Structural Engineering & Statics
where the load goes
Generator

The plane-sections 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.
Where plane sections stop staying planeStrain across a cut face at four span-to-depth ratios, with the straight line the theory assumes drawn faintly behind. For a slender beam the two coincide; for a beam as deep as its span the real distribution is nothing like a straight line, and beam theory has no claim on it.span ÷ depth = 8plane sections holdspan ÷ depth = 4plane sections holdspan ÷ depth = 2off by 19%span ÷ depth = 1off by 31%the assumption is the theory — everything else is arithmetic on top of it

2 essays call plane-sections. 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.

span ÷ depth = 8plane sections holdspan ÷ depth = 4plane sections holdspan ÷ depth = 2off by 19%span ÷ depth = 1off by 31%the assumption is the theory — everything else is arithmetic on top of it Sections and stress

Plane sections stay plane, and what the assumption costs

Beam theory rests on one sentence about geometry. It is very nearly true for a slender member, wrong for a deep one, and everything in the subject that fails does so where it stops holding.

 x = 1371200 mm² of steel, n = 7.5b = 30018.0 N/mm²371 kN in the steelz = 404C = T = 371 kN · C·z = 150.0 kNm = the applied momentcracked I 1139×10⁶ mm⁴ against uncracked 3422×10⁶ — 67% of the stiffness gone Sections and stress

When half the section has given up

Bending theory puts the neutral axis through the centroid. That is a consequence, not a rule — and when the tension side cracks, the same reasoning moves the axis somewhere else entirely.

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