flange deforms in a manner similar to asimple beam.The formation of plastic hinges is actually due to thedifferential shear deformation of end panels and they are notdirectly related to the stresses imposed by the inclined tensionfields. That is why plastic hinges do not occur in mid-panels. Itshould be emphasized that the shear stress distributions in allpanels are similar; that diagonal yield band occurs almost at thesame time in all panels; and that the bending moment in thecentral panels are higher than the end ones. It should also bementioned that most experiments on plate girders have beencarried out on 2-panel girders, similar to the one provided byShanmugam [41] in Fig. 11; and there are not many test reports onunrestrained multi-panel girders. However, experiments do
ARTICLE IN PRESSM.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–15061000Table 1Plate girder dimensions and failure Rigid End PostFailure rFlexuralShearShearFlexuralShearShearNon-rigid End PostApplied Load (kN)bf1503600No End Post400200005101520mid-span deflection (mm)hw ¼ 1000, a ¼ 1000 and L ¼ 4000 all dimensions are in mm.L 4000mmts 8mmTable 2AASHTO classification for flange thickness.tw 4mme 100mm2530tf 9mmbf 300mmFig. 12. Load vs. in-plane deflection curves for different end conditions.Flange 0.351000Rigid End PostApplied Load (kN)800Non-rigid End Post600No End Post400Formation of yield zones inweb panels200005101520253035404550Maximum out-of-plane displacement (mm)Fig. 13. Load vs. out-of-plane deflection curves for different end conditions.Fig. 10. Flange displacements at the occurrence of plastic hinges.Fig. 11. View after failure of a 2-panel girder [41].
ARTICLE IN PRESS1504M.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506confirm that plastic hinges appear in flanges, but they do notdemonstrate when, how and why they are formed.3.4. Effect of end-posts/stiffenersThe addition of end-posts or reinforcing end stiffeners providesmore fixity to flange plates and increases the ultimate resistanceof plate girders. This is illustrated in the load-deflection curves ofFig. 12, where P D curves of plate girders having different endposts are compared. Evidently, end stiffeners have no effect on theinitial stiffness of plate girders and only become effective afterweb panels yield in shear.Fig. 13 depicts the web panel maximum out-of-planedisplacement curves (P d) of girders. These out-of-planedisplacements are measured at the center of panels. Theapparent loss in the stiffness of girders is due to the formationof diagonal yield zones, as pointed out in the diagram. Accordingto Fig. 13, the ultimate resistance of the plate girder with low endstiffness coincides with the load at which inclined yield zonesform in panels. On the other hand, girders with rigid end-postscarry loads in excess of web yielding.According to Eurocode 3 [26], a rigid end-post should act as abearing stiffener resisting the reaction from bearing at the girdersupport, and as a short beam resisting the longitudinal membranestresses in the plane of the web. A rigid end-post may comprise oftwo double-sided transverse stiffeners that form the flanges of ashort beam of length hw, see Fig. 7(b). The strip of web platebetween the stiffeners forms the web of the short beam.Alternatively, an end-post may be in the form of a rolled section,connected to the end of the web plate. Also, each double-sidedstiffener consisting of flat plates should have a cross-sectionalarea of at least800A¼ð3Þwhere A is the area of the two end stiffeners, and e (40.1hw) is thecenter-to-center distance between them (see Fig. 7). Therefore, forthe plate girder with web height of hw ¼ 1000 mm and thicknessof tw ¼ 3.33 mm, one would have eZ100 mm and AZ444 mm2.Hence, the thickness of end stiffeners is derived as thin astseZ1.5 mm. To elaborate on the effect of the rigidity of end-posts,more models having different e and tse were analyzed and theirultimate capacities are given in Fig. 14.Fig. 14 shows that for a constant e, the increase of the endstiffener thickness brings more fixity to the top flange andincreases the ultimate capacity of girders. Furthermore, doublingthe distance e, does considerably increase the ultimate capacityfor small values of tse; but this increase is not considerable ingirders with thicker end stiffeners. Hence, the minimum-requiredthickness of the end stiffeners specified in Eurocode 3 seems to betoo thin.e 200mm750Ultimate Load (kN)24hw twee 100mm700650600010203040Thickness of end stiffener (mm)tw 3.33mmtf 10mm50603.5. Occurrence of shear plastic hingesThe load vs. central out-of-plane displacement curves for atypical web panel in plate girders with various end-posts aredepicted in Fig. 15. These curves are presented to demonstratebf 300mmFig. 