beam to support a uniformly distributed load $($UDL$)$ of $10$ kN$/$m over a span of $6$ meters. The beam is $300$ mm wide and $500$ mm deep. Assuming a characteristic compressive strength of concrete $($f$\_$ck$)$ of $25$ MPa and a yield strength of steel $($f$\_$y$)$ of $400$ MPa, calculate:

a$)$ The maximum bending moment $($M$)$ experienced by the beam.