A $9-$meter Post$-$tensioned prestressed concrete gutter beam with a section dimensions shown in the figure. Assume the shear center is located at $150mm$ from the top fiber. The beam is reinforced by a cable with an area of $190sq.mm.$ in a parabolic drape and with $4$ pes.$-20$mm$-$dia. Rebars. Compute the following:

a$).$ Initial Stresses for bending and shear stresses $(25pts)$

b$).$ Final stresses at Top and Bottom fibres at total working load at centre span. $(25p$ Uniform Liveload $=2,850\frac{N}{m}$ and Concentrated Liveload $=12KN$

Tendons: Initial Stress, fs $=1160$MPa; Final stress, fs $=985$MPa;

Rebars: $fs=138$MPa, $fy=$

Concrete: $f^{\text{'}}c=9$MPa, S$.$G$.$

$M_{\text{m}\text{a}\text{x}}=\frac{PL}{3}+\frac{W{L}^2}{8}$