KEVOS® MAKEOS · Strength
Shaft Diameter for Bending and Torsion
What shaft diameter carries this bending moment and torque at the allowable shear stress?
Minimum solid shaft diameter for combined bending and torsion by the maximum-shear-stress theory with shock and fatigue factors, and the stress in a chosen diameter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Maximum bending moment | N·m | Largest bending moment at the section, from the shaft’s bending moment diagram. |
| Torque | N·m | Torque transmitted through the section. |
| Shock and fatigue factor, bending (Km) | Combined shock and fatigue factor for bending, from your design method (the ASME code suggests about 1.5 for gradually applied loads on rotating shafts). | |
| Shock and fatigue factor, torsion (Kt) | Combined shock and fatigue factor for torsion (about 1.0 for gradually applied loads in the ASME code). | |
| Allowable shear stress | MPa | Allowable shear stress from your design method; the ASME code uses the lower of 0.3 × yield and 0.18 × tensile strength. |
| Keyway at the section | choice | A keyway at the section reduces the allowable stress by 25% in the ASME code method. |
| Actual diameter to check (0 = none) | mm | Diameter of an existing or proposed shaft to check. |
Method and formulas
- Equivalent torque Te = √((Km M)² + (Kt T)²).
- Required d = (16 Te ÷ (π τ_allow))^(1/3), with τ_allow × 0.75 when a keyway is present.
- Check: τ = 16 Te ÷ (π d³).
- Example: M 300 N·m and T 500 N·m need at least 48.516 mm; a 50 mm shaft runs at 27.407 MPa.
Limitations
- Solid circular shafts; for hollow shafts use the polar section modulus.
- Stress concentrations at shoulders and grooves need a fatigue check (see the Goodman tool); deflection and critical speed are separate checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size line shafts, pulley and gear shafts
- Check an existing shaft after a load change
- Compare the effect of a keyway
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Required diameter
- Equivalent torque
- Shear stress and safety ratio in the checked diameter
Interpreting the result
- Round up to a standard size and check bearing seats, key and deflection.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
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