A $20$ in$.x20$ in$.$ square concrete column is reinforced with four #$9$ bars, on each opposite face. A normal weight concrete with $f_c=4500$ psi; and grade $60$ steel is used. Compute:

i$)$ The concentric axial$-$load capacity $P_o$ and maximum axial$-$load capacity $P_{n(max)}.(5$ points$)$

ii$)$ The $$ ultimate axial load $P_v,$ bending moment $M_u,$ and corresponding eccentricity $e_b,$ for balanced failure.

iii$)$ The $,$ ultimate axial load $P_u,$ bending moment $M_w,$ and corresponding eccentricity $e,$ for the limiting tension failure

$(10$ points$)$