The previous chapter addressed the shear stress distribution due to a shear force. In this chapter we look at the sh ear stresses caused by torsional moments. We will also look at the deformation due to torsion.
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In Engineering Mechanics, Volume 4, we cover the complete Hooke’s law.
See Section 1.2.
Twisting or torsional moments act in the plane of the cross-section. They are shown by means of bent arrows in the plane of the cross-section, but also, as in Figure 6.4, by means of straight arrows with a double arrow head, normal to the plane of the cross-section. See Engineering Mechanics, Volume 1, Sections 3.3.1 and 10.1.3.
They apply not only to thin-walled tubes but also to members with other crosssections.
Adhémar Jean Claude Barré de Saint Venant (1797–1886) published many important papers on the theory of elasticity and on the strength of materials. In 1853 he developed the fundamental differential equation for elastic torsion.
Warping is not restrained.
Rudolph Bredt (1842–1900), German engineer, developed the theory for a thinwalled tube subject to torsion and published it in 1896.
See also Engineering Mechanics, Volume 1, Section 15.3.2.
Sometimes It is called the torsional moment of inertia. This unfortunate nomenclature is due to the analogy of the constitutive relationships Mt = GItχ and M = EIκ for torsion and bending respectively. For bending, the quantity I is known as the moment of inertia.
The moment vector has a double arrow head and is normal to the plane in which the moment acts. The direction of the moment vector and the direction of rotation of the moment are related via the corkscrew rule or right-hand rule, see Engineering Mechanics, Volume 1, Section 3.3.1.
See Engineering Mechanics, Volume 1, Section 10.1.3.
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(2007). Bar Subject to Torsion. In: Engineering Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5763-2_6
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