Problem $4.$

A tied$-$column with square cross section supports an ultimate load of $P_u=350$ kips and ultimate moment of $M_u=90$kip$-ft.$ The column is in a braced frame and has an unsupported length of $8$ ft $.$ Assume $f_y=60$ ksi and $f_c^{\text{'}}=4000$ psi.

$($a$)$ Estimate the gross cross$-$sectional area and the dimensions.

$($b$)$ Use the interaction diagram to find the reinforcement ratio and propose a bar size and number of bars. Assume the bars will be arranged in two faces. Identify which interaction diagram Fig A$-6$a$,$ Fig A$-6$b$,$ etc. you used.