14. Ultimate resistance of girders having different end-post dimensions.Non-rigid End Post e 200mm1000900Rigid End Post e 100mmApplied Load (kN)800700No End Post600500Non-rigid End Post e 100mmFormation of diagonalyield zones400300Formation ofplastic hinges20010000510152025303540Maximum out-of-plane displacement (mm)Fig. 15. Formation of plastic hinges.4550
ARTICLE IN PRESSM.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506how early the shear-oriented plastic hinges form in the plategirder web plates. They also clarify the relation between theplastic hinge occurrence with respect to the formation of inclinedyield zone and the ultimate capacity of plate girders. The figureshows that plastic hinges occur much later than their ultimatecapacities. In fact, plastic hinges do not occur before the ultimateload and at most they may take place concurrently [42]. Themaximum load that a plate girder can resist is very close to thestep at which diagonal yield zones form in panels. Therefore, oncethe web panel loses its shear capacity, the flanges and transversestiffeners somehow act as a Vierendeel girder and ultimatelyflanges fail under shear deformation.1505depends on the rigidity of end-posts as shown in Fig. 16. Thelocation of plastic hinges does not directly depend on the width ofthe tension field. However, the hinge location and the width oftension fields are both related to the rigidity of end stiffeners andflange dimensions. Fig. 16 presents the stress distribution and theposition of plastic hinges in two typical girders.3.7. Ultimate capacity of plate girdersFig. 17 presents the comparison of results for the ultimatecapacities of a number of plate girders extracted from the currentFE analyses to those given by different codes and theories.It is observed that, in general, there is more divergence in theresults of girders with thinner flanges. The Eurocode 3 gives themost conservative results, while the Porter’s approach largelyoverestimates the girder capacities. The AISC results for themedium to thick flange plates best fit the FEM. The AASHTO andBasler results are very similar and they always overestimate thegirders ultimate capacity. On the other hand, the Hoglund’s theoryfor thicker flanges is always safe and reasonably close to FEM.Further elaborations on these results and the state of stresses indifferent elements of plate girders will be presented in the futurepaper.3.6. Location of plastic hingesThe position of plastic hinges in the end panel, regardless ofthe width and thickness of flange plates, is directly related to therigidity of end stiffeners. According to the results, the position ofplastic hinges in different girders varied from 0.20 to 0.35 of panelwidth measured from end stiffeners (0.20aoco0.35a) and4. ConclusionsNonlinear large deflection finite element analyses of full-scalesteel plate girders were performed to characterize their shearfailure mechanism. The analyses concluded that: Detached plates simulation does not represent the truebehavior of plate girder web panels. Shear-induced plastic hinges occur only in the flanges of end Fig. 16. The position of plastic hinges in two typical girders: (a) Girders with lessrigid end stiffeners and (b) girders with more rigid end stiffeners.panels after the formation of partial-inclined yield zones inwebs. They do not occur in mid-panels.The formation of plastic hinges is due to the shear deformationof girders, directly pertained to the stiffness of end-posts andflange dimensions. The location of plastic hinges is not directlyrelated to the stresses imposed by the inclined tension fields.2.0EquityVu (FE) / Vu (codes, HTO0.8Eurocode0.605101520253035tf (mm)Fig. 17. Comparison of ultimate capacities of different codes and theories.
