How to use the Torsion of Shafts Calculator
- 1. Pick the jobCheck an existing shaft, or find the diameter you need.
- 2. Enter the loadPower and speed, or the torque directly, with shaft length and G.
- 3. Get the answerShear stress, twist, or minimum diameter, with each step shown.
Torsion equation
The torsion equation is T / J = τ / r = Gθ / L. Torque from power is T = 60P / (2πN), with P in watts and N in rpm.
- Solid shaft: J = πD⁴/32, so τ = 16T / (πD³).
- Hollow shaft: J = π(D⁴ − d⁴)/32, so τ = 16TD / [π(D⁴ − d⁴)].
- Angle of twist: θ = TL / (GJ) in radians.
- Design for strength: D = [16T / (πτ(1 − k⁴))]^(1/3), where k = d/D.
- Design for rigidity: D = [32TL / (πGθ(1 − k⁴))]^(1/4).
When both limits are given, use the larger diameter. If the torque varies, design for the maximum torque.
Worked example and exam tips
A solid shaft transmits 97.5 kW at 180 rpm with an allowable shear stress of 60 MPa. T = 60 × 97 500 / (2π × 180) = 5172.5 N·m. D = (16 × 5 172 500 / (π × 60))^(1/3) = 76.0 mm, so use the next standard size, 80 mm.
- Convert everything to N and mm: torque in N·mm, G in N/mm².
- The shear stress is zero at the centre and largest at the outer surface. That is why a hollow shaft of the same weight is stronger.
- Twist is usually limited to about 1° over a length of 20 diameters, or 0.25° per metre. Use the value given in your question.
Frequently asked questions
Why is a hollow shaft stronger for the same weight?
Material near the centre carries very little stress. Moving it outwards raises J, so a hollow shaft carries more torque per kilogram.
What value of G should I use?
About 80 GPa for steel is common in textbooks, but use the value given in your question or data book.
What does the max to mean torque ratio do?
Engines and compressors give a varying torque. The shaft must be designed for the peak, so the mean torque is multiplied by this ratio.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.