고체역학 (Gere) — Torsion: Problem 3.4-22

3.4-22 Two tubes ($AB$, $BC$) of the same material are connected by three pins (pin diameter $d_p$) just left of $B$ as shown in the figure. Properties and dimensions for each tube are given in the figure. Torque $2T$ is applied at $x = 2L/5$ and uniformly distributed torque intensity $t_0 = 3T/L$ is applied on tube $BC$. (a) Find the maximum value of load variable $T$ (N·m) based on allowable shear ($\tau_a$) and bearing ($\sigma_{ba}$) stresses in the three pins which connect the two tubes at $B$. Use the following numerical properties: $L = 1.5\text{ m}$, $E = 74\text{ GPa}$, $\nu = 0.33$, $d_p = 18\text{ mm}$, $\tau_a = 45\text{ MPa}$, $\sigma_{ba} = 90\text{ MPa}$, $d_1 = 85\text{ mm}$, $d_2 = 73\text{ mm}$, and $d_3 = 60\text{ mm}$. (b) What is the maximum shear stress in the tubes for the applied torque in part (a)?