QUESTION $4(25$ Marks$)$

Determine the adequacy of the floor joist as shown in figure $4$ below. The joists are nominal $210$ members of Southern Pine and contain a notch at one end. The joists are spaced at $24$ inches on centre and are sheathed on the top with structural wood panels that are attached with nails. The deflection of the joists must be L$/360$ or less when subjected to un$-$factored live loads.

Reference Values

$F_b=1050,F_V=175,E=1,600,000,C_D=1\mathrm{.}0$

$C_M=1\mathrm{.}0,C_r=1\mathrm{.}15,C_t=1\mathrm{.}0,C_f=1\mathrm{.}0$

$C_i=1\mathrm{.}0$

Deduce $($stating reasons$)$ the beam stability factor $C_L.$

rigure $4$