Shaft Torsion

Torsional shear stress and angle of twist of a circular shaft, solid or hollow.

ShaftTorsionStiffness

Maximum shear stress τ39.8MPa

METHOD

How it is calculated

J = π·(D⁴ − d⁴) / 32
τ_max = T · (D/2) / J
φ = T · L / (G · J)

ASSUMPTIONS & NOTES

G ≈ 80 GPa for steel, ≈ 26 GPa for aluminium, ≈ 40 GPa for cast iron.
Stiffness often governs before strength; twist matters for gear and belt shafts.

Results are for preliminary design and checking; base the final design on the governing standard and safety factors.

RELATED TOOLS

Deflection, moment, shear and bending stress for simply supported and cantilever beams, with a section table.

Area, second moment, section modulus, radius of gyration and mass per metre for rectangles, rounds, tubes, boxes and I-sections.

Critical buckling load of a strut using Euler or Johnson by slenderness, plus the allowable load.

Plane stress: principal stresses, maximum shear, principal angle, von Mises and Tresca equivalent stress.

Length change with temperature and the thermal stress in a fully restrained member.

Minimum solid shaft diameter under combined bending and torsion (ASME shaft code), with a standard size.