$(5)$ A beam, simply supported at ends A and B is loaded with two point loads of $30$ kN each at a distance of $2$ m and $3$ m respectively from end $A.$ Determine the position and magnitude of the maximum deflection. Take $E=2{10}^5\frac{N}{m}{m}^2$ and $I=7200c{m}^4.$ Use Macaulay's principle.

$(20$ Marks$)$