Question $2$: $15$ points

Consider the cantilevered beam structure shown in Figure $3.$

Figure $2.$ Front elevation view of a cantilevered beam structure.

Vertical loads of $P(kN)$ and $kP(kN)$ are applied at the mid$-$spans of beam segments $A-B$ and $B-C,$ respectively.

$[2$a$](3$ pts$)$ Briefly explain how the principle of superposition $-$ hint, hint hint! $-$ can be applied to this problem.

$[2$b$](8$ pts$)$ Use the method of moment$-$area to show that the clockwise rotation of point $A$ is:

${}_A=[\frac{3-4k}{12}]\frac{P{L}^2}{EI}.$

$[2$c$](4$ pts$)$ Draw and label the deflected shape of the beam when $k=\frac{3}{4}.$ Indicate sections of beam where the fibre is in tension$/$compression$,$ and where the curvature is zero.