Consider the three$-$span prismatic beam with constant cross section, shown in the figure below. Assuming that this reinforced concrete beam can be treated as if it were made of a linear, infinitely elastic material, calculate and draw the bending moment and shear force diagrams for the four load combinations shown in the figure, where:

$P_1=G_1+G_2$

$P_2=1\mathrm{.}35G_1+1\mathrm{.}5G_2+1\mathrm{.}35Q$

are the fundamental load combinations for design at ultimate limit state, $G_1=5\mathrm{.}0k\frac{N}{m}$ is the dead load of structural elements, $G_2=2\mathrm{.}4k\frac{N}{m}$ are non$-$structural permanent loads and $Q=3\mathrm{.}0k\frac{N}{m}$ is the live load.

Notes

Draw all diagrams to scale, clearly indicate the values of maximum negative and positive bending moments for all supports and spans.

Make sure that all intermediate calculations are clearly presented.