Problem $4.$ A wood beam $(1)$ is reinforced on its lower surface by a steel plate $(2)$ as shown in Figure P$8\mathrm{.}44.$ Dimensions of the cross section are $b_1=220mm,d=380mm,b_2=160mm,$ and $t=20mm.$ The elastic moduli of the wood and steel are $E_1=12\mathrm{.}5$GPa and $E_2=200$GPa, respectively. The allowable bending stresses of the wood and steel are $7\mathrm{.}5$ MPa and $150$ MPa $,$ respectively. This cross section is used for a simply supported beam that spans $9$ m $.$ What is the largest uniformly distributed load that can be applied to the beam?

FIGURE P$8\mathrm{.}44$