10.2. Work Done in Deformation

Consider a set of forces (applied forces and reactions) P_k(k ≈ 1, 2,..., m), acting on an elastic body (Fig. 10.1), for example, a beam, truss, or frame. Let the displacement in the direction of P_k of the point at which the force P_k is applied be designated δ_k. It is clear that δ_k is attributable to the action of the entire force set, and not to P_k alone. Suppose that all the forces are applied statically, and let the final values of load and displacement be designated P_k and δ_k. Based on the linear relationship of load and deflection, the work W done by the external force system in deforming the body is given by .

Figure 10.1. Displacements of an elastic body acted on by several forces.