A standard technique for finding the shear stress-strain relation of a material employs a torsion test on a solid circular cylinder. It is shown that the exact solution is easily obtained as a correction to the sometimes-used quasielastic approximation. The solution is extended to the case of hollow cylinders. The analysis is shown to be applicable also to the case where a constant axial stress is present, and to a special case of planar isotropic materials.

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