Engineering & mechanics
Circular shaft torsion
Calculate elastic shear stress and twist for solid or hollow circular shafts.
A clear answer. Here’s how.
Uses J=π(Do⁴−Di⁴)/32, maximum shear stress=T Do/(2J), and twist=TL/(GJ). Inner diameter must be less than outer diameter. Assumes a uniform circular shaft, elastic material and pure Saint-Venant torsion. Stress concentrations, combined bending, yielding and end effects are excluded.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Outer diameter (mm)
- 30
- Inner diameter (mm; zero for solid)
- 0
- Torque magnitude (N·m)
- 100
- Shaft length (m)
- 1
- Shear modulus (GPa)
- 80
Example result
- Polar second moment J (m⁴)
- 0.000000079521564044
- Maximum shear stress (MPa)
- 18.8628080702
- Twist angle (radians)
- 0.0157190067251
- Twist angle (degrees)
- 0.900632743487