For the short, concentrically loaded square tied column shown, the applied dead load is $150$ kips $(DL=150$kips $),$ and the applied axial live load is $250$kips $(LL=250$Kips $).$ Assuming that the longitudinal reinforcing bars are all the same size. Determine the minimum size of each longitudinal reinforcing bar. $f_c^{\text{'}}=4000,f_y=60,000(20pts)$

$f^{\text{'}}C=4000$ PSi $=4$Asi

$f_y=60000$ PSi $=60$ksi

Gross Area $=1818=324i{n}^2=Ag$

Square Tied Column:

$($A$)$ No$.3$

$=0\mathrm{.}65$

$($B$)$ No$.4$

$DL=150k,LL=250k$

$($C$)$ No $5$

$($D$)$ No $6$

$pu=1\mathrm{.}2(150)+1\mathrm{.}6(250)$

$pu=580k=p_n$

$[0\mathrm{.}85f^{\text{'}}C(Ag-$Ast$)+fy(A{s}^2)]$

$\mathrm{.}50\mathrm{.}8[0\mathrm{.}854(324-$Ast$)+60$Ast$]$

$\mathrm{.}5i{n}^2$

$P_n=0\mathrm{.}8[0\mathrm{.}85f^{\text{'}}C(Ag-$Ast$)+f_y(A{s}^2)]$

$580=0\mathrm{.}650\mathrm{.}8[0\mathrm{.}854(324-$Ast$)+60$ Ast $]$

Ast $=0\mathrm{.}25i{n}^2$

Provide $8$#$3$ bars $=0\mathrm{.}88i{n}^2$