Basic Study of Plate Girders

7/31/2019 Basic Study of Plate Girders

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CONSULTING ENGINEERS02 07 - 2010

PLATE GIRDER: A plate girder is basically an I-beam built up fromplates using riveting or welding. It is a deep flexural member used to

carry loads that cannot be economically carried by rolled beams.

For Heavy Loads And Long Spans, choice is

Two or more regular beamsBeam with cover plates

Plate girdersSteel truss


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Plate girders provide maximum flexibility and economy.


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upper economical limit of plate girder spans: depend on the followingfactors.(a) Whether the bridge is simple or continuous

(b) Whether it is a highway or railway bridge(c) The length of the section which can be transported in one piece

In general, P.G are economical for railway bridges of spans 15-40 m and for highway bridges of spans 24-46 m

P.G vs Trusses

ADVANTAGES(v) The cost of fabrication is lower compared to trusses(v) Erection is faster and cheaper(v) P.G require smaller vertical clearances than trusses(v) P.G are safer than trusses(v) Points where stresses may be critical are fewer in plate girders compared to trusses(v) P.G is more easily painted than a truss

DISADVANTAGES(v) Heavier than trusses for the same span and loads(v) Larger no. of connections are required between webs and flanges(v) Larger exposed wind area compared to truss(v) Low torsional stiffness


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Difference between beams and plate girders

qBeams are rolled in mills to standard sizes, whereas plate girders areassembled by welding of platesqWeb stiffeners are not used commonly in beams and they are used widelyin plate girdersqThe principle difference between the design of a rolled beam and thedesign of a plate girder is that the structural designer has considerablefreedom in proportioning a P.G

Elements of a plate girder(a) Web plate(b) Flange plate with or without cover plates(c) Bearing stiffeners or end post(d) Intermediate transverse stiffeners(e) Longitudinal stiffeners(f) Web splices(g) Flange splices



Shear stressdistribution

Bending stressdistribution



Resistance to shear buckling:Shall be verified when.

WhereKv=shear buckling coefficient

=5.35 when transverse stiffeners are provided only at supports=4+5.35/(c/d)2 for c/d



PROPORTIONING OF WEBvMinimum web thickness:(a) Serviceability requirement

1) when transverse stiffeners are not providedd/tw 200 (web connected to flanges along both longitudinal edges)d/tw 90 (web connected to flanges along one longitudinal edge only)

2) when only transverse stiffeners are provideda) d/tw 200w for 3dc d

b)c/tw 200w for 0.74d c dc)d/tw 270w for c < 0.74dd) for c>3d, the web is considered as unstiffened

3) when transverse stiffeners and longitudinal stiffeners are provided at onelevel only, at 0.2d from the compression flange

a) d/tw 250w for 2.4dc db)c/tw 250w for 0.74d c dc)d/tw 340w for c < 0.74d

4) when there is a second longitudinal stiffener provided at neutral axisa) d/tw 400w



(b)Compression flange buckling requirement1) when transverse stiffeners are not provided

d/tw 345f2

2) when only transverse stiffeners are provideda) d/tw 345f2 c 1.5db) d/tw 345f for c



b) Post buckling Behaviour

vAfter the web buckles along the direction of the principal compressive stress, a newload carrying mechanism is developed along the principle tensile direction-called tension

field action. Any further increase in shear beyond elastic critical shear stress will besupported by this new mechanism.

vThe tensile field is constituted by the portion of the plate in the principal tensile directionand anchored at the boundaries along the top and bottom flanges and the stiffenermembers on either side of the web

vThe stress in the web plate at this stage will be the sum of the applied critical shearstress, cr,e when the web plate buckled and the post buckled membrane tensilestress(ft) due to tension field action.

vThe pull exerted by the tensile membrane stresses in the web on the flexible flanges willcause the flanges to bend inwards.



Tension fieldaction

vAs the web begins to buckle, the web loses its ability to resist the diagonal

compressionvDiagonal compression is transferred to the TS & Flanges.vThe vertical component of diagonal compression is supported by stiffeners &flanges resist horizontal componentvThe web resist only the diagonal tension

c) Collapse Behaviour:


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c) Collapse Behaviour:

vOn increasing the load further, the tensile membrane stress developed in the webcontinues to exert increasing pull on the flanges. Eventually the resultant stress reachesthe yield value, and the web yields.

vA shear mechanism occurs when four plastic hinges form in the flanges.

vFor plastic hinges to form in flanges, the flanges must be classified as plastic sections.

vFor very strong flanges st=c, the hinges will form at the four corners of the flanges.

vIf the flanges are compact, semi-compact, or slender the tension field will be supportedentirely by the transverse stiffeners.

vFor very thick web of girder the web will yield before its buckling (fcr=fyw)


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SHEAR BUCKLING DESIGN METHODSA) Simple post critical methodB) Tension field method

Simple post critical method:

This is based on the shear buckling strength. This method can be used for web of Isection girders, with or without intermediate transverse stiffeners, provided that theweb has transverse stiffeners at the supports

The Nominal shear strength is given byVn=Vcr

Where Vcr = d tw b6b = shear stress corresponding to buckling, determined as follows:

a) When w 0.8

b) When 0.8 < w< 1.2

c) When w6 1.2 b =fyw/( 3 w2)

w= non-dimensional web slenderness ratio for shear buckling stress, given by

6cr= The elastic critical shear stress of the web


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END PANEL DESIGN:

Without using tension field actionqEnd panel along with stiffeners should be checked as a beam spanningbetween the flanges to resist a shear force, Rtf and a moment Mtf due totension field force.

qAlso end stiffener should be capable of resisting the reaction plus acompressive force due to the moment, equal to Mtf

End panels designed using tension field action


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End panels designed using tension field actionIn this case the end panel (panel B) shall be designed according to tension fieldmethod.Additionally it should be provided with an end post consisting of a single or doublestiffener, satisfying the following

Single stiffener:qThe top of the end post should be rigidly connected to the flange using full strengthwelds.qThe end post should be capable of resisting the reaction plus a moment from theanchor forces equal to 2/3 MtfqThe width and thickness of the end post are not to exceed the width & thickness of the

flange.

