Forces and equilibrium

A force is a push or pull with a size, a direction and a point where it acts. Civil engineers deal with forces all day: the weight of a slab, wind on a hoarding, water against a dam, a truck braking on a bridge. Before anything can be designed we must know whether the forces on a body balance.

A body is in equilibrium when it neither starts to move nor starts to rotate. In a flat (two-dimensional) problem that gives exactly three conditions: the forces must add to zero horizontally, add to zero vertically, and their turning effects (moments) about any point must add to zero. Three equations means we can find at most three unknown forces from statics alone, which is why a simply supported beam, with one pin and one roller, can be solved by hand.

The working method is always the same. Isolate the body, draw every force acting on it (the free-body diagram), choose a sign convention, then write the three equations. Taking moments about a point where unknown forces meet removes those unknowns from the equation and shortens the algebra.

Equilibrium is the first check on every structure in this library, from a lintel to a cable-stayed bridge. If a structure has more unknown support forces than equations, it is statically indeterminate and needs the deformation methods taught in Structural Analysis.