Torsion—Pure Shear

Abstract

State of stress and strain in torsion. Shear strain and its relation with angle of twist. Relation between shear modulus and Young’s modulus. Torsional stresses in elastic range. Relation between torque, shear modulus and angle of twist. Torque computation in practical applications. Polar moment of inertia, shear stress and angle of twist for solid and hollow cylindrical shaft and thin-walled tube subjected to torsion. Behaviour of thin-walled tubes of non-circular cross-section under torsion. Torsional stresses for plastic strains, and ultimate torsional shear strength or modulus of rupture. Shape of torque-angle of twist diagram for a solid or hollow cylindrical shaft and for a thin-walled tubular specimen of a ductile material subjected to torsion. Specimen and equipment for torsion test. Different elastic and inelastic properties in torsion. Comparison between torsion and tension tests with respect to state of stress and strain developed in each test and ductile behaviour of materials. Torsional shear stress–strain diagram from tensile flow curve and failure under torsion. Problems and solutions.