The beam whose section is shown in Figure $3$ is a seating element in a grandstand. It is reinforced with eight post$-$tensioning prestressing stands, as shown, each of area $120$ mm$2$ and stressed to $70\%$ of their yield strength. There are $20\%$ losses between transfer and service. The characteristic concrete cylinder strength is$,$ fck $=50$ N$/$mm$2$ and the yield strength of the strand is fyk $=1820$ N$/$mm$2.$ Young$$s modulus for the strand is $195,000$ N$/$mm$2.($a$)$ Assuming that the prestressing strand has yielded and that $0\mathrm{.}8$x $>75$ mm$,$ calculate the depth to the neutral axis, x$.($b$)$ Check both of these assumptions. $($c$)$ Calculate the ultimate moment capacity of the section.