Gere & Goodno — Stresses in Beams (Basic Topics): Problem 5.4-4

5.4-4 A cantilever beam $AB$ is loaded by a couple $M_0$ at its free end (see figure). The length of the beam is $L = 2.0\text{ m}$, and the longitudinal normal strain at the top surface is $\epsilon = 0.0010$. The distance from the top surface of the beam to the neutral surface is $c = 85\text{ mm}$. (a) Calculate the radius of curvature $\rho$, the curvature $\kappa$, and the vertical deflection $\delta$ at the end of the beam. (b) If allowable strain $\epsilon_a = 0.0008$, what is the maximum acceptable depth of the beam? [Assume that the curvature is unchanged from part(a)]. (c) If allowable strain $\epsilon_a = 0.0008$, $c = 85\text{ mm}$, and $L = 4\text{ m}$, what is deflection $\delta$?