Metric shaft key stress
- Input
- 25 mm shaft, 8 x 7 x 40 mm key, 120 N m torque.
- Method
- Convert torque to tangential force and divide by areas.
- Formula
- F = 2000T/d; tau = F/(wL); sigma_b = 2F/(hL)
- Intermediate steps
- F = 2000 x 120 / 25 = 9600 N
- tau = 9600/(8 x 40) = 30 MPa
- sigma_b = 2 x 9600/(7 x 40) = 68.57 MPa
- Final result
- Shear about 30 MPa and bearing about 68.6 MPa.
- Interpretation
- Compare these stresses to selected allowable values and check shaft/hub design.
- Limitation
- The worked example is a planning illustration only and must be checked against standards, supplier data, CAD documentation, manufacturing limits, and professional engineering judgement.