Free Keyway Stress Calculator
Calculate the shear and compressive (bearing) stress on a parallel key transmitting torque.
Shear Stress on Key
20.8 MPa
Shear Stress on Key vs Transmitted Torque (T)
Parallel Key Stress Analysis
A key transmits torque between a shaft and a hub (gear, pulley, coupling).
Formulas
The tangential force at the shaft surface: F = 2T / d
Shear stress = F / (w x L) (shear across the key width)
Bearing stress = F / ((h/2) x L) (crushing on half the key height)
where T is torque, d is shaft diameter, w is key width, h is key height, and L is key engagement length. Bearing stress is usually the governing criterion.
Example Calculation
A 12x8 mm key, 40 mm long, on a 40 mm shaft transmitting 200 N-m.
- 01F = 2 x 200,000 / 40 = 10,000 N
- 02Shear stress = 10,000 / (12 x 40) = 20.8 MPa
- 03Bearing stress = 10,000 / (4 x 40) = 62.5 MPa
- 04Bearing stress governs. For mild steel key (allowable bearing ~90 MPa), the key is adequate.
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