$*7\mathrm{.}91$ The beam $AB$ is subjected to the uniformly distributed load shown and to two unknown forces $P$ and $Q.$ Knowing that it has been experimentally determined that the bending moment is $+20kN*m$ at $D$ and $+19kN*m$ at $E,($a$)$ determine $P$ and $Q,($b$)$ draw the shear and bending$-$moment diagrams for the beam.

Answers: a$.)$ P $=5$ kN $($down$),$ Q $=2$ kN $($down$)$ b$.)$ V max $=16\mathrm{.}5$ kN at A$,$ M max $=21\mathrm{.}5$ kN$*$m$,2\mathrm{.}88$ meters from A