Q$.1$ A column is supported by a square footing with the following design parameters:

Design Parameters

Side length of the square footing, $L=3000mm$

$,,$Overall depth of the footing $=h$

$,$Dimensions of the column, $c=500mm$

$,,,$Cover to rebar $=50mm$

$,,$Grade of concrete, $f_{cu}=35$MPa

$,$Preferred size of main bars $=20$

$,$Dead load from column, $G_k=1200kN$

$,,,($s$/$w of column and footing included$)$

$,$Imposed Load from column, $Q_k=600kN$

$($a$)$ What is the maximum allowable shear stress?

$($b$)$ Determine the design shear force at the perimeter of column.

$($c$)$ Express the maximum shear stress at the column face in term of the effective depth, d$.$

$($d$)$ According to $($a$)$ and $($c$),$ determine the minimum thickness, h$,$ of the footing.