Structural Engineering & Statics
where the load goes
Concept

Reciprocity — where it appears

Maxwell's theorem: the deflection at one point caused by a load at another equals the deflection at the second caused by the same load at the first. It halves the work of building influence lines and flexibility matrices, and it holds for any linear elastic structure.

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

10^-610^-410^-210^-1610^-1410^-1210^-1010^-8size of the dummy loadrelative errorround-offand nothing elsebest 2e-16∂U/∂P = 1.720635e-2 · unit load = 1.720635e-2

The deflection that is a derivative

A structure's strain energy is one number. Differentiate it with respect to a load and out comes the displacement under that load — and the trick that makes it a method rather than an identity is that the load does not have to be there.

deflection · strain energy 00.20.40.60.8100.20.40.60.81along the memberdensity ÷ its peak, and running sharewhere it comes fromrunning totalhalf nearest the root: 87.5% of it · worth 7.0× stiffening the other half

Where a deflection comes from

The unit-load method gives a deflection as an integral, and this collection has treated that integral as a number to evaluate. It is not a number. It is a density, and it says which millimetres of the member produced the answer — which is not the same map as where the moment is largest.

deflection · deflection distribution

Named alongside it

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

DeflectionStrain energyVirtual workCastiglianoComplementary energyCurvatureDummy loadFlexibilityHaunchInfluenceLinearityMoment diagram

All concepts