Hollow circular shaft torsion

Relates torque to outside/inside diameter for a hollow circular shaft in pure torsion.

VERIFIED FORMULA RECORD

T = (πτ/16)((Do⁴ − Di⁴)/Do)

Relates torque to outside/inside diameter for a hollow circular shaft in pure torsion.

Machine DesignVerifiedReviewed 2026-08-09

Variables and units

T = torque (N·mm)

τ = selected allowable shear stress (N/mm²)

Do = outside diameter (mm)

Di = inside diameter (mm)

Conditions and limitations

  • Uniform hollow circular section
  • Pure torsion
  • Outside diameter is solved numerically

Source: J. E. Shigley et al., Mechanical Engineering Design, torsion of circular shafts.

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