고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-3

5.5-3 A thin, high-strength steel rule (\(E = 200 \text{ GPa}\)) having a thickness \(t = 4 \text{ mm}\) and length \(L = 1.5 \text{ m}\) is bent by couples \(M_0\) into a circular arc subtending a central angle \(\alpha = 40^\circ\) (see figure). (a) What is the maximum bending stress \(\sigma_{\text{max}}\) in the rule? (b) By what percent does the stress increase or decrease if the central angle is increased by 10%? (c) What percent increase or decrease in rule thickness will result in the maximum stress reaching the allowable value of 290 MPa?