Betti's theorem, also known as the Maxwell-Betti reciprocal work theorem, was discovered by Enrico Betti in 1872. It states that for a linear elastic structure subjected to two different sets of forces, the work done by the first set of forces acting through the displacements produced by the second set equals the work done by the second set acting through the displacements produced by the first. The theorem is used in structural engineering to define influence lines and to derive the boundary element method.
Facts
StatementBetti's theorem states that for a linear elastic structure subject to two sets of forces, the work done by the first set of forces acting through the displacements produced by the second set of forces equals the work done by the second set of forces acting through the displacements produced by the first set of forces. 2 Classification
Statement Form Connections
Has Statement Form
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. Wikipedia: Betti's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Betti's theorem, also known as Maxwell-Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {Pi} i=1,...,n and {Qj}, j=1,2,...,n, the work done by the set P through the displacements produced by the set Q is equal to the work done by the set Q through the displacements produced by the set P.
2. Betti's theorem - Wikipedia
Lead paragraph
the work done by the set P through the displacements produced by the set Q is equal to the work done by the set Q through the displacements produced by the set P
Lead paragraph, discovery year
discovered by Enrico Betti in 1872
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.