Structural Engineering & Statics
where the load goes
Concept

Bredts formula — where it appears

The shear flow round a closed thin-walled section under torque: the torque divided by twice the area enclosed by the wall's centreline. It is constant round the circuit whatever the wall thicknesses, which is why a closed section is hundreds of times stiffer in torsion than an open one of the same material.

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

One slit, and the torsional stiffness falls by a factor of hundreds. A 200 by 200 box of 8 mm wall, drawn closed and then slit along its length. Closed, the torque runs round the wall as a shear flow and the torsion constant is 5.66×10⁷ mm⁴; slit, the loop is broken and only each wall's own thickness resists, giving 1.31×10⁵ mm⁴. The ratio is 432 to one, so the same torque twists the slit section 432 times as far and raises a peak shear stress 36 times as high. Nothing about the material changed.

The slit that costs a factor of six hundred

Bending stiffness cares where the material is, and changes by a factor of two or three between sensible sections of the same area. Torsional stiffness cares whether the material forms a closed loop, and the penalty for not doing so is an order of magnitude squared.

sections · Torsional constant Two webs of one box, carrying different amounts of the same load. The equivalent stress on each web of a 3.0 × 2.0 m box along the half span, under 40 N/mm at an eccentricity of 1500 mm, with the bending stress alone drawn for comparison. The two webs carry the same bending and opposite torsion, so one gets the sum and the other the difference: at the quarter point the loaded web is at 116 N/mm² and the far web at 11, a ratio of 10.9. A check made on the section rather than on the wall reports the average of two numbers that differ by that much.

Three actions on one web

A load applied off the centreline of a box girder is three actions at once, and every textbook decomposes it into them. What the decomposition does not say is that all three land on the same piece of plate — added on one web and subtracted on the other, so the two walls of one section differ by a factor of ten.

sections · Multicell torsion

Named alongside it

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

Shear flowTorsionWarpingBimomentBox girderClosed sectionDecay lengthDiaphragmDistortionEccentricityEquilibriumEquivalent stress

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