Structural Engineering & Statics
where the load goes
Concept

Second moment — where it appears

The integral of area times the square of its distance from an axis, which is what makes depth the cheapest strength there is.

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

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 rectangle±100 of 600 mm33.3% of the depth

The middle third

A material that cannot be pulled imposes a condition on where the load may land, and the condition is a region rather than a point. For a rectangle it is the famous middle third; for every other section it is a shape nobody quotes, and one ordinary section's is nearly twice as generous as the rule allows.

sections · kern

Named alongside it

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

Bearing pressureBending stressBiaxial bendingEccentricityKernNeutral axisNo tension materialPrincipal axesProduct of inertiaSection modulusShear centreThrust line

All concepts