Q$3.[$Total: $22$ marks$]$

A group of $3$ piles support a $500$ mm square column which is subjected to an axial load of $4500$ kN $($factored$).$ The plan for the pile cap $($square section$)$ is shown in Figure Q$3.$ The effective depth of the cap is $1175$ mm $.$ Check against the axial capacity of the pile. Use the strut$-$and$-$tie method to calculate the force in the "tie" and design the reinforcement $($tension$)$ in each "tie". There is no need to consider the self$-$weight of concrete and soil in calculation. Assume the piles are end bearing ones ignoring the pile group effect. Assume $\backslash (\backslash$mathrm$\{$f$\}\_\{\backslash$mathrm$\{$ck$\}\}=40\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )($concrete$),\backslash (\backslash$mathrm$\{$f$\}\_\{\backslash$mathrm$\{$yk$\}\}=500\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )($steel$).$

Figure Q$3$: Pile Cap Plan $($unit: mm$)$