$(6$ pts$)$ A continuous circular rigid shaft ABCDE is supported with three journal bearings at $A,B$ and $D$ at the orientation shown in the figure below. The shaft is subjected to two point$-$force at $E$ in the $x$ and $y$ directions, $P_{Ex}=100N$ and $P_{Ey}=80N,$ and a triangle distributed force along $DC$ in the negative $z$ direction with the highest load magnitude of $w_{uz}=20\frac{N}{m}.$ Ignore the size of the journal bearings and diameter of the shaft in your calculations.

a$.$ Draw the freebody diagram of the shaft showing the applied forces and reactions

b$.$ Calculate the reactions at the journal bearings $A,B,$ and $D.($Should be Ay$,$ Az$,$ By$,$ Bz$,$ Dx$,$ Dz$)$

Note: section ABC is along the $x$ axis, section $DC$ is parallel to $y$ axis and section $DE$ is parallel to the $z$ axis.