Shaft diameter calculator
Estimate the minimum solid shaft diameter for combined bending and torsion, using an allowable shear stress.
How it is calculated
Equivalent torque Te = √(M² + T²). Minimum diameter d = ∛(16 × Te ÷ (π × τ)), with Te in N·mm and τ in MPa.
Worked example
T = 500 N·m, M = 0, τ = 40 MPa: d = ∛(16 × 500,000 ÷ (π × 40)) = 39.93 mm.
Steps
- Enter the bending moment at the critical section.
- Enter the torque transmitted by the shaft.
- Enter the allowable shear stress, then round the result up to a standard diameter.
Frequently asked questions
How do I pick the allowable shear stress?
A common design value is 0.18 to 0.3 of the yield strength, with a safety factor. Use your design code for the final value.
Does this include stress concentration?
No. Keylways, shoulders and fillets need a fatigue factor (Kt). Apply it to M and T before using this calculator, or use a full fatigue analysis.
Is this for hollow shafts?
No. This is a solid round shaft only.
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References
Maximum shear stress theory for combined bending and torsion (Shigley, Mechanical Engineering Design, ASME shaft method).
Estimates for information only. Verify critical values with a qualified engineer or your supplier standards.