Structural Engineering & Statics
where the load goes
Concept

Shear buckling — where it appears

The out-of-plane rippling of a thin web under shear, on a diagonal at roughly forty-five degrees to the flanges. It occurs at a stress proportional to the square of the web's thickness, and a web that has buckled can still carry considerably more load as a tension field.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

Pull it along the girder and it just unfolds. One period of a 30° trapezoidal corrugation, 300 mm of flat and 260 mm of incline, and the same period pulled along the girder's axis. The fold opens by bending the inclined panels out of the web's own plane, so the axial flexibility contains the plate's t³ where a flat web's would contain t — and the effective modulus that comes back from solving the cell as a frame is 222 N/mm², which is 10.6 parts in ten thousand of the steel's 210 GPa. A web with a thousandth of the stiffness carries a thousandth of the stress, which is why the flanges of a corrugated girder carry the whole moment and why the section has 9 per cent less second moment than the flat-webbed girder it replaces. The fold buys freedom from stiffeners and pays for it here.

The web that carries no bending

A corrugated web needs no stiffeners, because the folds give it in one direction a depth it does not have in its thickness. In the other direction the same folds make it an accordion — and a web that cannot be stretched cannot carry a bending stress at all.

sections · Corrugated web A 10 mm plate, and the width it can be. The elastic critical stress of a plate in compression against its width, with the yield stress drawn across it. Below 462 mm the plate reaches yield before it buckles; above it the plate ripples first, and the fraction of the width still carrying load falls away — at 900 mm only 46 per cent of it is still working.

The coefficient that is not four

A plate's buckling stress carries a coefficient that looks like a constant and is not. It is 4 for an internal element, 0.43 for an outstand and 23.9 for a panel in shear — and the width a 10 mm plate may be runs from 152 mm to 1,130 across that range.

stability · Plate buckling A buckled panel is a truss that nobody drew. A 1500 × 2000 panel of 8 mm web, at d/t = 188. It buckles in shear at 41.0 N/mm², which is 492 kN — and it then carries 1187 kN, 2.41 times as much, because the tension diagonal takes over from the compression one that has gone. The band runs at 18.5° with a membrane stress of 348 N/mm² over a width of 788 mm, and it pulls on the flange at 280.2 N per millimetre of its length. A web that never buckled at all would have reached 2460 kN, so the panel ends at 48% of a stocky web's capacity on a fraction of its steel.

The tension has to pull on something

A buckled web carries its shear on a diagonal band of membrane tension, and the band pulls sideways on the flanges and stiffeners that bound it. That pull is the design output nobody plots — it runs from 72 to 603 newtons per millimetre across ordinary panel proportions, it is largest exactly where the panel is most efficient, and at the end of the girder there is nothing beyond to take it.

stability · Tension field Two models of one buckled web. The shear resistance of a web 1500 mm deep and 8.0 mm thick in steel of 355 N/mm², as a share of its plastic shear 2,460 kN, against the spacing of its intermediate stiffeners as a multiple of the depth, by Basler's tension field, by the rotated stress field with a rigid end post and with a non-rigid one, and by buckling alone; the dots at the right-hand edge are the same web with no intermediate stiffeners. With stiffeners at the depth Basler gives 0.71 and the rotated field 0.50; at three depths 0.38 and 0.42; with none, 0.14 — buckling alone — and 0.41. The two cross at a spacing of about 2.6 depths. Basler's reserve is a band the stiffeners anchor and it narrows to nothing as they move apart; the rotated field's is spread over the whole web and anchored at its ends, and the spacing reaches it only through the buckling stress.

Two reserves for one buckled web

A slender web keeps carrying shear after it buckles, and design uses two models of how: Basler's band of tension anchored on the stiffeners, and the rotated stress field spread over the whole web and anchored at its ends. Given the same 1,500 × 8 mm panel they agree about the buckling and disagree about everything after it — and in particular about what an intermediate stiffener is for. One says stiffeners save 37 per cent of the steel; the other, 1 per cent.

stability · Tension field

Named alongside it

The objects these essays reach for when they reach for this one.

Plate bucklingStiffenerPost-bucklingSlendernessAnchorageFlangePlate girderWebAccordion effectBoundary conditionsBuckling coefficientCorrugated web

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