(i) Show that for a solid cylinder with diameter D, the polar second moment of area, J, is given by Eq. 2.1: J=32D4 (ii) What is the external diameter of a hollow shaft needed to transmit a torque of 50kNm if the shear stress is not to exceed 75MPa ? The shaft has an external diameter 1.5 times the internal diameter? [Take Modulus of rigidity, G = 90MPa ]. State the assumptions made in deriving the torsional equations. Consider Fig 2.0 which shows a stepped shaft having a fillet radius R=5mm and consisting of solid circular segments (d=44mm and D=53mm ). (i) Define stress concentration factor Kt in torsion. (ii) Calculate the stress concentration factor, Kt of the shaft. (iii) Compute the maximum shear stress at the stress concentration given that the maximum permissible torque, Tmax is 810.56Nm. Fig. Q2.0: Stress concentration in circular shaft with fillets under torsion