$($a$)$ A rectangular continuous concrete beam is of $9m$ span and with width of $250mm.$

Check the acceptability of an effective depth of $550mm$ when $f_{yk}=500\frac{N}{m}{m}^2$ and $f_{ck}=$

$40\frac{N}{m}{m}^2$ for steel reinforcement and concrete respectively. By calculation, the required

steel reinforcement area, As$,$req $=1250m{m}^2$ and $3No\mathrm{.}25mm$ diameter reinforcing bars,

As$,$prov $=1470m{m}^2$ are provided in the interior span.

$[10$ marks$]$

$($b$)$ Assuming the beam is now simply supported with $12m$ span, check the acceptability of

an effective depth of $550mm$ with all the other beam properties the same as in $($a$)$ above.

If not acceptable, recommend an acceptable effective depth accordingly.