Question $3)(40$ marks$)$ For the ribbed slab plan with section as shown below:

Determine the total slab and beam thickness. $(8$ marks$)$

Design the topping slab. $(5$ marks$)$

$3.$calculate the dead and live load for each rib. $(10$ marks$)$

$4.$Design the rib for flexure and shear. Assume the envelope positive moment$(20KN.m),$ the envelope negative moment$(22KN.m$ and the shear force from $d$ of face of support $(17KN).$use $d_{\text{b}\text{a}\text{r}}=12mm$ and dsttirubs $=10mm.$ Make all necessary check.$(17$ marks$)$

The concrete strength is $f^{\text{'}}c=24$MPa, and the yield strength of the stirrups and steel is $f_y=420$MPa and the width of rib is $14cm.$ and assume $\frac{O}{?}$ for flexture $=0\mathrm{.}9$ and $A{s}_{\text{m}\text{a}\text{x}}$ for positive moment $=2457\mathrm{.}95mm2$ and $A{s}_{\text{m}\text{a}\text{x}}$ for negative moment $=637\mathrm{.}25m{m}^2$ and $A{s}_{\text{m}\text{i}\text{n}}=137\mathrm{.}2m{m}^2$

Take the material's density from the table below.

$2$

$\backslash$table$[[$Material$,\backslash$table$[[$Quality Density$],[K\frac{N}{m^3}$