고체역학 (Gere) — Torsion: Problem 3.4-11

3.4-11 A tapered bar $AB$ with a solid circular cross section is twisted by torques $T = 2035\text{ N}\cdot\text{m}$ (see figure). The diameter of the bar varies linearly from $d_A$ at the left-hand end to $d_B$ at the right-hand end. The bar has length $L = 2.4\text{ m}$ and is made of an aluminum alloy having shear modulus of elasticity $G = 27\text{ GPa}$. The allowable shear stress in the bar is $52\text{ MPa}$ and the allowable angle of twist is $3.0^\circ$. If the diameter at end $B$ is 1.5 times the diameter at end $A$, what is the minimum required diameter $d_A$ at end $A$?