Problem $1(50$ points$)$

Determine the nominal and design positive moment resistance of the fully prestressed concrete beam represented below according to the ACl provisions. The following information is provided: low relaxation strands are used, $A_c=309i{n}^2,A_{ps}=2\mathrm{.}1i{n}^2,f_c=7000,f_{pu}=270$ksi,$f_{pe}=0\mathrm{.}567f_{pu},f_{py}=0\mathrm{.}9f_{pu},y_t=11\mathrm{.}99$ in$,y_b=12\mathrm{.}01in,d_p=20\mathrm{.}14in,e_0=8\mathrm{.}15in,{}_p=0\mathrm{.}28.$