Structural Engineering & Statics
where the load goes
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Multicell torsion — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The web down the middle carries no torsion at all. A 2-cell box 3.0 m wide and 1.5 m deep under 4000 kNm of torque. Statics gives one equation, T = 2 Σ q_i A_i, and there are 2 unknown flows — so the section is torsionally redundant and the missing statements are that every cell twists by the same amount. Solving that system gives 444.4 and 444.4 N/mm in the cells, so the internal web carries 0.00 N/mm — 0.00 per cent of the outer wall's. J is 2.3679e+12 mm⁴ against 2.3679e+12 for the same outline with no internal web at all, a ratio of 1.000000. The same walls slit open would give 7.413e+10, so closure is worth 32 times and the internal web is worth what the ratio says.

    Two cells, one equation, and a web with nothing in it

    Bredt's formula answers a single closed cell because a single closed cell has one unknown and one equation. Put a web down the middle and there are two unknowns and still one equation — and the answer, when the missing statement is supplied, is that the new web carries exactly nothing.

    part 1 · sections
  2. 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.

    part 2 · sections

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