Show all calculations and steps clearly. Do not skip any step. The symbols have their usual meaning. Use ACI$-318.$ Assume a reasonable value of any parameter if needed.

Problem $1.$

A tied$-$column with square cross section supports an ultimate load of $P_u=400$ kips and ultimate moment of $M_u=100$kip$-ft.$ The column is in a braced frame and has an unsupported length of $9$

ft $.$ Assume $f_y=60$ksi and $f_c^{\text{'}}=4000.$

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

$($b$)$ Check whether the slenderness of the column can be neglected.

$($c$)$ 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. Show all calculations.