Structural Engineering & Statics
where the load goes
Generator

The reciprocity 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.
Maxwell's reciprocal theoremA load at one point and the deflection it causes at another, against the same load moved to the second point and the deflection read at the first. Both integrals return 93.3335, and neither calculation was told about the other. The two deflected shapes are entirely different; the two readings are identical.20 at 2δ at B = 93.33320 at 6δ at A = 93.334the shapes have nothing in commonand the two readings agree to 1e-14which is why an influence line can be measured by pushing the structure where it is easy to push

2 essays call reciprocity. 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.

20 at 2δ at B = 93.33320 at 6δ at A = 93.334the shapes have nothing in commonand the two readings agree to 1e-14which is why an influence line can be measured by pushing the structure where it is easy to push Deflection

The theorem that swaps the question round

Push here and measure there; push there and measure here. The two readings are identical, for every elastic structure, whatever its shape — and that fact turns an influence line into something a model can be asked for directly.

 this support 0.01 lowmoment19.6 sagging24.5 hogging30.6 if the spans were simplereactions 14.0 38.5 38.5 14.0 — the inner supports carry far more than a sharethe continuous case needed stiffness; the comparison did not Deflection

The support that moved

A redundant structure knows things statics cannot see. Settle one support by ten millimetres and a complete set of bending moments appears — in equilibrium with no load at all, and larger for a stiffer beam.

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