Ausvex Engineering Tools

Shaft Stress & Torsion Calculator

Preliminary elastic torsion analysis for solid and hollow circular shafts. Calculate the polar second moment, maximum torsional shear stress and angle of twist, with an optional allowable-stress check.

Inputs

Shaft type

Applied torque T (N·m)

Outer diameter dₒ (mm)

Inner diameter dᵢ (mm)

Shaft length L (mm)

Shear modulus G (GPa)

Allowable shear stress (MPa), optional

Shaft section & torque

Solid circular shaft

Shear stress distribution

Calculate to plot the linear stress distribution through the material.

Results

Enter the inputs and calculate.

Method & assumptions

Uniform circular shaft under pure torque, using linear elastic Saint-Venant torsion.
Polar second moment J = π(dₒ⁴ − dᵢ⁴)/32.
Maximum shear stress τmax = Tr/J at the outer radius.
Angle of twist θ = TL/(GJ).
For a hollow shaft, the stress distribution is shown only through the annular material region.

Engineering aid only. This does not assess stress concentrations, keyways, splines, fatigue, yielding, buckling, combined loading or detailed design-code requirements.