Gere & Goodno — Torsion: Problem 3.3-10

3.3-10 The steel shaft of a socket wrench has a diameter of 8.0 mm and a length of 200 mm (see figure). If the allowable stress in shear is 60 MPa, what is the maximum permissible torque \( T_{max} \) that may be exerted with the wrench? Through what angle \( \phi \) (in degrees) will the shaft twist under the action of the maximum torque? (Assume \( G = 78 \) GPa and disregard any bending of the shaft.)