/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 0.8.7 ] */

/* [wxMaxima: input   start ] */
kill(all);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
equilibrium equations
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
eqtrx : UA = 0;
eqtry : VD = 0;
eqtrz : -F+WA+WD = 0;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
eqrOx : ThetaD +0*VD +b*WD -c*F ;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
eqrOy : PhiA + a*F -a*WA + 0*UA ;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
eqrOz : 0 = 0 ;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
blindly solve the equations
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
linsolve(
[ eqtrx , eqtry, eqtrz , eqrOx , eqrOy, eqrOz ],
[UA,PhiA, WD,VD,ThetaD]
) , globalsolve=True;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
the WA unknown reaction force has been removed from
the unknowns list, thus obtaining a parametric
representation of the reaction forces and moments, 
with WA as a parameter (like F)
   [wxMaxima: comment end   ] */

/* [wxMaxima: comment start ]
to obtain the actual value of WA, the deflection in the 
z direction of the A point has to be evaluated and
zeroed. Castigliano's Theorem fits.
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
N  : 0;
Sx : -VD;
Sy : -WD;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
equilibrium with respect to rotation along the
local Cz axis 
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
linsolve( Mt + ThetaD - e*WD + f*VD , Mt)
,globalsolve=true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
equilibrium with respect to rotation along the
local Gx and Gy axes
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
linsolve( Mx +WD*s =0, Mx), globalsolve=True;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
linsolve ( My - VD*s =0,My  ), globalsolve=true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Internal energy for the DB beam
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
U : integrate(
(Jyy*Mx^2+Jxx*My^2+2*Jxy*Mx*My)
 /
(2*E*(Jxx*Jyy-Jxy^2))

+

N^2/2/E/A

+

( chix * Sx^2 + chiy * Sy^2 + chixy * Sx*Sy )
 /
(2*G*A)

+

Mt^2/2/G/Kt

,s,0,a);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Castigliano's Theorem is now applied to obtain the 
z deflection at A
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
linsolve(
    diff( U , WA ) = 0,
    WA
), globalsolve=true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
U : ev(U);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
I check that all the WA terms hidden within U are now
expressed as functions of F
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
diff( U , 'WA) ;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
the z deflection at the L point is evaluated for the
quarter ladder frame structure, constrained according 
to two skew-symm planes
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
d : diff(U , F);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
dw : diff(4*U , F);
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$