A $22$ kg compressor impeller wheel is driven by a $13$ kg turbine mounted on a common steel shaft, as shown in Figure $1$ below. $E=207$GPa. Assuming the bearings to be stiff and acting as supports.

Calculate:

a$)$ The reactions of the supports at A and $C$

b$)$ The shaft deflection at $B$ and $D$ using Macaulay's method.

$[4]$

$[11]$

Figure $1$: Turbine shaft