For the short column cross section shown in Fig. $3,$ answer the following questions. Use $f_x=60$ksi and $f_c^{\text{'}}=4$ksi. Approximate the tensile yield strain of the reinforcing steel as $0\mathrm{.}002$

$($a$)(10$ points$)$ Compute the $P_n$ and $M_n$ in the interaction diagram for pure compression condition.

$($b$)(20$ points$)$ Compute the $P_n$ and $M_n$ in the interaction diagram for balanced condition. Draw the necessary strain diagram.

$($c$)(10$ points$)$ ACl uses a factor of $$ to reduce $P_n$ to consider "accidental" eccentricities. However, this can only consider small eccentricities. Using the results from part $($a$)$ and part $($b$),$ estimate the eccentricity it can account for, if $=0\mathrm{.}80$ is used for this tied column. You need to draw a sketch for illustration. Hint: you can use a straight line to approximate the interaction diagram.