Problem $1$: $(30$ points$)1.$ Draw the design P$-$M diagram $($moment about the X$-$axis$)$ for a $18$x $18$ column reinforced with $4$#$11($As$=$ As$=3\mathrm{.}12$ in$2).$The concrete strength Fc$=6$ ksi and Fy$=60$ ksi. The clear cover is $2\mathrm{.}5$ to the bars centroid.Show calculations for the following five points:

a$)$ Pure axial compression

b$)$ Balanced Failure

c$)$ Strain in tension steel $=0\mathrm{.}0$ in$/$in

d$)$ Stress in tension steel $=0\mathrm{.}5$ Fy

e$)$ Strain in tension steel $=0\mathrm{.}004$ in$/$in

f$)$ Pure axial tension$2.$

Design the ties required