Problem $2$: A simply supported beam $12$ ft $.$ long carries a uniformly distributed load of $100lb\frac{s}{f}t.$ Assume that the beam is $1-\frac{1}{2}in.9-\frac{1}{2}in.$ in cross section and is laterally braced. Also assume that the beam is made of timber which has an allowable stress in bending of $1200lb\frac{s}{i}{n}^2$ and in shear of $150lb\frac{s}{i}{n}^2.$ a$)$ Is the beam safe with respect to bending and shear stress considerations? b$)$ What is the maximum deflection of the beam? Assume that $($:$E=1\mathrm{.}6{10}^{6}l\frac{b}{i}{n}^2.c$