Question $2$

The frame shown in hereunder figure supports the following service loads:

Dead Load: $,W_{DL}=15k\frac{N}{m}$

Live Load: $,W_{LL}=25k\frac{N}{m}$

Wind Load: $,Q=12kN($This is an approximation for the wind load effect$)$

$($a$)$ Using manual calculations only, calculate the factored normal force on columns DC for the following three load combinations: $,{}_{D}D+({}_{L}L+{}_{w}W)$

Combination $1$: ${}_D=1\mathrm{.}25,=1\mathrm{.}0,{}_L=1\mathrm{.}5,{}_w=0\mathrm{.}0$

Combination $2$: ${}_D=1\mathrm{.}25,=1\mathrm{.}0,{}_L=0\mathrm{.}0,{}_w=1\mathrm{.}25$

Combination $2$: ${}_D=1\mathrm{.}25,=0\mathrm{.}7,{}_L=1\mathrm{.}5,{}_w=1\mathrm{.}25$

$($b$)$ Check the adequacy of an IPE $360$ section for the axially loaded column DC if a vertical bracing system is provided as shown in the figure. In calculating the in$-$plane effective buckling length of this column, you have to consider that the side sway of the frame is permitted. Use steel ST $52.$