A design is required with two ASTM$-$A$992$ Grade $345$ steel beams, fixed at one end and subjected to the load shown in the figure. Plot the shear force and bending moment diagrams for one beam. Select an S$-$type beam $($the most economical$)$ that ensures the maximum deflection at the free end is not greater than $4$ mm$.$ w $=6$ kN$/$m$,$ L $=5$ m$,$ M $=20$ kN$-$m$,$ and confirm that the maximum stress does not exceed a design stress considering a safety factor of $4\mathrm{.}0$