Q$2.$ A $200$ mm thick flat slab is loaded on an area of $\backslash (400\backslash$mathrm$\{$~mm$\}\backslash$times $400\backslash$mathrm$\{$~mm$\}\backslash )$ as shown in Figure Q$2.$ The slab is made of concrete strength class C$30/37$ and reinforced with two mutually orthogonal layers of longitudinal steel rebars placed in an effective depth of $160$ mm and $170$ mm along $\backslash (\backslash$mathbf$\{$y$\}\backslash )$ and $\backslash (\backslash$mathbf$\{$z$\}\backslash )$ directions, respectively. Each reinforcement layer consists of $10$ mm diameter rebars spaced at $150$ mm centre to centre. The reinforcement is made of steel grade $500(\backslash ($ f$\_\{$y k$\}=500\backslash$mathrm$\{$MPa$\}\backslash )).$ The slab does not have any shear reinforcement.

Conforming to Eurocode $2,$

$($a$)$ Calculate the punching shear resistance of the slab at the basic control perimeter.

$($c$)$ Calculate the maximum punching shear resistance at the edges of the loaded area.

$($d$)$ Determine the maximum ultimate load that can be carried by the slab.