## some further checks on the internal action components at nodes

double check all the nodal values!

Fig 2 graphs

l:a-h$

 [ M1A, M1B, M1C, M1D, M1E] :
 [  0 ,  0 ,  0 ,  0 ,  a ]*P
+[  0 ,  0 ,  0 , -b , -b ]*YA
+[  0 ,  h ,  a ,  a ,  0 ]*XA
+[ -1 , -1 , -1 , -1 , -1 ]*PsiA
+[  0 ,  0 , -l , -l , +h ]*F;

comparison with the previously defined M1

fullratsimp(
    [M1A,M1B,M1C,M1D]-[M1Ap,M1Bp,M1Cp,M1Dp]
);

fullratsimp(
    [M1B,M1C,M1D,M1E]-[M1Bm,M1Cm,M1Dm,M1Em]
);

a null difference, WOW!!! 

Figure 3 graphs, bending moment component 2

fullratsimp(
  - [M2Ap,M2Bm,M2Bp,M2Cm,M2Cp,M2Dm,M2Dp,M2Em]
  + [   0,   0,   0,   0,   0,  -b,   0,  -a]*H
  + [   0,  +h,  +h,  +a,   0,  +b,  -a,   0]*ZA
  + [  +1,  +1,  +1,  +1,   0,   0,  -1,  -1]*ThetaA
  + [   0,   0,   0,   0,  -1,  -1,   0,   0]*PhiA
  + [   0,   0,   0,   0,   0,   0,   0,  -a]*I
);

torsional moment

fullratsimp(
  - [MtAp,MtBm,MtBp,MtCm,MtCp,MtDm,MtDp,MtEm]
  + [   0,   0,   0,   0,   0,   0,  -b,  -b]*H
  + [   0,   0,   0,   0,  +a,  +a,  +b,  +b]*ZA
  + [   0,   0,   0,   0,  +1,  +1,   0,   0]*ThetaA
  + [  +1,  +1,  +1,  +1,   0,   0,  -1,  -1]*PhiA
  + [   0,   0,   0,   0,   0,   0,   0,   0]*I
);