Shaft torsion
How torque, selected allowable shear stress and circular shaft geometry are related in a transparent preliminary sizing check.
ENGINEERING PRINCIPLE
Torque produces a linearly varying shear stress through a circular shaft section; the maximum is at the outside radius.
τmax = 16T/(πd³)Variables and units
- T in N·mm
- d in mm
- τ in N/mm² (MPa)
Worked example
For 98,793 N·mm and selected τ = 37.5 MPa, d = ∛(16T/(πτ)) = 23.7 mm before rounding upward to a selected stock or manufactured size.
Calculation method
- Convert torque to N·mm.
- Choose an allowable shear stress that reflects the material condition and design policy.
- Solve for d, then assess bending, fatigue, keyways and stiffness separately.
Practical applications
- Motor and gearbox output shafts
- Rotating process equipment
- Power-transmission sizing studies
Review boundary and reference
- Pure torsion is not a complete shaft design.
- Use the applicable code and a documented load spectrum for final release.
Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.
Source: J. E. Shigley et al., Mechanical Engineering Design, torsion of circular shafts.