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On the cross section of minimum stress concentration in the Saint-Venant theory of torsion

✍ Scribed by L. E. Payne; L. T. Wheeler

Book ID
104619050
Publisher
Springer Netherlands
Year
1984
Tongue
English
Weight
130 KB
Volume
14
Category
Article
ISSN
0374-3535

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✦ Synopsis

A lower bound is derived for the maximum stress in the torsion of cylindrical solids of simply-connected cross section. This bound, which is expressed in terms of the applied torque and the cross-sectional area, is isoperimetric in that it coincides with the maximum stress when the cross section is circular. It confirms the notion that given the applied torque and the area of the cross section, the least maximum stress occurs when the section is circular. Related isoperimetric upper bounds are derived for the minimum value of the stress at boundary points.

πŸ“œ SIMILAR VOLUMES

Upper and lower bounds for the shear str
Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure
✍ Lewis Wheeler; Cornelius O. Horgan πŸ“‚ Article πŸ“… 1976 πŸ› Springer Netherlands 🌐 English βš– 722 KB

Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness. ## RI~,SUMI~ On d6rive des limites sup6rieures et inf