Problem $14\mathrm{.}48$

A $412($S$4$S$)$ hem$-$fir timber beam carries a superimposed uniformly distributed load of $325l\frac{b}{f}t$ on a simple span of $12$ ft $.$ Determine the maximum bending stress and maximum shear stress and compare with the allowable stresses. Be sure to include the beam self$-$weight. Assume an allowable bending stress of $1000$ psi and an allowable shear stress of $150$ psi $.$