고체역학 (Gere) — Torsion: Problem 3.4-19

3.4-19 A prismatic bar AB with a solid circular cross section (diameter d) is loaded by a distributed torque (see figure). The intensity of the torque, that is, the torque per unit distance, is denoted t(x) and varies linearly from a maximum value \( t_A \) at end A to zero at end B. Also, the length of the bar is L and the shear modulus of elasticity of the material is G. (a) Determine the maximum shear stress \( \tau_{max} \) in the bar. (b) Determine the angle of twist \( \phi \) between the ends of the bar.