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- 1. N.W.F.P. University of Engineering and Technology P h T h l Peshawar Lecture 13: Plate Girder By: Prof Dr. Akhtar Naeem Khan chairciv@nwfpuet.edu.pk 1
- 2. Plate Girders A girder is a flexural member which is required to carr hea loads on relati el long spans carry heavy relativelyCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 2
- 3. Plate GirderCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 3
- 4. Plate Girder Plate girders are typically used as long-span g yp y g p floor girders in buildings, as bridge girders, and as crane girders in industrial structures. g Commonly term girder refers to a flexural x- section made up of a number of elements elements. They are generally considerably deeper than the y g y y p deepest rolled sections and usually have webs thinner than rolled sections.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 4
- 5. Plate Girder Modern plate girders are normally fabricated by welding together two flanges and a web p plate.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 5
- 6. Plate Girder Plate girders are at their most impressive in modern b id construction where main spans of d bridge t ti h i f well over 200m are feasible, with corresponding cross-section d th h ti depths, haunched over th h d the supports, in the range of 5-10m.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 6
- 7. Plate Girder Because plate girders are fabricated separately, each may be designed p y, y g individually to resist the applied actions using proportions that ensure low self-weight and high load resistance. resistanceCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 7
- 8. Plate Girder Changes in X-Section There is also considerable scope for variation of cross-section in the longitudinal direction. Ad i designer may choose t reduce th fl h to d the flange thickness (or breadth) in a zone of low applied moment moment. Equally, in a zone of high shear, the designer might choose to thicken the web plate.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 8
- 9. Plate Girder Changes in Material Alternatively, higher g y g grade steel might be g employed for zones of high applied moment and shear, while standard grade would be used elsewhere. S d l h So-called "h b id" girders ll d "hybrid" i d with different strength material in the flanges and the web offer another possible means of more closely matching resistance to requirements. requirementsCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 9
- 10. Plate GirderCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 10
- 11. Plate GirderCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 11
- 12. Plate Girder Any cross-section of a plate girder is normally subjected to a combination of shear force and bending moment. The primary function of the top and bottom flange plates of the girder is to resist the axial compressive and tensile forces arising from the applied bending moment. moment The primary function of the web plate is to resist the applied shear force.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 12
- 13. Plate Girder Plate girders are normally designed to support heavy loads over long spans in situations where it is necessary to produce an efficient design by providing girders of high strength to weight ratio. To produce the lowest axial flange force for a given bending moment, the web depth (d) must be made as large as possible. To reduce the self weight, the web thickness (tw) must be reduced to a minimum minimum. As a consequence, in many instances the web plate is of slender proportions and i th f l t i f l d ti d is therefore prone to buckling at relatively low values of applied shear shear.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 13
- 14. Plate Girder For efficient design it is usual to choose a relatively deep girder, thus minimizing the required area of flanges for a given applied moment, Msd. t This obviously entails a deep web whose y p area will be minimized by reducing its thickness to the minimum required to carry the applied shear, Vsd. h li d h Such a web may be quite slender ( y q (i.e. a high g d/tw ratio) and may be prone to local buckling and shear buckling.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 14
- 15. Plate Girder Web buckling does not determine the ultimate strength of a plate girder. lti t t th f l t id Plate elements do not collapse when they p y buckle; they can possess a substantial post- buckling reserve of resistance. For an efficient design, any calculation relating to the ultimate limit state should take g the post-buckling action into account.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 15
- 16. Design Criteria Criteria for design of plate girder may be based on Elastic bend-buckling strength Elastic h El ti shear-buckling strength b kli t th Post-bend-buckling Post bend buckling strength Post shear buckling(Tension Post-shear-buckling(Tension field)strengthCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 16
- 17. Design Criteria The designer has the choice of following four combinations 1. Elastic bend buckling + Elastic shear buckling g g (conventional flexural behavior) 2. 2 Elastic bend buckling + Post shear buckling 3. Post bend buckling + Elastic shear buckling g g 4. Post bend buckling + Post shear bucklingCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 17
- 18. Elastic Bend Buckling Strength The extreme f fiber bending stress at which a perfectly flat web buckles is given byCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 18
- 19. Elastic Bend Buckling Strength Using a FOS of 1.25 w.r.t service load bending stress fb gives an eqnuation which is AASHTO slenderness limit for plat girders webs Using AASHTO allowable stress fb=0.55Fy “ h/t=165 f A36 steel “ h/t 165 for t lCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 19
- 20. Elastic Bend Buckling Strength The bend buckling resistance of beam webs can be increased considerably by reinforcing the slender webs with Longitudinal stiffeners. Means webs thinner than those given by the equation can be used. used A typical longitudinally stiffened girder is shown after failureCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 20
