rbar2.m

% Example: rbar2
% ~~~~~~~~~~~~~~
% This example calculates the deflection of
% a rigid bar suspended by a set of cables.
% This version uses the regular loop
% indexing.
%
% Data is defined in the declaration statements
% below, where:
%
% W      - gravity load
% Xcable - vector containing x location for
%          each cable
% Lcable - vector containing cable lengths
% Acable - vector containing cable areas
% Ecable - vector containing cable Es
% No_W_load_pts - number of solutions to
%          generate for different positions
%          of applied W
%
% User m functions required:
%    genprint
%----------------------------------------------

clear;
%...Input definitions
Problem=1;
if Problem == 1
  W=100000; No_W_load_pts=10;
  Xcable=[   0      48   120  192 ];
  Lcable=[  72     120    84   96 ];
  Acable=[   1       2  0.75  0.5 ];
  Ecable=[30e6  10.6e6  30e6  30e6];
end
No_cables=length(Ecable);

%...Calculate AE/L and X ratio for each cable
for i=1:No_cables
  Cael(i)=(Acable(i)*Ecable(i))/Lcable(i);
  Xratio(i)=Xcable(i)/Xcable(No_cables);
end
  
%...Setup and solve simultaneous equations
A=zeros(2,2);
for i=1:No_cables
  temp=Xratio(i)*Cael(i);
  A(1,1)=A(1,1)+Cael(i)-temp;
  A(1,2)=A(1,2)+temp;
  A(2,1)=A(2,1)+Xcable(i)*Cael(i)*(1-Xratio(i));
  A(2,2)=A(2,2)+Xcable(i)*temp;
end
b(1)=W; 

%...Solve for extreme locations of W
Xleft=A(2,1)/A(1,1); Xright=A(2,2)/A(1,2);

%...........................................
%...Loop to solve for deflection, force, and
%...stress in each cable as load is moved
%...across allowable range
%...........................................
X_inc=(Xright-Xleft)/No_W_load_pts;
Xw=Xleft:X_inc:Xright;
for j=1:No_W_load_pts+1
  %...Solve simultaneous equations
  b(2)=W*Xw(j); x=A\b';
  %...Calculate remaining quantities
  for i=1:No_cables
    Delta(j,i)=(1-Xratio(i))*x(1)+ ...
               Xratio(i)*x(2); 
    Fcable(j,i)=Cael(i)*Delta(j,i);
    Stress(j,i)=Fcable(j,i)/Acable(i);
  end
end
Delta=-Delta;

fprintf('\nRigid Bar Suspended by Cables');
fprintf('\n-----------------------------');
fprintf('\n\nAcceptable Range of Load Point\n');
fprintf(  '\n  X (left):  %g',Xleft);
fprintf(  '\n  X (right): %g',Xright);
for j=1:No_W_load_pts+1
  fprintf('\n\nW at x = %g',Xw(j));
  for i=1:No_cables
    fprintf('\n  Cable # %g',i);
    fprintf('\n    Force:      %g',Fcable(j,i));
    fprintf('\n    Stress:     %g',Stress(j,i));
    fprintf('\n    Deflection: %g',Delta(j,i));
  end
end
fprintf('\n');

clf; plot(Xcable,Delta);
  title(['Rigid Bar Positions for Each' ...
         ' Load Location']);
  xlabel('x Position Along Rigid Rod');
  ylabel('Displacement'); drawnow;
% genprint('rod-xy');
  disp('Press key to continue'); pause

clf; meshz(Xcable,Xw,Delta);
  title(['Rigid Bar Positions for Each' ...
         ' Load Location']);
  xlabel('x Position Along Rigid Rod');
  ylabel('Location of W');
  zlabel('Displacement'); 
  view(-45,60); drawnow;
% genprint('mesh-rod');