Structural Engineering & Statics
where the load goes
Concept

Saint-Venant's principle

2 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
2012.57.5shear 7.5moment 22.5the cut, at x = 5nothing was applied here — the internal forces are what the left-hand piece needs

What a cut reveals, and why it was there all along

Cut a beam anywhere and two quantities appear on the face — a shear force and a bending moment. Nothing was applied there. They are what the material was already doing.

internal-forces · internal forces 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

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.

sections · plane sections

Named alongside it

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

Bending momentDeep beamFree body diagramLoad pathNeutral axisPlane sectionsShear forceSign conventionSpan to depth ratioStrain distributionStress resultantStrut and tie

All concepts