$5\mathrm{.}6-9$ A floor system in a small building consists of wood planks supported by $2-$in$.($nominal width$)$ joists spaced at distance $s$ and measured from center to center $($see figure$).$ The span length $L$ of each joist is $12$ ft $,$ the spacing $s$ of the joists is $16$ in $.,$ and the allowable bending stress in the wood is $1250$ psi. The uniform floor load is $1201\frac{l}{f}{t}^2,$ which includes an allowance for the weight of the floor system itself.

a$.$ Calculate the required section modulus $S$ for the joists, and then select a suitable joist size $($surfaced lumber$)$ from Appendix G$,$ assuming that each joist may be represented as a simple beam carrying a uniform load.

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$212$

b$.$ What is the maximum floor load that can be applied to your final beam selection in part $($a$)?$

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$W_{\text{m}\text{a}\text{x}}=137\mathrm{.}31\frac{b}{f}t{t}^2$