Q$.1$ A five$-$span R$.$C$.$ ribbed slab has equal effective spans of $5\mathrm{.}0m.$ The cross$-$section is as shown in Fig Q$\mathrm{.}1.$ The ribbed slab is constructed without permanent blocks. It is subjected to the following loadings and material properties:

Characteristic dead load:

Self$-$weight $=3\mathrm{.}37k\frac{N}{m^2}$

$20mm$ thick finishes $($unit weight $=20k\frac{N}{m^3})$

Services and Partition $=1\mathrm{.}0k\frac{N}{m^2}$

Characteristic imposed load: $3\mathrm{.}0k\frac{N}{m^2}$

Properties of structural material used:

$f_{cu}=40\frac{N}{m}{m}^2,f_y=500\frac{N}{m}{m}^2$

nominal cover $=30mm,$ Size of main bars $=12mm$

$($a$)$ Design the bending reinforcement for the end span and the first interior support of the ribbed slab.

$($b$)$ Check the adequacy of the ribbed slab section against deflection by using span$-$effective depth ration approach; and

$($c$)$ Check the necessity to provide shear reinforcement for the ribbed slab.

Fig. Q$.1$