고체역학 (Gere) — Torsion: Problem 3.11-13

3.11-13 A thin-walled rectangular tube has uniform thickness $t$ and dimensions $a \times b$ to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio $\beta = a/b$ if the total length $L_m$ of the median line of the cross section and the torque $T$ remain constant? From your results, show that the shear stress is smallest when the tube is square ($\beta = 1$).