Saint-Venant's theorem, named for the French engineer and mathematician Adhemar Jean Claude Barre de Saint-Venant, concerns beams of constant cross section under torsion. It states that, among all simply connected cross-sectional shapes of a given area, the circle has the greatest torsional rigidity, a measure of how strongly a shape resists twisting. Saint-Venant conjectured the result in 1856, but a rigorous proof wasn't supplied until 1948, by George Polya, with further proofs given afterward by Harold Davenport and by Endre Makai.
Facts
StatementThe simply connected cross section with maximal torsional rigidity is a circle. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Saint-Venant's theorem - Wikipedia
Proved By
Source Saint-Venant's theorem - Wikipedia
Sources
1. Saint-Venant's theorem - Wikipedia
Introduction, sentence 2
Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity is a circle.
Body, paragraph after the torsional rigidity definition
A rigorous proof of this inequality was not given until 1948
Proved By: George Pólya, Lead
A rigorous proof of this inequality was not given until 1948 by Pólya.
In Branch: Mathematical Physics, Lead section
In solid mechanics, it is common to analyze the properties of beams
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.