Determine the design moment, phi$*$M$\_\{$n$\}$ of a T$-$beam, which exists in a system of T$-$beams spaced at $4-$ft$.$ on center. The span length of the beam system is $18-$ft$.$ The overall depth of the T$-$beam section is $24-$in$.,$ the width of the web is $14-$in$.,$ and the height of the flange is $5-$inThe reinforcement is $4$ No$.9$ bars at an effective depth of $21-$in$.$ Assume f$\_\{$y$\}=60000$ psi and f c $^,=4,000$ psi.

Determine the design moment, $M_n,$ of a T$-$beam, which exists in a system of T$-$beams spaced at $4-ft.$ on center. The span length of the beam system is $18-ft.$ The overall depth of the T$-$beam section is $24-$in$.,$ the width of the web is $14-$in$.,$ and the height of the flange is $5-$in$.$ The reinforcement is $4$ No$.9$ bars at an effective depth of $21-$in$.$ Assume $f_y=60,000$ psi and $f_c^{\text{'}}=4,000$ psi.