The $12$ in$.$ x $20$ in$.$ tied column shown in Figure $2$ is used to support the following service loads: $P_D=115$ kips; $P_L=120$ kips; $M_D=70$ k$-$ft and $M_L=85$ k$-$ft$.$ For your design use $f_c\text{'}=4,000$ psi and $f_y=60,000$ psi.

a$)$ Design the steel reinforcement and select the bars to be used in two end faces $($as shown in the figure$)$ using the interaction diagram provided below.

b$)$ Design the shear reinforcement $($ties$)$;

c$)$ Determine the theoretical maximum axial load capacity of the column and compare it to the one obtained from the graph;

d Find the theoretical values $P_n$ and $M_n$ at balanced conditions and compare them to the findings from the graph.