Structural Engineering & Statics
where the load goes
Concept

Sign convention — where it appears

The agreement about which direction counts as positive, which every diagram in structural analysis depends on and none of them contains. Sagging positive, tension positive and compression positive are all in use, and a number is meaningless until one of them is named.

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

The same beam, cut at x = 5. A beam separated at one station. On the exposed face a shear force and a bending moment appear, equal and opposite on the two pieces, with values obtained by summing the forces on whichever piece is easier.

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 Load, shear and moment — a simple span. The applied load, the shear force it produces and the bending moment that follows, drawn one above another to the same horizontal scale. Shear is the integral of the load and moment is the integral of shear.

The diagram is an integral, and that is why it can be drawn by eye

Load, shear and moment are one function and its two integrals. Once that is seen, the diagrams stop being things to calculate and become things to sketch.

internal-forces · Diagram relations

Named alongside it

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

Area ruleBending momentDiscontinuityFree body diagramIntegrationLoad pathMoment diagramSaint-Venant's principleShear diagramShear forceStress resultantTorsion

All concepts