Structural Engineering & Statics
where the load goes
Concept

Plastic neutral axis — where it appears

The axis dividing a fully plastic section into equal areas, which is the centroid only for a symmetric shape and moves as a section yields. It divides the section into equal areas because the fully plastic stress block is two rectangles of equal stress, so equilibrium of axial force needs equal areas rather than equal first moments.

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

00.20.40.60.8100.20.40.60.81moment ÷ plastic momentaxial force ÷ squash loadrectangle: 25.0% of Mp outside the lineI-section: 6.0% of Mp outside the linethe straight-line rule

Two ways to fail, and the curve between them

A column carrying both compression and bending has two capacities and a rule for sharing them out. The rule is a straight line, the truth is a curve, and for a rectangle the straight line gives away a quarter of the plastic moment at half the squash load.

materials · interaction the same, laid flatZ top 7.5 × 10³Z bottom 7.5 × 10³the same both wayssquareZ top 27.4 × 10³Z bottom 27.4 × 10³the same both waystall rectangleZ top 100.0 × 10³Z bottom 100.0 × 10³the same both waysI-sectionZ top 242.9 × 10³Z bottom 242.9 × 10³the same both waysthe two solid lines are the extreme fibresthe bar is the smaller section modulus, to scale

Two strengths, depending which way up

A symmetric section has one section modulus. A tee has two, differing by a factor of three, so the same member has two bending strengths and which applies is decided by the sign of the moment. Turn it over and it is a different beam.

sections · asymmetric section

Named alongside it

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

Equal area axisNeutral axisAsymmetric sectionCentroidEccentricityElastic section modulusExtreme fibreFree bodyInteractionPlastic modulusPlastic momentSecond moment of area

All concepts