/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 19.01.2x ] */
/* [wxMaxima: title   start ]
Rollbar
   [wxMaxima: title   end   ] */


/* [wxMaxima: comment start ]
Il rollbar è una struttura prottetiva disposta per proteggere gli occupanti di una vettura in caso di incidente di qualsiasi genere e gravità. Si può schematizzare come una struttura a portale mostrato nella figura 1.
   [wxMaxima: comment end   ] */


/* [wxMaxima: caption start ]

   [wxMaxima: caption end   ] */
/* [wxMaxima: image   start ]
png
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
   [wxMaxima: image   end   ] */


/* [wxMaxima: comment start ]
Si vuole calcolare la cedevolezza nel punto B, ossia la sua deflessione. Il punto B corrisponde al punto estremo che gli occupanti dell'abitacolo possono raggiungere durante un incidente. Si assume che la trave abbia una sezione costante e che il materiale sia isotropo omogeneo. Si inizia definendo le lunghezze:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
l:a-h;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si deve assumere che le lunghezze siano positive:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
assume(l>0,a>h,h>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si svincola la struttura nel punto A sostituendo con le reazioni vincolari che darebbe l'incastro. Le reazioni dovute all'incastro E sono esattamente le stesse di A. La figura  2 mostra gli andamenti del momento flettente dovuto ai vari contributi: carico P, reazioni vincolari di A YA,XA e CA e nell'ultima figura la forza fittizia inserita per calcolare lo spostamento in B secondo il teorema di Castigliano. Si è trascurato lo sforzo normale.
   [wxMaxima: comment end   ] */


/* [wxMaxima: caption start ]

   [wxMaxima: caption end   ] */
/* [wxMaxima: image   start ]
png
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
   [wxMaxima: image   end   ] */


/* [wxMaxima: comment start ]
Si procede ora con gli equilibri. 
Equilibrio alla traslazione in direzione x:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
eqtx:-P-F+XA+XE=0;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
equilibrio alla traslazione in direzione y:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
eqty:YA+YE=0;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Per quanto riguarda la convenzione dei segni del momento flettente, si assume positivo se causa trazione nell'intradosso e negativo se invece causa compressione.
 Equilibrio alla rotazione in z rispetto al punto E:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
eqrEz:-P*a+YA*b+XA*0+CA-F*h+CE+XE*0+YE*0=0;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si calcolano le reazioni vincolari dell'incastro E XE, YE e CE risolvendo il sistema di equilibrio tramite il comando linsolve (globalsolve=true:dopo aver risolve il sistema viene assegnato il risultato alle variabili e mantenuto anche per le stringhe successive):
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
linsolve([eqtx,eqty,eqrEz],[XE,YE,CE]),globalsolve=true;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si scrive la funzione del momento flettente come funzione di interpolazione lineare: si costruisce un'ascissa curvilinea normalizzata e dati i 2 estremi la funzione dovrà essere al più nulla all'inizio e massima alla fine in un intervallo [0,1] e in seguito si fa muovere il momento flettente al variare dell'ascissa curvilinea all'interno dell'intervallo.
Si considera 0 l'inizio della trave e 1 la sua fine:
N0(0)=1, N0(1)=0
N1(0)=0, N1(1)=1
 Definiamo due costruzioni per definire la funzione:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
define(
N0(pippo),
1-pippo
);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
N1(pippo):=pippo;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
N0(0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
N0(1/2);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
N1(0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
In questo modo si è generalizzato ogni singolo tratto di trave, rendendo più semplice il calcolo dei momenti.
Ora si considera ogni tratto della struttura e si va a sommare i vari contributi dei momenti flettenti trovati precedentemente nei 5 diagrammi:
Tratto AB:
Estremo 1 (A): P,YA,XA,CA,F
Estremo 2(B):P,YA, XA,CA,F
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
MfAB:expand((0+0+0-CA+0)*N0(xi)+(0+0+XA*h-CA+0)*N1(xi));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Tratto BC, estremo1=B e estremo2=C
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
MfBC:expand((0+0+XA*h-CA+0)*N0(xi)+(0+0+XA*a-CA-F*l)*N1(xi));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Tratto CD,estremo1=c e estremo2=D
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
MfCD:expand((0+0+XA*a-CA-F*l)*N0(xi)+(0-YA*b+XA*a-CA-F*l)*N1(xi));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Tratto DE:estremo1=D e estremo2=E
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
MfDE:expand((0-YA*b+XA*a-CA-F*l)*N0(xi)+(P*a-YA*b+0-CA+F*h)*N1(xi));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si calcola ora l'energia potenziale elastica dei singoli tratti di trave (tramite integrale secondo il teorema di Castigliano):
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
UAB:integrate(MfAB^2/(2*E*J)*h,xi,0,1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
UBC:integrate(MfBC^2/(2*E*J)*l,xi,0,1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
UCD:integrate(MfCD^2/(2*E*J)*b,xi,0,1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
UDE:integrate(MfDE^2/(2*E*J)*a,xi,0,1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Energia potenziale elastica totale:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
U:UAB+UBC+UCD+UDE;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si calcolano i cedimenti in A facendo la derivata dell'energia potenziale elastica tramite il secondo teorema di Castigliano,
si calcola cioè la minima energia di deformazione elastica.
uA: spostamento in x di A.
vA:spostamento in y di A.
rA:rotazione in A.

   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
uA:diff(U,XA);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
vA:diff(U,YA);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
rA:diff(U,CA);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si impone che queste reazioni vincolari siano uguali a 0, perchè in A si ha un incastro:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
eqns:[uA=0,vA=0,rA=0];
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Ora si hanno 3 equazioni dalle quali è possibile ricavare XA,YA e CA tramite la funzione linsolve: 
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
linsolve( eqns, [XA,YA,CA] );
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si associa la soluzione alle variabili, in modo tale da poterle usare in altre stringhe.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
sols:%;
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Ora si richiede di valutare un espressione (in questo caso U) per le variabili trovate e si sostituiscono i valori di tali variabili (in questo caso le variabili trovate in sols):
   [wxMaxima: comment end   ] */


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


/* [wxMaxima: comment start ]
Fattorizzo i termini per compattarli:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
U:fullratsimp(%)$
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Ora si trova lo spostamento in B (che chiamiamo d) con il teorema di Castigliano (derivata dell'energia potenziale elastica totale rispetto alla 
forza fittizia F):
   [wxMaxima: comment end   ] */


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


/* [wxMaxima: comment start ]
Poichè F era una forza fittizia, la si elimina imponendola uguale a zero:
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
d:ev(d,F=0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Si è quindi trovato lo spostamento d in B.
   [wxMaxima: comment end   ] */



/* Old versions of Maxima abort on loading files that end in a comment. */
"Created with wxMaxima 19.01.2x"$