Only solve for case a$)$ in the table

$($Design of rectangular column sections$)$ For each assigned problem in Table $11\mathrm{.}4,$ design a rectangular column section to support the factored load and moment shown. Determine $,$ and h if not given; then choose adequate bars considering that $.$ The final total steel ratio, g$,$ should be close to the given values where applicable. Check the load capacity, $$Pn$,$ of the final section using statics and equilibrium equations. One solution for each problem is given in Table $11\mathrm{.}4.$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & & & & & & & $\backslash$multicolumn$\{2\}\{|$l$|\}\{$One Solution$\}\backslash \backslash$

$\backslash$hline Number & $\backslash ($ f$\_\{$c$\}^\{\backslash$prime$\}(\backslash )$ ksi$)$ & $\backslash (\backslash$boldsymbol$\{$P$\}\_\{\backslash$boldsymbol$\{$u$\}\}\backslash )($K$)$ & $\backslash ($ M$\_\{$u$\}(\backslash$mathrm$\{$~K$\}\backslash$cdot $\backslash$mathrm$\{$ft$\})\backslash )$ & b $($in$.)$ & h $($in$.)$ & $\backslash (\backslash$rho$\_\{$g$\}\backslash )\backslash \%$ & h $($in$.)$ & $\backslash ($ A$\_\{$s$\}-$A$\_\{$s$\}^\{\backslash$prime$\}\backslash )\backslash \backslash$

$\backslash$hline a & $4$ & $530$ & $353$ & $16$ & $-$ & $4\mathrm{.}0$ & $20$ & $5$ no$.10\backslash \backslash$

$\backslash$hline b & $4$ & $410$ & $205$ & $14$ & $18$ & $-$ & $18$ & $5$ no$.8\backslash \backslash$

$\backslash$hline c & $4$ & $480$ & $640$ & $18$ & $-$ & $3\mathrm{.}5$ & $24$ & $6$ no$.10\backslash \backslash$

$\backslash$hline d & $4$ & $440$ & $440$ & $20$ & $20$ & $-$ & $20$ & $6$ no$.9\backslash \backslash$

$\backslash$hline e & $4$ & $1125$ & $375$ & $20$ & $24$ & $-$ & $24$ & $6$ no$.10\backslash \backslash$

$\backslash$hline f & $4$ & $710$ & $473$ & $18$ & $-$ & $3\mathrm{.}0$ & $24$ & $5$ no$.10\backslash \backslash$

$\backslash$hline g & $5$ & $300$ & $300$ & $14$ & $-$ & $2\mathrm{.}0$ & $20$ & $3$ no$.9\backslash \backslash$

$\backslash$hline h & $5$ & $1000$ & $665$ & $20$ & $26$ & $-$ & $26$ & $6$ no$.10\backslash \backslash$

$\backslash$hline i & $6$ & $590$ & $197$ & $14$ & $-$ & $2\mathrm{.}0$ & $18$ & $2$ no$.10\backslash \backslash$

$\backslash$hline j & $6$ & $664$ & $332$ & $16$ & $20$ & $-$ & $20$ & $4$ no$.9\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$