"A civil engineer is tasked with designing a simple beam bridge to span a river with a length of $20$ meters and support pedestrian traffic. Using concrete with a density of $2400$ kg$/$m$^3$ and assuming a uniformly distributed load of $5$ kN$/$m along the length of the bridge:

a$)$ Calculate the total weight of the concrete needed to construct the bridge deck.

b$)$ Determine the maximum bending moment experienced by the beam at midspan.