Problem $1(100$ points$)$

Determine the area of prestressed reinforcement required to develop a design moment resistance $M_u=842\mathrm{.}55$ kips$-$ft and an $($ideal$)$ design moment resistance $M_u=842\mathrm{.}553$ kips$-$ft in the simply supported beam having the $T$ section shown in the figure and the material properties listed below. Assume that the section is tensioncontrolled $($ACI$).$

$f_c^{\text{'}}=5000$;

$f_{pu}=270$ksi;

$(d_c{)}_{\text{m}\text{i}\text{n}}=4in$;

${}_p=0\mathrm{.}4$