Beer & Johnston — Pure Bending: Problem 4.98

4.98 A prismatic bar of rectangular cross section is made of an alloy for which the stress-strain diagram can be represented by the relation \(\epsilon = k\sigma^n\) for \(\sigma > 0\) and \(\epsilon = -|k\sigma^n|\) for \(\sigma < 0\). If a couple \(M\) is applied to the bar, show that the maximum stress is \[\sigma_m = \frac{1 + 2n}{3n} \frac{Mc}{I}\]