$*13-28.$ Assume that $AB$ is made of steel and is pinned at its ends for $x-x$ axis buckling and fixed at its ends for $y-y$ axis buckling. $E_{st}=200$GPa,${}_y=360$MPa.

a$)$ Determine if the frame can support a load of $w=8k\frac{N}{m}$ if the factor of safety with respect to buckling of member $AB$ is $3.$

b$)$ Determine vertical deflection at mid$-$point of the beam span CB$.$

Probs $13-27/28$