Clapeyron's Theorem

Clapeyron's theorem, named after the French engineer and physicist Emile Clapeyron, states that the potential energy stored by the deformation of a body in equilibrium under a given load equals half the work that would be done by the external forces if those forces had remained constant, at their final value, throughout the loading process. A simple linear spring illustrates the result: stretching it from length L0 to equilibrium length L1 under a final force F stores potential energy of one-half F times the extension, even though the actual force built up gradually from zero. The same name is sometimes also given, in a different context, to the theorem of three moments used in the analysis of continuous beams and bridges.