Due: 09/28/2017 Develop a computer program for determining the static equilibriu

Question

Due: 09/28/2017 Develop a computer program for determining the static equilibrium position(s) of the system shown below. The program should determine the equilibrium values of g and 2, given values for the quantities ai, bi,nq, Fi, ki, li , xi, and yi , for i = 1, 2. The quantities k, and 1, are the stiffness and free length, respectively, of spring i. Specific test cases are: tenshn (x,y) Test Cases: a, = a2 = 10 inch b, = b2 = 20 inch 11 = 12 = 10 inch w1 = w2 = 12 lbf. k, = k2 = 5 lbf / inch Case 1: x1 = 20 inch, y1 0 inch, x2 20 inch, 2 0 inch F. Case II: x| = 40 inch, y, =0 inch. im =-20 inch. y220 inch Submit a listing of the computer program and the corresponding results for each case metla mathemntica

Explanation / Answer

% SPRING ELEMENT

clc;
tic;
format short eng
n=3;
DOF=1;
NNODE=4;
GR=DOF*NNODE;
GC=GR;
A(1)=440;A(2)=220;A(3)=77;
E(1)=0.7*10^5;E(2)=1*10^5;E(3)=2*10^5;
L(1)=308;L(2)=110;L(3)=110;
LOC=[1 2;2 3;3 4];

%INITIALIZING KG MATRIX
for ii=1:GR
for jj=1:GC
KG(ii,jj)=0.0;
end
end

% STIFFNESS MATRIX
for i=1:n
j=LOC(i,1);
KE(1,1)=A(i)*E(i)/L(i);
KE(1,2)=-KE(1,1);
KE(2,1)=-KE(1,1);
KE(2,2)=KE(1,1);
disp('i');
disp(i);
disp('KE');
disp(KE);
  
% KG MATRIX
N(1)=j;
N(2)=j+1;
for ii=1:2
for jj=1:2
ik=N(ii);
jk=N(jj);
KG(ik,jk)=KG(ik,jk)+KE(ii,jj);
end
end
end
GK=KG;
disp('KG');
disp(KG);

% BOUNDARY CONDITIONS

HR=1;
for HC=1:GC
KG(HR,HC)=0;
KG(HC,HR)=KG(HR,HC);
end
HR=4;
for HC=1:GC
KG(HR,HC)=0;
KG(HC,HR)=KG(HR,HC);
end
KG(1,1)=1.0;
KG(4,4)=1.0;

%KGB MATRIX
for u=1:GR
for v=1:GC
KGB(u,v)=KG(u,v);
end
end
disp('KGB');
disp(KGB);

% APPLIED LOADS(FORCES) VECTOR
for NE=1:GR
F(NE)=0.0;
end
F(2)=-5000;
F(3)=10000;
disp('Applied forces');
disp(F);

% DISPLACEMENT VECTOR
d=(KGB^(1))*F';
disp('Displacement Vector');
disp(d);

% SUPPORT REACTIONS
disp('Forces at nodes and support reactions');
FR=GK*d;
disp(FR);

% STRESS CALCULATION

disp('Element No, Stress');
for i=1:n
j=LOC(i,1);
j1=j;
k1=j+1;
de(1)=d(j1);
de(2)=d(k1);
sigma(i)=E(i)*(de(2)-de(1))/L(i);
fprintf('%d %f ',i,sigma(i));
end
toc

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