Elastic Torsion of a Circular Shaft

Mechanical Engineering

How It Works

When a circular cylindrical shaft is subjected to an external twisting moment or torque (T), internal torsional shear stresses are generated across its transverse cross-section. In accordance with Saint-Venant's torsion theory, plane circular sections remain plane and radius lines remain straight without warping. Torsional shear stress (τ) varies directly in proportion to radial distance from the central polar axis, reaching its maximum at the outer shaft radius.

Governing Equation
τ(r) = (T · r) / J , φ = (T · L) / (G · J) , J = (π · d⁴) / 32