Panel A: designed utilizing tension field action,Panel B: designed utilizing tension field action.Bearing stiffener and end post: designed for combination of compressive loads due to

bearing and a moment equal to 2/3 Mtf


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Double stiffener:qThe end post should be checked as a beam spanning between the flanges of thegirder and capable of resisting a shear force Rtf and a moment Mtf due to the tension

field forces

Panel A: designed utilizing tension field action,Panel B: designed utilizing tension field action.

Bearing stiffener: designed for compressive force due to bearingEnd post: designed for horizontal shearRtfand moment Mtf


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Splices in Flanges:

vA joint in the flange element provided to increase length of flange plate

vFlange splices should be avoided as far as possible

vFlange joints should not be located at points of maximum bending moment

Splices in Webs:

v

A joint in web plate provided to increase its lengthvSplices in the webs should preferably not be located at points of maximum shearforce and heavy concentrated loads

vSplices in the webs sall be designed to resist the shears and moments at thespliced section


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Curtailment of Flange plates

For a plate girder subjected to external loading, maximum bendingmoment occurs at one section

Usually Flange area designed to resist maximum bending moment is notrequired at other sections

Therefore flange plates may be curtailed where plate is no longer required

as bending moment decreases

At least one flange plate should be run for entire length of girder


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Stiffener Design:Intermediate transverse stiffener: Provided to improve the buckling strength ofa slender web due to shear

Load carrying stiffener:To prevent local buckling of the web due to

concentrated loading

Bearing stiffener:To prevent local crushing of the web due to concentratedloading

Horizontal stiffeners: Provided to increase the buckling resistance of the web

General requirements:vOutstand of web stiffenersThe outstand from the face of the web should not exceed 20tqWhen the outstand of web is between 14tq and 20tq , then the stiffener design should be on the basis of a core section with an outstand of 14tq ,

where tq= thickness of the stiffenervStiff bearing lengthTo determine the stiff bearing length(b1), the dispersion of load through asteel bearing element should be taken as 450 through solid material, such asbearing plates, flange plates, etc.vEccentricity

Where a load or reaction is applied eccentric to the centerline of the web orwhere the centroid of the stiffener does not lie on the center-line of the web,


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vBuckling Resistance of stiffenerShould be based on the design compressive stress fcd of a strut, the radius of gyrationbeing taken about the axis parallel to the web

The effective section is the full area of the stiffener together with an effective length ofweb on each side of the centerline of the stiffeners, limited to 20 times the web thickness

The effective length for intermediate stiffeners used in calculating the bucklingresistance, should be taken as 0.7*Length of stiffener

The effective length for load carrying stiffenersa) KL=0.7*L when flange is restrained against rotation in the plane of

stiffener( by other structural; elements)b) KL=L when the flange is not restrained


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Webs subjected to combined bending and shearThe combination of bending & shear makes the stress conditions in the

girder web more complex.vIn the region , the failure takes place by the shear mechanism.

vIn the region beyond point c, the failure takes place in any of the followingways:

*yielding of the flange*inward buckling of the compression flange

*lateral buckling of the flange

vThe coexistence of the bending moment with shear leads to the followingadditional considerations

a) Reduced buckling stress of the webb) Reduced plastic moment capacity of the flanges due to axial stresses,

caused by the bending momentc) The consequences of bending stresses on the web yielding capacity

Steps involved in the design of plate girders


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Steps involved in the design of plate girders

Assume the self weight of the girder. The s.w may be assumed as equal to W/200(where w is in kN/m and W the total factored load applied in kN).Estimate live loads.Calculate max. B.M &S.F

The optimum Depth & thickness of the P.G are determined. Check the web thicknessaccording to clause 8.6.1.1 & 8.6.1.2 of the code and adopt a suitable thickness

The flange area is computed. Select suitable flange plate thickness & width. Classifythe flange, plastic flanges are preferred.

Check formoment capacity as per clause 8.2.1 or 8.2.2 depending on whether the P.G

is laterally supported or unsupported.

Check forshear resistance of the web using eitherpost-critical method or tension fieldaction method. (Clause 8.4.2.2(a) or 8.4.2.2(b))

Design of the connection b/w the flange plate & web plate

Design ofbearing stiffeners & their connection (Clause 8.7.4,8.7.5 & 8.7.9 of the code)

Design ofLCS, if required & their connections.(Clause 8.7.5)


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Design ofIS, if required (Clause 8.7.2 & 8.7.1.2) & their connection (Clause 8.7.2.6)

Design ofweb splice and its connections.

Design offlange splice and its connections.


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"Crushing" resistance, where crushingis local yielding of theweb without any buckling,

"Crippling" resistance, where cripplingis localised buckling ofthe web in the presence of plasticity,

"Buckling" of the web occurs with out-of-plane deformationover most of the depth of the web.


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Basic Study of Plate Girders

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