Beer & Johnston — Torsion: Problem 3.60

3.60 A torque T is applied as shown to a solid tapered shaft AB. Show by integration that the angle of twist at A is \[ \phi = \frac{7TL}{12\pi Gc^4} \] (Fig. P3.60 shows a shaft of length \(L\) with a fixed support at end B. The radius at end A is \(c\) and the radius at end B is \(2c\). A torque \(T\) is applied at the free end A.)