A truss is an idealized structure made from straight members joined so that each member carries only axial force.

The usual idealizations are:

• joints behave as pins;
• external loads are applied at joints;
• member self-weight is neglected or represented through equivalent joint loads.

Under these assumptions, a truss member is a two-force member: the forces at its ends are equal, opposite and collinear. The member is therefore either in tension or compression.

Why triangles are fundamental

A triangle cannot change shape without changing at least one side length. A pin-jointed quadrilateral can deform while its side lengths remain unchanged, so diagonal bracing is needed to make it geometrically stable.

This is why larger trusses are usually assembled from triangular patterns.

External and internal forces

Before member forces can be found, the support reactions of the complete truss must be determined from static equilibrium.

The structure can then be analysed joint by joint or by cutting through selected members.