Structural Engineering & Statics
where the load goes
Concept

Torsion

5 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
2012.57.5shear 7.5moment 22.5the cut, at x = 5nothing was applied here — the internal forces are what the left-hand piece needs

What a cut reveals, and why it was there all along

Cut a beam anywhere and two quantities appear on the face — a shear force and a bending moment. Nothing was applied there. They are what the material was already doing.

internal-forces · internal forces closedJ = 5.66×10⁷ mm⁴twist 0.187° over 3.0 mpeak shear stress 8.5 N/mm²slit along its lengthJ = 1.31×10⁵ mm⁴twist 80.950° over 3.0 mpeak shear stress 305.2 N/mm²J closed ÷ J open = 432

The moment that will not lie flat

A plane cut exposes three actions. A real cut exposes six, and the fourth of them behaves unlike the others — torsion is resisted by a loop of shear, and one slit down the length of a tube destroys it.

internal-forces · internal forces the same, laid flatI = 0.06 × 10⁶1.0× the firstsquareI = 0.75 × 10⁶13.3× the firsttall rectangleI = 10.00 × 10⁶177.8× the firstI-sectionI = 24.29 × 10⁶431.8× the firstevery section here has an area of 3000 — only the shape differsthe bar is the second moment of area, to scale

The same steel in a different shape, and a factor of forty

Four sections of identical area, identical weight and identical cost. The stiffest is dozens of times the stiffest of the flattest, and the only thing that changed was the arrangement.

sections · section shape web centrelineshear centree = 31.7no twisttwiststhe flange flows are equal, opposite, and separated — which is a coupleand nothing about the section's 20.19 × 10⁶ second moment predicts it

The point that is not in the section

A channel loaded down its web twists. To stop it, the load must be applied through a point outside the steel entirely — in the air beside the section, where nothing can be attached.

sections · shear centre 2000400060008000100001200002004006008001000distance between lateral restraintsthey cross at 3803the plastic capacity of the sectionelastic critical momentSt Venant torsion alone — what is left at long lengthswarping dominates here

The beam that fails sideways

A deep narrow beam bending in its strong plane can, at a moment well below its capacity, swing out of that plane and twist. The failure has nothing to do with how much it can carry and everything to do with what is holding it.

stability · lateral torsional

Named alongside it

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

WarpingHollow sectionI-sectionOpen sectionShear centreShear flowStress resultantBending momentCompression flangeCritical momentEccentricityEffective length

All concepts