고체역학 (Beer) — Pure Bending: Problem 4.15

4.15 Knowing that for the casting shown the allowable stress is 5 ksi in tension and 18 ksi in compression, determine the largest couple M that can be applied. Geometric properties from Fig. P4.15: The cross-section consists of three rectangular segments. Top segment: width $w_3 = 0.5\text{ in.} + 1.0\text{ in.} + 0.5\text{ in.} = 2.0\text{ in.}$, thickness $t_3 = 0.5\text{ in.}$ Middle segment: width $w_2 = 1.0\text{ in.}$, thickness $t_2 = 0.5\text{ in.}$ Bottom segment: width $w_1 = 0.5\text{ in.}$, thickness $t_1 = 0.5\text{ in.}$ Total height of the section $H = 0.5 + 0.5 + 0.5 = 1.5\text{ in.}$ Allowable stresses: $\sigma_{\text{all, tension}} = 5\text{ ksi}$ $\sigma_{\text{all, compression}} = 18\text{ ksi}$