Beer & Johnston — Pure Bending: Problem 4.60

*4.60 A rectangular beam is made of material for which the modulus of elasticity is \(E_t\) in tension and \(E_c\) in compression. Show that the curvature of the beam in pure bending is \[\frac{1}{\rho} = \frac{M}{E_r I}\] where \[E_r = \frac{4 E_t E_c}{(\sqrt{E_t} + \sqrt{E_c})^2}\]