Mechanics of Materials: Torsional deformation at free end with torque at middle

[webtek23]

Homework Statement

A circular shaft AB has a torque T acting at the middle of the shaft, defined as plane C. Shaft end A is fixed while shaft end B is free to rotate (mounted in a thrust bearing). Finding the twist angle from A to C is not difficult, but the question requires that the twist angle from A to B be determined.

Homework Equations

phi=(T*L)/(G*I_p)

The Attempt at a Solution

I have looked back through all my class notes, homework, and mechanics of materials textbooks and can't seem to find any examples where a shaft has a free end with no reaction torques and where the twist angle is determined there. I have been able to find several sources which say that the twist angle rate should remain constant for the length of the rod, but I am not sure if this applies for a rod where there is no reaction torque on the free end. From a materials perspective, I would also not expect the twist angle rate to instantly change after plane C where the torque is applied. Can anyone help me out with understanding what would happen from C to B on the shaft?

 

[PhanthomJay]

Hint: Is there any torque in the section from C to B? What does that tell you about the twist at B relative to C? Or the twist at B relative to A?