The de Saint-Venant Problem

Paolo Maria Mariano and Luciano Galano
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Paolo Maria Mariano: University of Florence, DICeA
Luciano Galano: University of Florence, DICeA

Chapter Chapter 6 in Fundamentals of the Mechanics of Solids, 2015, pp 171-248 from Springer

Abstract: Abstract In this chapter, we discuss the classical de Saint-Venant problem: the equilibrium of a weightless right cylinder composed of a linear-elastic material, with boundary conditions foreseeing the action of external forces and couples just on the bases. The approach we follow is in terms of stresses. We derive a closed-form solution of the stress normal to the generic cylinder cross section using the balance and the Beltrami–Donati–Michell equations. Then we discuss the evaluation of the shear stresses due to shear and torsional actions. We include in this chapter 33 exercises. The chapter ends with a proof of Toupin’s theorem on de Saint-Venant’s principle.

Keywords: Shear Stress; Static Moment; Neutral Axis; Pure Torsion; Torsional Effect (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-3133-0_6

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DOI: 10.1007/978-1-4939-3133-0_6

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