DProb. $6\mathrm{.}8-8.$ A wood beam with nominal dimensions $4$ in$.8$ in$.$ is supported and loaded, as shown in Fig. P$6\mathrm{.}8-8.$ If the allowable shear stress for the wood is $({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_w=120,$ and if the load at $C$ is always three times the load at $A,$ that is$,3P$

and $P,$ respectively, calculate the maximum load value $P$ that may be applied to this beam. Include the weight of the beam in your calculations, using $=36l\frac{b}{f}{t}^3$ for the specific weight of the wood beam. $($See Appendix D$.8$ for the finish dimensions of structural lumber.$)$