Castigliano's Theorem:

In the earlier sections we have seen that the strain energy stored up in an elastic body is equivalent to the work completed by the external forces on the body throughout the process of deformation. It suggests that there must be some way by which one might determine the displacements of the body given the strain energy stored up in the body. A general theory for calculating displacements of points in an elastic body was primary stated by Castigliano. Castigliano stated that "If the net strain energy of a body or a framework is expressed in terms of the external loads & it is partially differentiate with respect to one of the loads, the result is the displacement of the point of application of the load in the direction of the load."