Question No$.2$: $(50\%)$

A typical floor plan of a $13-$story building is shown in the Figure $2.$ The following is required:

a$)$ Design Column $C5$ at the ground story as a spiral column with a circular cross section and draw the reinforcement details assuming that buckling is neglected $Pu($ultimate axial load$)4600kN($intially assume ${}_g=1\mathrm{.}7\%).$

b$)$ Re$-$design Column $C5$ as a spiral column with a circular cross section under the same axial load and an ultimate bending moment $(M_u)=500kN.m.$ Neglect the buckling effect and determine the required area of steel to be

Figure $2$ distributed in the column cross$-$section.

c$)$ Draw clear cross sections of the columns designed in $($a$)$ and $($b$)$ showing all reinforcement details.

d$)$ Comment on the final design of the two design cases in $($a$)$ and $($b$)$; i$.$e$.$ which case produces largest cross section and heighest steel ratio.

Given Data:

$fy=420$Mpa,$f_c^{\text{'}}=28$MPa, Use bar size $729$ or the longitudinal reinforcement. Assume any missing data.