31. A thin-walled tube is subject to a torque T. The only non-zero stress component is the shear stress rA-y, which is given by tVj, = 10,000 T(Pa), where Tis the torque in N.m. When the yield strength cry = 300 MPa and the safety factor N = 2, calculate the maximum torque that can be applied using

(a) Maximum principal stress criterion (Rankine)

(b) Maximum shear stress criterion (Tresca)

(c) Distortion energy criterion (Von Mises)