Q$5.$ A square plate $(a=b)$ is simply supported on all edges and is loaded by gravel such that

$q(x,y)=q_{0}sin\frac{mx}{a}sin\frac{ny}{b}$

$($a$)$ Determine the maximum deflection and the corner reaction. $($b$)$ Evaluate, by retaining the first two terms

of the series solution, the value of $q_0$ so that the maximum deflection is not to exceed $10mm$ for the following

data: $E=165$GPa,$v=0\mathrm{.}25,a=4m,$ and $t=25mm.$ Write all details