Structural Engineering & Statics
where the load goes
Concept

Reactions — where it appears

The forces and moments a support supplies to hold a structure in equilibrium. For a determinate structure they follow from statics alone; for an indeterminate one they depend on the relative stiffnesses and on any movement the supports have undergone.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A beam, its loads and its reactions. A free body: the beam cut away from everything it touches, with the forces that were doing the touching drawn on it. The reactions are computed from the loads, so their arrows are to scale relative to each other.

Everything adds to nothing, and that is the whole of statics

A structure that stays put obeys two statements — the forces on it sum to zero, and so do the moments. Every number in the subject comes out of those two sentences.

equilibrium · Equilibrium 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.

The free body is a choice, and choosing it well is the whole skill

Cutting a structure open is not a step in the method. It is the method — and where the cut is made decides whether the answer takes one line or twenty.

equilibrium · Free body Where to put the supports. Peak sagging and hogging moment for a uniformly loaded beam, against how far the supports are moved in from the ends. The best arrangement is where the two curves cross, and it is nowhere near the ends.

Where to put the supports, which is not at the ends

Moving the supports of a uniformly loaded beam inward by about a fifth of its length halves the worst bending moment. The load has not changed and nor has the beam.

internal-forces · Support layout

Named alongside it

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

Free body diagramBoundaryContinuityEquilibriumForce equilibriumHogging and saggingIdealisationInternal forcesMethod of sectionsMoment envelopeMoment equilibriumNewton's third law

All concepts