Torsion

Theory

For a circular shaft, the torsion formula gives shear stress τ = T·r/J, where T is torque, r is radial distance from centre, and J is the polar moment of inertia. Maximum shear stress occurs at the outer radius. The angle of twist φ = TL/GJ, where G is shear modulus and L is length. Thin-walled tubes resist torsion much more efficiently than solid sections of equal mass.

Application

Torsion is critical for drive shafts, rotary fixtures, motor mounts, and robot joints. FDM parts under torsion are particularly vulnerable because torsional shear acts at 45° to the principal axes: often intersecting with layer planes. Hollow sections (tube or box) carry torsion more efficiently than solid cylinders. For 3D-printed torsion members, orienting layers parallel to the dominant shear planes improves performance.

Common mistakes

The standard torsion formula assumes circular cross-sections. For non-circular sections (rectangular, I-beam), different formulas with Saint-Venant warping corrections apply. FDM parts with open cross-sections (C-channel, L-angle) have dramatically lower torsional stiffness than closed sections. Stress concentrations at keyways and holes under torsion amplify local shear stress by Kt factors of 1.5-3×.

Related terms: Shear Stress, Stiffness, Young's Modulus, Bending Moment