A PSC beam, $200mm$ wide and $350mm$ deep is used over an effective span of $6\mathrm{.}0m$ to support an imposed load of $4\mathrm{.}5k\frac{N}{m}.$ At the quarter span section of the beam, find the magnitude of$,$

$($i$)$ The concentric pre$-$stressing force necessary for zero fiber stress at the soffit when the beam is fully loaded.

$($ii$)$ The eccentric pre$-$stressing force located at $110mm$ from the bottom of the beam which would nullify the bottom fiber stress due to loading.