Shaft Strength Calculator

Finds the combined bending and torsion stress in a shaft by the von Mises and maximum shear theories, the safety factor against yield, the diameter for a target safety factor and the angle of twist.

How to use

1. Enter "Shaft diameter d"; for a hollow shaft tick "Hollow shaft" and enter "Inside diameter di".
2. Enter "Bending moment M" and "Torque T" in N·m, or choose "From power and speed" and enter "Transmitted power P" and "Speed n".
3. Enter "Yield strength Sy", "Shear modulus G" and the "Target safety factor".
4. Under "Stress concentration" pick a keyseat or shoulder. The stresses, safety factors, required diameter and twist appear at once.

How it works

• σ = Kt·M ÷ Z, τ = Kts·T ÷ Zp with Z = πd³ ÷ 32, Zp = πd³ ÷ 16. Von Mises σ' = √(σ² + 3τ²), maximum shear τmax = √((σ ÷ 2)² + τ²); safety factors Sy ÷ σ' and 0.5Sy ÷ τmax.
• Required diameter: d³ = 32n√(M² + 0.75T²) ÷ (π·Sy) (von Mises) or 32n√(M² + T²) ÷ (π·Sy) (maximum shear). Me and Te are shown too.
• Preset Kt values are the first-iteration estimates of Table 7-1 in Shigley's Mechanical Engineering Design, 10th edition. This is a static yield check; fatigue, deflection and critical speed are not covered.

Questions and answers

How do I calculate the diameter of a shaft?

With M = 200 N·m, T = 300 N·m, Sy = 345 MPa and a safety factor of 2, the maximum shear theory gives d ≈ 27.7 mm. A keyseat needs more.

How do I get torque from power and rpm?

T[N·m] = 9549.3 × P[kW] ÷ n[rpm]; 5.5 kW at 1450 rpm gives about 36.2 N·m.

Should I use von Mises or the maximum shear stress theory?

Both apply to ductile materials; maximum shear is about 15 % more conservative. The tool takes the larger required diameter.

Does this cover fatigue of a rotating shaft?

No. A rotating shaft sees reversed bending every revolution, so a separate fatigue design with endurance limit and correction factors is needed.