Out-of-Plane Displacements and Stresses in a Torus

by David J. McGill,

Serial Information: Journal of the Engineering Mechanics Division, 1967, Vol. 93, Issue 4, Pg. 55-68

Document Type: Journal Paper


The out-of-plane elasticity problem of solid tori, which involves the circumferential displacement and a pair of shearing stresses, is studied. A four-term perturbation solution for the displacement in power series of the torus radii ratio gives good convergence of displacements, and of resulting stresses and strains, over most of the range of possible radii ratios. The tori are loaded circumferentially by sinusoidal shearing stresses, and for small radii ratios they include the problem of rings loaded in this manner. The shearing stress in planes perpendicular to the radial coordinate is shown to have a maximum value two to three times larger than the amplitude of the applied shearing stress.

Subject Headings: Shear stress | Displacement (mechanics) | Load factors | Elastic analysis | Convergence (mathematics) | Stress strain relations | Radiation

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