Work out torsion of a shaft instantly with clear inputs, formula shown and shareable results.
Torsion of a circular shaft follows tau = Tr/J with J = pi d^4/32, so surface stress is highest and the centre carries almost nothing - which is why hollow shafts are so efficient. 1200 N m on a 50 mm shaft gives 48.9 MPa at the surface and twists a 1.5 m length by about 1.05 degrees.
Torsional shear stress
tau = T r / J, J = pi d^4 / 32
Angle of twist
theta = T L / (J G)
Because the material near the axis is barely stressed. Removing it saves weight with little loss of torsional strength.
Machine design practice limits it to about 1 degree per metre of length for power transmission shafts.