Structural Engineering & Statics
where the load goes
Generator

The moment-curvature generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
What it costs to reach the plastic moment, for two shapesMoment against curvature for two cross-sections of identical area (3000 mm²) and identical depth (200 mm), in mild steel, each divided by its own first-yield moment and its own first-yield curvature. The rectangle has a shape factor of 1.50 and reaches 98% of its plastic moment at 4.3 times the curvature at first yield; The I-section has a shape factor of 1.09 and reaches 98% of its plastic moment at 1.2 times the curvature at first yield. The dashed lines are the rigid-plastic moments, computed from the equal-area axis rather than read off the curves, and no curve reaches its own.02468101200.511.5curvature ÷ curvature at first yieldmoment ÷ moment at first yieldrectangle: 1.50× the yield moment, at 4.3× the yield curvatureI-section: 1.09× the yield moment, at 1.2× the yield curvature

5 essays call moment-curvature. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

00.5%1%2%2%0100200300400500600strainstress, N/mm²the 0.2% proof stress: 460 N/mm²mild steelhigh-strength steelaluminium Materials

The stress at which nothing in particular happens

One material in six has a yield point that a specimen actually does something at. For all the others the yield stress is a construction — a line drawn at an arbitrary offset — and every calculation on this site depends on it.

 00.5%1%2%2%050100150200250300350strainstress, N/mm²mild steelcast iron Materials

The property that appears in none of the equations

Ductility is in no design formula on this site. Every method on this site depends on it — and a brittle structure does not merely fail early, it makes the analysis wrong.

 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 Materials

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.

 neutral axisI-sectionstrainalways a straight linestressthe material's own curve, sidewaysC = 322.5 kN · T = 322.5 kN · lever arm 180 mm · M = 58.1 kNm0% of the area has yielded — 0 mm from the top, 0 mm from the bottom · Mp = 72.6 kNm · shape factor 1.09 Materials

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.

 flange outstandk = 0.4318.6 at 23515.2 at 35513.3 at 460quoted: 14ε1.33× the quoted limit, at every gradeweb, in bendingk = 456.8 at 23546.2 at 35540.6 at 460quoted: 42ε1.35× the quoted limit, at every grade0102030405060width ÷ thickness Materials

The section that cannot reach its own strength

A section classification looks like a table of arbitrary numbers. Set a plate's buckling stress equal to the yield stress and the numbers fall out of a formula written three phases ago — larger than the quoted ones by a constant factor, at every grade.

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