$4\mathrm{.}3$ Consider the simply supported T beam shown in the figure below. The live load is assumed to be $600$ plf$.$ The following design information is given:

Concrete: normal weight with unit weight $=150pcf$;$f_c^{\text{'}}=8000$;$f_{ci}^{\text{'}}=5600$;

Allowable stresses: $\frac{?}{\text{b}\text{a}\text{r}}({)}_{ti}=-224\frac{\text{;}}{b}ar({)}_{ci}=3360\frac{\text{;}}{b}ar({)}_{ts}=-536\frac{\text{;}}{b}ar({)}_{\text{c}\text{s}\text{u}\text{s}}=3600\frac{\text{;}}{b}ar({)}_{cs}=4800$;

Steel: $,f_{pu}=270$ksi;$f_{pe}=150$ksi;$f_{py}=240$ksi $($yield stress$)$; $=0\mathrm{.}8$;$d_{\text{c}\text{m}\text{i}\text{n}}=3in.$

The prestressing steel consists of half$-$inch diameter strands.

Figure $]$

Build the feasible domain and determine the minimum value of prestressing force and corresponding eccentricity at midspan. Round off your answer to correspond to an integer number of strands, assuming the cross$-$sectional area of one strand is $0\mathrm{.}153i{n}^2.$

Sketch a layout of the strands in your section. Ensure strand layout is feasible.