- 21. Web Stiffeners They usually consists of rectangular bars to welded to web. Transverse stiffeners may be in pairs, one on each side of web, or they may placed on one side of web. Longitudinal stiffeners are usually placed on one side of web.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 21
- 22. Web StiffenersCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 22
- 23. Web StiffenersCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 23
- 24. Web Stiffeners The main function of the longitudinal stiffeners is to increase the buckling resistance of the web with respect o bot s ea a d be d g loads. An t espect of both shear and bending oads effective stiffener will remain straight, thereby sub-dividing the web p g panel and limiting the g buckling to the smaller sub-panels. The resulting increase in the ultimate resistance of the girder g can be significant.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 24
- 25. Web Stiffeners Efficiency of stiffener is a function of its location in the compression zone The optimum location for a longitudinal stiffener has been determined to be at least h/5 from compression edge. In this case k=129. The corresponding allowable web k 129. slenderness is h/t=330 as compare to 165CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 25
- 26. Web Stiffeners Stiffener acts as a beam supported at the ends where a vertical stiffener holds the web in line line. Stiffener acts as a beam column and hence must be b proportioned i t ti d in terms of x-sectional area and f ti l d moment of inertia. AASHTO specifies Is as Stiffener acts as a beam supported at the ends where a vertical stiffener holds the web in line.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 26
- 27. Web Stiffeners The stiffeners must also be proportioned to resist local buckling. buckling For plates supported on one longitudinal p pp g edge AASHTO require b/t<1625/√fb Multiple longitudinal stiffeners are used for large depth webs. As longitudinal stiffener is also acting as a column so it must be satisfied for critical stress (Fcrs>0.6Fcrf)CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 27
- 28. Post buckling bending strength If bending strain increases after Fcr, the upper g , pp edge of panels shortens and bottom edge lengthens. If web were to remain flat there will be increase in stress. Because the web has buckled, the increase in stress is non linear non-linear.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 28
- 29. Post buckling bending strength As A variation i post-buckled state i not k i ti in t b kl d t t is t known, simplify assumptions are made. Non-linear compression is replaced with linear distribution acting on effective depth be.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 29
- 30. Post buckling bending strength Point A gives point that enables a girder to reach its full yield moment(925 /√Fy=154). If stiffeners at h/5 is provided gives point B B. Considering the post buckling A B strength, the 0.94 0.82 0 82 point where M/My reduction in web 0.4 effectiveness 0.18 0 18 begins s taken to 154 315 360 be 980/√Fy=170. 980/√Fy 170. h/tCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 30
- 31. Post buckling bending strength Equation connecting the revised point A with points corresponding t h/t 360 i ith i t di to h/t=360 isCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 31
- 32. Post buckling bending strength LRFD WhereCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 32
- 33. Compression Flange Vertical bucklingCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 33
- 34. Compression Flange Vertical buckling If plate girder web is too slender the compression plate-girder slender, flange may buckle in vertical plane at stress less than yield stress stress. The compression flange is a beam-column p g continuous over vertical stiffener as supports Its stability depends on stiffener spacing and relative stiffness of the flange and the web. Fcr isCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 34
- 35. Compression Flange Vertical buckling Slenderness of webs with vertical stiffeners is taken conservatively AISC ASD/LRFD li it the h/t by the given equation with limits th b th i ti ith Aw/Af =0.5CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 35
- 36. Shear buckling of beam webs Shear buckling is seldom a determining factor i d i f t in design of rolled section b t f ll d ti but plate girders have much larger h/t so it must be considered. tb id dCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 36
- 37. Shear buckling of beam webs Transverse stiffeners are used to increase th b kli strength b i the buckling t th by increasing factor k through a reduction in aspect ratio a/h.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 37
- 38. Transverse Stiffeners Transverse stiffeners play an important role in allowing the full ultimate load resistance of a plate girder to be achieved. In the first place they increase the buckling resistance of the web; Secondly they must continue to remain effective after the web buckles, to provide anchorage for p g the tension field; finally they must prevent any tendency for the flanges to move towards one another.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 38
- 39. Transverse Stiffeners The satisfactory performance of a transverse stiffener can best be illustrated by comparing the girders shown, after shown testing. Figure 2 g Figure 1 FiCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 39
- 40. Transverse Stiffeners In Figure 1 the stiffeners have remained straight. g g In Figure 2 the stiffener has failed and has been unable to limit the buckling to the adjacent sub- sub panels of the girder; instead, the buckle has run through the stiffener p g position extending over g both panels. Consequently, significant reduction in the failure load of the girder occurred. In Figure 1 One can also see the effect of aspect ratio,i.e greater a/ less k a d s a Fcr. at o, e g eate a/h ess and small cCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 40
