A beam with a rectangular cross section of dimensions a x $1\mathrm{.}5$a is made from a brittle material as seen

in the figure below. The ultimate strengths in tension and compression are TU $=290$ MPa and CU $=520$

MPa, respectively. The beam is subjected to a bending moment, M $=12$ kN$-$m and an axial compressive

force, P $=55$ kN$.$ Use the Mohr Failure Criterion and a safety factor of $2$ to determine the dimensions of

the beam$$s cross section in mm$.$ NOT DRAWN TO SCALE