A simple analysis, using the method of joints, assumes that external forces will only act at the joints, and that the beams are perfectly rigid. This allows for only longitudinal forces in the beams. Given these assumptions, the truss is stable if and only if the vertical and horizontal components of the forces at each joint sum to zero. For example, in the joint shown to the left, the beams are under compression. Their internal forces, therefore, tend to act against the compression and out against the joint.
Static equilibrium demands that and .
In particular, using the capital letters to denote the magnitude of force along a beam, Because each joint will give such equations, the total number of equations that can be written, under our assumptions, is twice the number of joints. Normally, we are interested in finding the internal beam forces and the reaction forces at the support under some external load. Thus the number of unknowns is the number of beam forces plus the number of reaction forces. This is because the basic buliding blocks are triangular shapes. Thus, under our assumption of perfect rigidity, the truss cannot move even under some external load.