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.
Facts
StatementThe potential energy of deformation of a body 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 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Clapeyron's theorem - Wikipedia
Introduction, sentence 1Quote, Introduction, sentence 1
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
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