Calculo de las Acciones Internas

Acciones Internas y Cargas de Empotramiento.pdf

Cargas Puntuales con Deformaciones de Cortante

clc
clear variables

% Calculo de acciones de empotramiento perfecto con deformaciones de
% cortante

syms E A I a b u1 u2 Px Py
assume([E,A,I,a,b,u1,u2,Px, Py],'real')

Af=[Px,Py,0]'

sm1=[E*A/a,0,0;
   0,12*E*I/(a^3*(1+u1)),-6*E*I/(a^2*(1+u1));
    0,-6*E*I/(a^2*(1+u1)),(4+u1)*E*I/(a*(1+u1))];
sm2=[E*A/b 0 0
    0 12*E*I/(b^3*(1+u2)) -6*E*I/(b^2*(1+u2))
    0,-6*E*I/(b^2*(1+u2)) (4+u2)*E*I/(b*(1+u2))];

sm=blkdiag(sm1,sm2)

CMJ=sym(zeros(6,9));
CMJ(:,1)=[1 0 0 -1 0 0]';
CMJ(:,2)=[0 1 0 0 -1 0]';
CMJ(:,3)=[0 0 1 0 -b -1]';
CMJ(:,4)=[-1 0 0 0 0 0]';
CMJ(:,5)=[0 -1 0 0 0 0]';
CMJ(:,6)=[0 -a -1 0 0 0]';
CMJ(:,7)=[0 0 0 1 0 0]';
CMJ(:,8)=[0 0 0 0 1 0]';
CMJ(:,9)=[0 0 0 0 0 1]';

CMJ

Sj=CMJ'*sm*CMJ

Sff=Sj(1:3,1:3)
Srf=Sj(4:end,1:3)

Df=Sff^-1*Af
Ar=Srf*Df

% Compute simplified symbolic expression
simplifiedExpr = simplify(Ar,"Steps",6400)

G=2.04*10^6/(2*(1+0.3));
xx=12*2.04*10^6*(30*40^3/12)/(G*5/6*30*40*400^2);
yy=12*2.04*10^6*(30*40^3/12)/(G*5/6*30*40*200^2);

results=subs(Ar,[E,A,I,a,b,u1,u2,Px, Py],[2.04*10^6,30*40,30*40^3/12,400,200,xx,yy,7071.07, 7071.07]);
results=vpa(results,4)

clc
clear variables

% Calculo de acciones de empotramiento perfecto con deformaciones de
% cortante

syms E A I a b u1 u2 Px Py M
assume([E,A,I,a,b,u1,u2,Px, Py,M],'real')

Af=[0,0,M]'

sm1=[E*A/a,0,0;
   0,12*E*I/(a^3*(1+u1)),-6*E*I/(a^2*(1+u1));
    0,-6*E*I/(a^2*(1+u1)),(4+u1)*E*I/(a*(1+u1))];
sm2=[E*A/b 0 0
    0 12*E*I/(b^3*(1+u2)) -6*E*I/(b^2*(1+u2))
    0,-6*E*I/(b^2*(1+u2)) (4+u2)*E*I/(b*(1+u2))];

sm=blkdiag(sm1,sm2)

CMJ=sym(zeros(6,9));
CMJ(:,1)=[1 0 0 -1 0 0]';
CMJ(:,2)=[0 1 0 0 -1 0]';
CMJ(:,3)=[0 0 1 0 -b -1]';
CMJ(:,4)=[-1 0 0 0 0 0]';
CMJ(:,5)=[0 -1 0 0 0 0]';
CMJ(:,6)=[0 -a -1 0 0 0]';
CMJ(:,7)=[0 0 0 1 0 0]';
CMJ(:,8)=[0 0 0 0 1 0]';
CMJ(:,9)=[0 0 0 0 0 1]';

CMJ

Sj=CMJ'*sm*CMJ

Sff=Sj(1:3,1:3)
Srf=Sj(4:end,1:3)

Df=Sff^-1*Af
Ar=Srf*Df

% Compute simplified symbolic expression
simplifiedExpr = simplify(Ar,"Steps",6400)

G=2.04*10^6/(2*(1+0.3));
xx=12*2.04*10^6*(30*40^3/12)/(G*5/6*30*40*400^2);
yy=12*2.04*10^6*(30*40^3/12)/(G*5/6*30*40*200^2);

results=subs(Ar,[E,A,I,a,b,u1,u2,Px, Py],[2.04*10^6,30*40,30*40^3/12,400,200,xx,yy,7071.07, 7071.07]);
results=vpa(results,4)