Solved: Instead of a tensile force, consider the bar in
Chapter 4, Problem 4-6(choose chapter or problem)
Instead of a tensile force, consider the bar in Prob. 4-5 to be loaded by a torque T.
(a) Use Eq. (4-5) in the form of \(\theta=\int_0^l[T /(G J)] d x\) to show that the angle of twist of the tapered portion is
\(\theta=\frac{32}{3 \pi} \frac{T l\left(d_1^2+d_1 d_2+d_2^2\right)}{G d_1^3 d_2^3}\)
(b) Using the same geometry as in Prob. 4-5b with \(T=1500 \mathrm{lbf} \cdot\) in and G = 11.5 Mpsi, determine the angle of twist in degrees for each portion.
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