Torsional stress occurs when a material is subjected to a twisting force, or torque, causing it to rotate about its axis. This type of stress is common in shafts, gears, and other rotating components where torque is transmitted. Torsional stress is a form of shear stress, as it results from forces acting tangentially along a circular cross-section. The formula for torsional stress in a solid circular shaft is:
torsional stress = (torque × radius) / polar moment of inertia or τ = (T × r) / J,
where τ (tau) is the torsional stress, T is the applied torque, r is the radius of the shaft, and J is the polar moment of inertia, which depends on the cross-sectional shape.
Torsional stress is crucial in the design of drive shafts, axles, and couplings, where excessive twisting can lead to failure. Engineers analyze torsional stress to ensure components can handle applied torques without experiencing yielding, fatigue, or fracture.
