$8\mathrm{.}4-5$ A beam with a width $b=150mm$ and depth

$h=200mm$ is simply supported at A and $B.$ The beam

has a length $L=3m$ and is subjected to a linearly vary$-$

ing distributed load with peak intensity $q_0=22k\frac{N}{m}.$

Calculate the state of plane stress at point $C$ located

$75$ mm below the top of the beam and $30$ mm to the

left of point $B.$ Also find the principal stresses on

element $C.$ Neglect the weight of the beam.