A circular bar AB with ends fixed against rotation has a hole extending for half of its length (see figure). The outer diameter of the bar is d2 3.0 in. and the diameter of the hole is d1 2.4 in. The total length of the bar is L 50 in. at 30.12 in from the left hand end of the bar a torque is applied so that the reactive torques at the supports are equal.
What is theta max and where does it occur? assume that To=87.4 kips-in and G=10600 ksi.