In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the external forces computed assuming these forces had remained constant from the initial state to the final state.[1]
It is named after the French scientist Benoît Clapeyron.
For example, consider a linear spring with initial length L0 and gradually pull on the spring until it reaches equilibrium at a length L1 when the pulling force is F. By the theorem, the potential energy of deformation in the spring is given by:
| 1 | |
| 2 |
F(L1-L0).
The actual force increased from 0 to F during the deformation; the work done can be computed by integration in distance. Clapeyron's equation, which uses the final force only, may be puzzling at first, but is nevertheless true because it includes a corrective factor of one half.
Another theorem, the theorem of three moments used in bridge engineering is also sometimes called Clapeyron's theorem.