A shaft is made of three parts, as shown in the accompanying figure. Parts?AB?and?CD?are made of the same material with a modulus of rigidity of?G?= 9.8 ? 10³?ksi, and each has a diameter of 1.5 in. Segment?BC?is made of a material with a modulus of rigidity of?G?= 11.2 ? 10³?ksi and has a diameter of 1 in. The shaft is fixed at both ends. A torque of 2,400 lb.?? in is applied at?C. Using three elements, determine the angle of twist at?B?and?C?and the torsional reactions at the boundaries.

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2 ft 1.5 ft 2 ft 2 ft 1.5 ft 2 ft