A uniformly tapered aluminum-alloy tube AB of circular cross section and length L is fixed against rotation at A and B, as shown in the figure. The outside diameters at the ends are d_A and d_B = 2(d_A). A hollow section of length L/2 and constant thickness t=d_A/10 is cast into the tube and extends from B halfway toward A. Torque T_0 is applied at L/2.
a.) Find the reactive torques at the supports, T_A and T_B. Use numerical values as follows: d_A = 2.5 in., L = 48 in., G = 3.9*10^6 psi, T_0 = 40000 in.-lb.
b.) Repeat part (a) if the hollow section has constant diameter d_A.