$6\mathrm{.}2-5$ A simple beam on a $12$ ft span supports a uniform load of intensity $600\frac{Ib}{ft}($see figure$).$ The beam consists of a wood member $(4in.11\mathrm{.}5in.$ in cross section$)$ that is reinforced by $0\mathrm{.}25in.$thick steel plates $on$ top and bottom. The moduli of elasticity for the steel and wood are $E_s=30{10}^6$psi and $E_w=1\mathrm{.}5{10}^6$psi, respectively.

Calculate the maximum bending stresses ${}_s$ in the steel plates and ${}_w$ in the wood member due to the uniform load.