Problem $2$: APPROXIMATE $($VOLUME$)$ DENSITIES OF SELECTED MATERIALS

Determine the total gravity load $($dead load $+$ live load$)$ of a typical residential floor constructed of $2$ X $12($nominal$)$ Douglas fir floor joists spaced $16$ in$.$ on center. The sub floor consists of $\frac{3}{4}-$in$.-$thick plywood and a $\frac{1}{4}-$in$.-$thick hardboard underlayment, as shown in Figure. Vinyl tiles arc used as floor finish, and the ceiling consists of $\frac{1}{2}-$in$.-$thick gypsum wallboard.

Note: A $($nominal$)2x12$ floor joist has actual dimensions of $\frac{11}{2}in.$ X $11\frac{1}{4}in.$