kill(all);

/home/ebertocchi/_shared/ffcd26/001_shaftdeflection/shaftdeflection_withpeak_image__sAB_is_actually_sAC.png

FIXME     : s_AB in figure is actually s_AC!!
FIXME also: the reaction force due to P at A is actually P*[...]

Let's type bending moment expressions

MfCD : +        F*b/(a+b)*(a+sCD) - F*sCD
                 -C/(a+b)*(a+sCD) + C
       + P*(1-xi)*b/(a+b)*(a+sCD);
        

MfBD : ( F*a/(a+b) + C/(a+b) + P*(a+xi*b)/(a+b) ) * sBD;

MfAC : ( 
   +        F*b/(a+b)
   -          C/(a+b)
   + P*(1-xi)*b/(a+b)
)*sAC;

let's check [dis-]continuity of the typed bending moment expressions;

continuity at D

shouldbezero:
ratsimp(
  ev(MfCD, sCD=   xi *b) 
- ev(MfBD, sBD=(1-xi)*b)
);

wow...

shouldbeC:
ratsimp(
- ev(MfAC, sAC=a) 
+ ev(MfCD, sCD=   0)
);