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$($a$)$ A $400$ mm thick deck slab has a maximum applied ultimate limit state sagging moment of

$250$kNm$//$m$.$ Assume a $55$ mm cover to the main reinforcement and C$30/35$ concrete.

Given that f$\_($cd$)=30$MPa,a$\_($cx$)=0\mathrm{.}85,$gamma$\_($c$)=1\mathrm{.}5,$ and assume rectangular stress box. Determine

the required reinforcement area for adequate ultimate moment of resistance using

rectangular stress blocks. Use B$500$B as the reinforcement.

$[5$ Marks$]$