Forces in structural frameworks
At nodes pinned to external rigid supports the induced reaction forces must also be accounted in the overall equilibrium. In a plane framework, two equations of static equilibrium (f.H = 0 and EV = 0) may be obtained for each joint. Thus, a total of 2j equations will be available for the solution of m member forces and s support reactions; i.e. for a perfect frame:
m + s = 2j [2.2] In calculating a value for s, the degrees of freedom at each joint must be considered. For example, a joint pinned to a horizontal roller: no horizontal reaction force can be developed, i.e. H = 0, and thus s = 1. At a pin-joint support, s = 2.