Structural Engineering & Statics
where the load goes
Concept

Plastic modulus — where it appears

The first moment of a section's two halves about its equal-area axis, which multiplied by the yield stress gives the fully plastic moment.

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

024681000.511.5curvature ÷ curvature at first yieldmoment ÷ moment at first yieldrectangle: 1.50× the yield moment, at 4.1× the yield curvatureI-section: 1.09× the yield moment, at 1.1× the yield curvature

The section that yields from the outside in

A rectangle has half again as much moment in reserve past first yield as its elastic capacity suggests, and an I-section has a seventh. Read as a ranking that gets it backwards — the reserve is bought with curvature, and the rectangle pays four times as much of it.

materials · moment curvature 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.

Neutral axisSection modulusShape factorAsymmetric sectionCentroidDuctilityElastic section modulusEqual area axisExtreme fibreMoment curvaturePlane sectionsPlastic moment

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