A nonprismatic bar ABC of solid circular cross section is loaded by distributed torques (see figure). The

Question:

A nonprismatic bar ABC of solid circular cross section is loaded by distributed torques (see figure). The intensity of the torques, that is, the torque per unit distance, is denoted t(x) and varies linearly from zero at A to a maximum value T0/L at B. Segment BC has linearly distributed torque of intensity t(x) = T0/3L of opposite sign to that applied along AB. Also, the polar moment of inertia of AB is twice that of BC, and the shear modulus of elasticity of the material is G.
(a) Find reaction torque RA.
(b) Find internal torsional moments T(x) in segments AB and BC.
(c) Find rotation (C.