Structural Engineering & Statics
where the load goes
Concept

First yield — where it appears

The moment at which a section's furthest fibre reaches the yield stress, the elastic modulus times the yield stress. It marks when an edge has reached its limit, and a ductile section goes on carrying more; what it measures is how far that fibre stands out from the neutral axis.

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

A I-section at 80% of its plastic moment. The same I-section drawn three ways: the shape, the strain across its depth, and the stress that strain produces in mild steel. The strain diagram is a straight line, because plane sections stay plane whatever the material is doing. The stress diagram is not: 0% of the area has yielded, working inward from both faces, and the neutral axis sits at 70.9 mm against a centroid at 100.0 mm. The compression resultant is 322.5 kN and the tension resultant 322.5 kN, on a lever arm of 180.1 mm, which multiplies back to the 58.1 kNm the section is carrying. A rolled residual stress pattern of ±30% of yield is locked in before any load arrives.

The stress that was there before the load

A rolled steel section leaves the mill carrying eighty N/mm² of stress with nothing applied to it, in a pattern that sums to no force and no moment. It is invisible to every calculation and it is the knee in every column curve.

materials · Residual stress Cutting off the tips raises one strength and lowers the other. A diamond's first-yield modulus, plastic modulus and area, each as a share of the whole section's, against the height kept. At 0.889: the elastic modulus 1.053, the plastic 0.966, the area 0.988.

The section stronger for being cut

Take a square bar standing on its corner, and saw a ninth off its top and bottom tips. It has lost material from the places where material does most for bending, and its first-yield moment has gone up by 5.35 per cent. Nothing has gone wrong with the arithmetic. The bar's plastic moment has gone down in the same cut, and at every curvature the whole bar still carries more than the cut one. What the cut exposes is that a first-yield moment was never a measure of how much a section can hold. It is a measure of how far its furthest fibre stands out.

sections · Shape factor

Named alongside it

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

Column curveImperfectionMoment-curvaturePlastic modulusPlastic momentProof stressResidual stressSection modulusSelf-equilibratingShape factorTangent modulusWelding

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