DIVE-LD reference desk

Shaft Torsion Reference

Shafts

Core relationships

τ = Tr/J

θ = TL/(JG)

Solid: J = πd⁴/32

Tube: J = π(dₒ⁴−dᵢ⁴)/32

Geometry insight

Diameter has a fourth-power effect on J. Material near the outer radius contributes more strongly to torsional stiffness than material near the center.

Review connections

  • Keyways and splines
  • Shoulders and fillets
  • Cross holes
  • Press fits
  • Bearing seats
  • Couplings

Beyond simple torsion

  • Combined bending + torsion
  • Fatigue and load spectrum
  • Critical speed / vibration
  • Surface finish and residual stress
  • Stress concentration