Concept

Shear centre — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
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
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
40 kNm26.7 kNm13.3 kNmthe step at the load is 40 kNm, and the diagram closes

The internal force with no diagram

A cut through a member reveals four things, and this collection has drawn diagrams for three of them. The fourth is a torque, it obeys exactly the same rules, and whether it exists at all can depend on a decision the designer is free to make.

internal-forces · torsion
the axis the drawing suggestsneutral axis, -30.6°it moves this wayprincipal axes at 45.0° · I₁/I₂ = 3.90

Loaded straight down, and it moves sideways

Every section this collection has drawn had an axis of symmetry, and that symmetry has been doing silent work. Take it away and a vertical load produces a neutral axis that is not horizontal, a deflection that is not vertical, and on one ordinary section a sideways movement larger than the downward one.

sections · principal axes

Named alongside it

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

Shear flowTorsionWarpingOpen sectionTorsion constantBending stressBiaxial bendingCompatibility torsionEccentricityHollow sectionI-sectionInternal forces

All concepts