On the surface of the shaft, determine (a) the principal stresses, and (b) the directions of the principal planes relative to the shaft axis. Make a diagram to clearly show the direction of the principal planes and stresses relative to the shaft axis. [U.L.][90.8, 14.7, 98.4, -83.7 MN/m^2; 47° and 137°]
13.14 (B) A hollow shaft is 460 mm inside diameter and 25 mm thick. It is subjected to an internal pressure of 2 MN/m^2, a bending moment of 25 kN m and a torque of 40 kN m. Assuming the shaft may be treated as a thin cylinder, make a neat sketch of an element of the shaft, showing the stresses resulting from all three actions. Determine the values of the principal stresses and the maximum shear stress. [21.5, 11.8, 16.6 MN/m^2.]