고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-1

5.5-1 A thin strip of hard copper (\(E = 110 \text{ GPa}\)) having length \(L = 2.3 \text{ m}\) and thickness \(t = 2.4 \text{ mm}\) is bent into a circle and held with the ends just touching (see figure). (a) Calculate the maximum bending stress \(\sigma_{\text{max}}\) in the strip. (b) By what percent does the stress increase or decrease if the thickness of the strip is increased by \(0.8 \text{ mm}\)? (c) Find the new length of the strip so that the stress in part (b) (\(t = 3.2 \text{ mm}\) and \(L = 2.3 \text{ m}\)) is equal to that in part (a) (\(t = 2.4 \text{ mm}\) and \(L = 2.3 \text{ m}\)).