- 41. Transverse Stiffeners The stiffener must be of adequate rigidity in th di ti perpendicular t i idit i the direction di l to the plane of the web to prevent web buckling. This condition is satisfied p provided the stiffener has a second moment of area Is that satisfies the following empirical formulae:CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 41
- 42. Transverse Stiffeners AISC/LRFD Moment of Inertia of stiffener is: tiff i whereCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 42
- 43. Transverse Stiffeners Transverse stiffeners spacing can be determined from the followingCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 43
- 44. Tension Field Action The resulting shear stresses on an element of a web are equivalent t l t f b i l t to principal stresses, one Tensile and one Compressive, at 45 to the shear stress.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 44
- 45. Tension Field Action Once a web panel has buckled in shear, it p , loses its resistance to carry additional compressive stresses. stresses On the other hand tensile principal stress p p continues to increase in strain in the diagonal direction. direction Such a panel has a considerable p buckling strength, p post g g , since increase in tension is limited only by yield stress.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 45
- 46. Tension Field Action In this post b ckling range a ne load carr ing post-buckling range, new load-carrying mechanism is developed, whereby any additional shear load is carried by an inclined tensile membrane stress field. This tension field anchors against the top and bottom flanges and against the transverse stiffeners on either side of the web panel. The load-carrying action of the plate girder than becomes similar to that of the N-truss In the post-buckling range, the resistance offered by the web plates is analogous to that of the diagonal tie bars in the truss.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 46
- 47. Tension Field Action Phases of behavior up to collapse of a typical panel in shear Prior to Buckling Post Buckling CollapseCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 47
- 48. Tension Field Action The load-carrying action of the plate girder load carrying than becomes similar to that of the N-truss In the post-buckling range, the resistance offered by the web plates is analogous to that of the diagonal tie bars in the truss.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 48
- 49. Tension Field ActionCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 49
- 50. Tension Field ActionCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 50
- 51. Tension Field Action ft V V Vt=Tsinφ Vt = ft ht cosφ sinφ T=ft ht cosφ Vt = (1/2)ft ht sin2φ φ Vt =(1/2) ft ht φ=45 Vty=(1/2) Fy ht………….(1)CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 51
- 52. Tension Field Action Vty =(1/2) Fy ht = Fy Vy Fvy ht 2Fvy Vty = √3 Vy = 0.87 Vy 2CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 52
- 53. Tension Field Action The angle φ for which Vt is maxCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 53
- 54. Tension Field Action WhereCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 54
- 55. Tension Field Action (1) Taking inelastic and strain hardening range (2) (3)CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 55
- 56. Tension Field Action Codal equations are derived from eqn;(1),(2),(3)CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 56
- 57. Tension Field Action AISC/LRFD k a/hCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 57
- 58. Combined Bending & Shear of Webs Interaction diagram is based on Tension- field f fi ld of webs b If the web is completely yielded in shear,any accompanying moment must be b resisted entirely b fl i t d ti l by flanges.CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 58
- 59. Combined Bending & Shear Bending & shear Interaction Curve B B C D V vyAw) V/(F A E 1/√3 0.75 0.83 1.0 1.07 1.12 M/MyCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 59
- 60. Combined Bending & Shear 1.0 Mu/φMn 0.8 0.6 LRFD I t Interaction Curve ti C 0.4 0.2 0.2 0.4 0.6 0.8 1.0 Vu/φVnCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 60
- 61. Web Proportioning NotationsCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 61
- 62. Web Proportioning Depth of girder is influenced by many factors: Headroom Clearance for high water in deck bridges Traffic passing beneath the bridgeCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 62
- 63. Web Proportioning Depth: Overall girder depth, h, will usually be in the range Lo/12 ≤ h ≤ Lo/8 /8, occasionally lighter loads may be accommodated with Lo/20 /20. Flange: g The breadth, b, will usually be in the range h/5 ≤ b ≤ h/3,CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 63
- 64. Design Procedure 1. Maximum Moment & Shear for Factored Load 2. Web D i 2 W b Design 1. p girder L/12 ≤ h ≤ L/8 Assume depth of g 2. Depth of Web hw=h-2tf 3. Web slenderness 1. For a/h <5 ……………. 2. and for a/h > 5 …………………… 3. 3 hw/tw= 970/√Fy 4. Select optimum twCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 64
- 65. Design Procedure 4. Flange Design 1. Find Af 2. Select suitable tf and bf 3. 3 Flange slenderness 1. bf/ 2tf < 65/√Fy …………….CompactCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 65
- 66. Design Procedure 5. 5 Check trial girder section 1. Web local buckling limit state 1. hw/tw< 640/√Fy…………………..Compact 2. 640/√Fy< hw/tw < 970/√Fy……Non-Compact 3. hw/tw > 970/√Fy…………………..Slender 2. Flange local buckling limit state 1. bf/ 2tf < 65/√Fy …………….Compact 3. Lateral Torsional Buckling g 1. Calculate Iy 2. A=Af+Aw/6 3. ry= √Iy/A 4. Find Lb/ry 5. λp= 300/√Fy ………….. λ< λp ______CompactCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 66
- 67. Design Procedure 6. Bending strength 1. Calculate C l l t Ix 2. Calculate Sxt 3. . 4. . 5. φMn≥ MuCE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 67
- 68. Procedure for Design 6. Bending strength 1. Calculate Ix 2. 2 Calculate Sxt 3. . 4. . 5.CE-409: Lecture 13 φMn≥ Mu Prof. Dr Akhtar Naeem Khan

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