please answer all parts and explain fully, this is for study purposes so concepts matter. thank you!!!

$(20)$ The steel bar $\backslash ($ A B $\backslash )$ has a rectangular cross section as shown and is pin$-$connected in both the $\backslash ($ x $\backslash$& y $\backslash )$ directions at its ends. The material is A$-36$ structural steel.

a$.$ Will the bar buckle about the $\backslash ($ x $\backslash )$ or $\backslash ($ y $\backslash )$ axis?

b$.$ Calculate the critical buckling load for column $\backslash ($ A B $\backslash ).$

c$.$ Using a factor of safety with respect to buckling of $1\mathrm{.}5,$ determine the maximum allowable intensity $\backslash ($ w $\backslash )$ of the distributed load that can be applied to $\backslash ($ B C $\backslash )$ without causing $\backslash ($ A B $\backslash )$ to buckle. Be sure to include any necessary free$-$body diagrams.

d$.$ If the proportional limit of the material is $0\mathrm{.}9$ times the yield stress, does Euler buckling apply? Use calculations to support this conclusion.

Figure P$3$: Steel bar structure with column and distributed load.