Consider the Euler$-$Bernoulli beam model. Derive the distribution of the verti$-$

cal normal stress ${}_y(x,y)$ in an arbitrary longitudinal position $x$ and the cross

section is uniform rectangular one. The load $q(x)$ is acting on the top of the

beam. Are the stress boundary conditions satisfied at the top and bottom of

the beam? Draw the distribution of ${}_y$ as a function of $y$ coordinate.

Hint. See the example $3\mathrm{.}3$ in the lecture notes.