Structural Engineering & Statics
where the load goes
Concept

Force equilibrium — where it appears

The requirement that the forces on a free body sum to zero in every direction, which supplies two equations in a plane and three in space. It is necessary and not sufficient: a body in force balance can still be turning.

Named by 2 essays across one field — 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 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. The moment of everything on the body is summed about three marked points, and every sum comes to zero. Nothing here is a new equation: with only vertical forces on the body, the moment about a point does not depend on that point's height, so every centre anywhere on the plane returns the same equation — and the third equilibrium equation, the horizontal sum, reads nothing equals nothing.

The equation that is not new, and the three that are

A plane free body yields exactly three independent equations. Most attempts at a fourth are one of the first three wearing different clothes — and on a beam under vertical load, one of the three is already saying nothing.

equilibrium · Equilibrium

Named alongside it

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

Free body diagramMoment equilibriumRigid bodyDeterminacyIdealisationIndependent equationsLine of actionMoment centreReactions

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