A simple beam is $6$m long and has a cross section of $200$mm wide by $300$mm deep. It is carrying a total imposed uniformly distributed load of $30$ kN$/$m$.$ Assume E $=100$ GPa.

$1.$ Solve for the maximum deflection $($mm$).$

$2.$ Solve for the maximum bending stress at a fiber $50$mm above the top of the beam at a section $2$m from the left support $($MPa$).$

$3.$ Solve for the deflection at a section $2$m from the left support $($mm$).$

$4.$ Solve for the maximum bending stress at a fiber $50$mm below the top of the beam at a section $2$m from the right support $($MPa$).$