$4\mathrm{.}5\mathrm{.}11$ Simple beam AB supports a triangular load with

maximum intensity q$0=10$ lb$/$in$.$ acting at mid$-$span, and a concentrated load P $=80$ lb acting at mid$-$span $($see figure$).$ Draw the shear force and bending moment diagrams for this beam, and add the slope and deflection diagram of the beam using the method of cuts. PROB. $4\mathrm{.}5\mathrm{.}11$