Problem $5.$ A wooden beam $(1)$ is reinforced with steel plates $(2)$ rigidly attached to its top and bottom surfaces, as shown in Figure P$8\mathrm{.}40.$ Dimensions of the cross section are $b_1=6$ in$.,d_1=12in.,b_2=4in.,$ and $d_2=0\mathrm{.}5in.$ The elastic moduli of the wood and steel are $E_1=1,250$ksi and $E_2=30,000$ksi, respectively. The allowable bending stresses of the wood and steel are $1,200$ and $20,000,$ respectively. Determine the largest concentrated vertical load that can be applied at midspan if a simply supported beam with this cross section spans $18$ ft $.$