Please dont use chat gpt to do it$.$ A frame ABCD as shown in figure below is constructed of A$36$ steel members $($RH$400200813)$ and subjected to triangularly distributed loads of maximum intensity $q_0=2700k\frac{N}{m}$ acting along the vertical members. In addition, a $44$ kN concentrated load $Q$ is applied also at the mid span of member BC$.$ Given that the distance between supports is $L=3m$ and the height of the frame is $h=0\mathrm{.}2m$ and the members are rigidly connected at B and C $,$ use AISC$-$LRFD design method to check whether this structure is capable to resist the applied load.

Note: RH$400\backslash$times $200\backslash$times $8\backslash$times $13$:

$A=8192m{m}^2$;$I_x=2\mathrm{.}296{10}^{8}m{m}^4$;$I_y=1\mathrm{.}735{10}^{7}m{m}^4$;

$S_x=1\mathrm{.}148{10}^{6}m{m}^3$;$S_y=1\mathrm{.}735{10}^{5}m{m}^3$;$Z_x=1\mathrm{.}286{10}^{6}m{m}^3$;

$Z_y=2\mathrm{.}660{10}^{5}m{m}^3$;$E=200$GPa;$G=77$GPa;