Question 1 (50%) A solid shaft of 100 mm diameter has a strain gauge mounted on the surface at 30 to the axis of the shaft at point O, as shown in Figure 1. In service an axial force P = 500 kN and a torque Tare applied to the shaft and the strain gauge reads &=-3x 104. The shaft is made from steel with the Young's modulus E=200 GPa, Poisson's ratio = 0.3 and yielding stress oy = 400 MPa. (1) Calculate the magnitude of the torque T. (2) Calculate the principal stresses and the maximum shear stress of point O. (3) Calculate the principal strains and the maximum shear strain of point O. (4) Express the stresses of point O on the Mohr's circle. (5) Check the safety of the shaft according to the shear-strain energy theory. P T Figure 1 P