Printable reference · V0.7
Shaft Torsion Reference
A printable reference for circular-shaft torsion, stiffness and design-review prompts.
DIVE-LD reference desk
ShaftsShaft Torsion Reference
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