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This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) section at support Fig. 17.7 Lateral torsional buckling V D Ètw( dw - hh) ˘ = t ÎÍ g mg f3 ˚˙ l Design of steel bridges to BS 5400: Part 3 489 Lateral restraint quarter length of buckled beam section at restraint (vertical displacement) support -- 1w section between restraints (vertical horizontal and rotational displacements) where tw and dw are the thickness and depth of the web respectively, hh is the height of the largest cut-out within the panel being considered, gm and gf3 are partial material and load factors respectively, and tl is the limiting shear stress. For slender webs tl is governed by shear buckling, which becomes significant in webs with depth to thickness ratios greater than about 80. The actual shear strength of a web panel is dependent on the following: (a) Yield stress (suitably factored) (b) Depth-to-thickness ratio of web (c) Spacing of stiffeners (d) Conditions of restraint provided by flanges
This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) 490 Plate girders (a) tension field stress plastic hinge \ (b) (c) yield zone Fig. 17.8 Tension field theory (a) pure shear (b) tension field (c) collapse mechanism The web of a plate girder between stiffeners acts similarly to the diagonal of a Pratt truss (this phenomenon, known as tension field action, is described in Reference 6). The theory stipulates that the web will resist the applied loading in three successively occurring stages (see Fig. 17.8): Stage 1 A pure shear field Stage 2 A diagonal tension field Stage 3 A collapse mechanism due to the formation of plastic hinges in the flanges In slender web panels the limit of stage 1, i.e. the pure shear field, is reached when the applied shear stress reaches the elastic critical stress t c. To allow for the effects of residual stresses and initial imperfections in stocky plates, t c is limited to less than its actual value when it is greater than 0.8 times the shear yield stress t y, and to t y when its actual value exceeds 1.5 times t y. The elastic critical stress t c for a plate loaded in shear is given by t c 2 p E Ê t = K 2 12 1 -n Ë d ( ) where E and n are the elastic modulus and Poisson’s ratio of the steel respectively, and 4 K = 534 . + 2 f when f ≥1 534 . K = 4 + 2 f when f < 1 a f = panel aspect ratio = dwe w we ˆ ¯ 2 The criteria outlined previously have been incorporated in computing the value of tc as follows:
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