Design a rectangular sunk key for a shaft of 50 mm diameter. The shearing and crushing stresses for the key material are 42 MPa and 70 MPa. From the standard key table the key is 16 mm wide and 10 mm thick. The key must transmit the full torque of the shaft, whose allowable shear stress is also 42 MPa. Find (a) the shaft torque (answer in N·mm), (b) the key length from shear and (c) the key length from crushing (answers in mm).