Q$3.[$Total: $26$ marks$]$

A group of $4$ piles, with the pile cap plan shown in Figure Q$3,$ support a $500$ mm square column which is subjected to an axial load of $5000$ kN $($factored$).$ The effective depth of the cap, $\backslash ($ d $\backslash ),$ is $875$ mm $.$ There is no need to consider selfweight of the concrete and the soil in calculation. Assume $\backslash (\backslash$mathrm$\{$f$\}\_\{\backslash$mathrm$\{$yk$\}\}=500\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash ),\backslash (\backslash$mathrm$\{$f$\}\_\{\backslash$mathrm$\{$ck$\}\}=35\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$

a$)$ Use the strut$-$and$-$tie method to calculate the area of reinforcement $($tension$)$ in each "tie" and check against the minimum reinforcement requirement.

$[16$ marks$]$

b$)$ Sketch the control section for the punching shear caused by the column loading $($no calculation of punching shear checking needed$)$ and explain your reason.

$[10$ marks$]$