A rigid beam $AB$ rests on the two short posts as shown in this figure. $AC$ is made of steel and has a diameter of $30$ mm $,$ and $BD$ is made of aluminium and has a diameter of $50$ mm $.$ Determine the displacement of point $F$ on AB if a vertical load of $90$ kN is applied over this point. Take $E=200$GPa $($steel$)$ and $E=70$GPa $($aluminium$).$