Given: ${}_x=$AMy,$\frac{dM}{dx}=S(x),\frac{dS}{dx}=-f$

where, A$-$constant, M$-$Bending Moment, S$-$total shear force, $f-$load$/$length

Show that

${}_{xy}=\frac{6S}{b{d}^3}[(\frac{d}{2}{)}^2-y^2]$ and ${}_y=\frac{6f}{b{d}^3}(\frac{d^{2}y}{4}-\frac{y^3}{3}-\frac{d^3}{12})$ here sigma$($x$)$ is given find out t$($xy$)$ and sigma$($y$)$ using $2$D stress transformation equilibrium equation.