ARTICLE IN PRESS1506M.M. Alinia et al. / Thin-Walled Structures 47 (2009) 1498–1506 When the flange thickness is more than three times the web thickness, the failure mode is always in shear and if this ratio isless than two, the flexure failure mode governs. In theintermediate ranges, the failure mode depends on the webslenderness ratio. Compact webs collapse in flexural mode,while slender webs fail in shear.The addition of end-posts provides more fixity to flange platesand increases the ultimate resistance of plate girders.Eurocode 3 gives the most conservative ultimate capacity forplate girders, while the Porter’s model overestimates them. TheAISC results for medium to stocky flanges produce closestresults to the FEM. The AASHTO and Basler results are verysimilar and they always overestimate the capacity. TheHoglund’s theory is always safe and reasonably close to FEM.References[1] Alinia MM. A study into optimization of stiffeners in plates subjected to shearloading. Thin-Walled Struct 2005;43(5):845–60.[2] Alinia MM, Moosavi SH. A parametric study on the longitudinal stiffeners ofweb panels. Thin-Walled Struct 2008;46(11):1213–23.[3] Alinia MM, Moosavi SH. Stability of longitudinally stiffened web plates underinteractive shear and bending forces. Thin-Walled Struct 2009;47(1):53–60.[4] Wilson JM. On specifications for strength of iron bridges. Trans Am Soc CivEng 1886;15(1):401–3 489–490.[5] Wagner H. Flat sheet metal girder with very thin metal web. TechMemorandum 604–606, National Advisory Committee for Aeronautics(NACA), Hampton, Va, 1931.[6] Basler K, Thurliman B. Plate girder research. In: Proc Nat Eng Conf., New York:American Institute of Steel Construction, 1959.[7] Fujii T. On an improved theory for Dr. Basler’s theory. Final Rep., IABSE 8thCongress, New York, 1968.[8] Basler K. New provisions for plate girder design. In: Proc AISC Nat Eng Conf.New York: American Institute of Steel Construction. 1961, p. 65–74.[9] Basler K. Strength of plate girders under combined bending and shear. J StructDiv, ASCE 1961;87(2):97–181.[10] Basler K. Strength of plate girders in shear. Transaction of ASCE 1961 NewYork, American Society of Civil Engineers.[11] American Institute of Steel Construction, AISC. Seismic provisions forstructural steel buildings. Chicago, 1997.[12] American Association of State Highway and Transportation Officials, AASHTO.LRFD bridge design specifications, 1st ed., Washington, D.C., 1994.[13] Galambos TV
allowable stress design based on elastic buckling as a limiting condition; and (ii) strength design based on ultimate strength, including postbuckling as a limit state. Till 1960s, the elastic buckling concept was basically used in the design of plate girders and the postbuckling strength was only indirectly accounted for
Concrete contribution to the shear force capacity of a beam [N] V d Design shear force [N] V s Steel stirrups contribution to the shear force capacity of a beam [N] V p Axial load contribution to the shear force capacity of a beam [N] V i Other contributions to the shear capacity of a beam [N] V frp FRP contribution to the shear capacity [N]
Shear Stress vs Shear Displacement 0 20 40 60 80 100 0 2040 6080 100 Shear Displacement (mm) Shear Stress (kPa) Normal Stress - 20.93 kPa Field id: MID-AAF-0002-1 Measured Cohesion 14.99 Water Content 5.62 Shear box size 5.08 Peak Shear Stress 31.34 Intrinsic Cohesion 14.45 Wet Density 2240 Matri
modes of unstiffened beam-to-column web shear tabs. On the other hand, she determined that shear plate buckling is the governing failure mode in stiffened beam-to-column web shear tabs. Baldwin-Metzger (2006) tested four beam-to-column flange extended shear tabs. These connections failed due to weld tearing and/or beam failure.
3. In a steel shear wall, the story shear is carried by tension field action of the steel plate after buckling of diagonal compression. In a composite shear wall, the concrete wall restrains the steel plate and prevents its buckling before i
The gravity load is resisted entirely by a steel space frame and the lateral load is resisted by the reinforced concrete shear walls in the first two stories and steel plate shear walls in the upper four stories. The steel shear wall panels in this building are 25 ft wide and 15.5 feet high with th
The CAN/CSA S16-01 seismic design process for steel plate shear walls follows the selection of a lateral load resisting system (i.e., shear walls with rigid or flexible beam-to-column connections), calculation of the appropriate design base shear, and distribution of that base shear along the building height by the usual
A-3 Short Beam Shear (ASTM D 2344) A-4 Two-Rail Shear (ASTM D 4255) A-5 Three-Rail Shear (ASTM D 4255) A-6 Shear Strength by Punch Tool (ASTM D 732) A-7 Sandwich Panel Flatwise Shear (ASTM C 273) A-8 Special Sandwich Panel Shear Fixture (ASTM C 273) SEZIONE B: PROVE DI COMPRESSIONE B-1 Wyoming Combined Loading Compression (ASTM D 6641) B-2 Modified ASTM D 695 (Boeing BSS 7260) B-3 IITRI .
Shear Tab fits in beam T dimension. Shear Tab moment capacity is less than the bolt group moment capacity. Shear Tab weld size is adequate. Shear Tab weld is double sided. Weld develops the strength of the Shear Tab. Bolt spacing is adequate. Bolt edge distances are adequate. Design Loads
