Free-body diagrams

A free-body diagram is a sketch of one body cut away from everything around it, with every external force drawn on it. It is the single most useful habit in mechanics, because most mistakes come from a missing or doubled force rather than from bad algebra.

To draw one, first decide what the body is: a whole beam, one joint of a truss, half of a frame cut at a section, or a block of soil. Then replace each support or contact with the forces it can supply. A roller gives one force normal to the surface. A pin gives two components. A fixed end gives two components and a moment. A cable can only pull along its own line. Self-weight acts at the centre of gravity. Distributed loads may be replaced by their resultant for reaction calculations, acting at the centroid of the load diagram.

Unknown forces are drawn in an assumed direction. If the answer comes out negative, the true direction is opposite. Internal forces never appear on the diagram unless you cut the body, and when you do cut it, the forces on the two cut faces are equal and opposite.

Good free-body diagrams carry dimensions, so lever arms can be read straight off. They are the starting point for reactions, truss member forces, retaining wall stability and slope stability alike.