Shaft Key Shear Stress
Shaft Key Shear Stress
A key transmits torque between a shaft and a hub and is sized so it shears before the shaft does — a deliberate weak link.
The tangential force is F = T/r and the key shear stress is τ = F/(w·L). where T is the torque, r the shaft radius, w the key width and L the key length.
Inputs
T := 250 N·m=250 Nm
r := 20 mm=20 mm
w := 8 mm=8 mm
L := 40 mm=40 mm
The torque acts at the shaft surface as a tangential force.
F := T/r=12500 N
That force is carried in shear across the key’s side area.
tau := F/(w·L)=39.06 MPa
Results
The shear stress must stay below the key material’s allowable. A longer or wider key reduces it; bearing on the keyway sides should also be checked.
Assumptions & limitations
- Uniform shear across the key.
- Torque carried entirely by one key.
- Bearing/crushing checked separately.