prstrex.m

% Example: prstrex
% ~~~~~~~~~~~~~~~~
% This example determines the principal
% stresses for an element.
%
% Data is defined in the declaration statements
% below, where:
%
% No_angs - number of angles to calculate
%           stress values for
% Sigma_x - normal stress on x-axis
% Sigma_y - normal stress on y-axis
% Tau_xy  - shear stress
% Angle   - angle (in degrees) to determine
%           stresses for
% 
% NOTES: 1) normal stresses are + for tension,
%           - for compression
%        2) shear stresses are + when they
%           are directed down on the positive
%           x-axis face
%
% User m functions required:
%    prstress, strangle, prplot, arrows,
%    polarstr, genprint
%----------------------------------------------

clear;
%...Input definitions
Problem=2;
No_angs=90;
if Problem == 1
  %...Hydrostatic case
  Sigma_x=10; Sigma_y=10; Tau_xy=0;
elseif Problem == 2
  %...Other
  Sigma_x=70; Sigma_y=10; Tau_xy=40;
end
degrad=pi/180; raddeg=180/pi;

%...Find principal stresses
[Key,Smax,Smin,Savg,Tmxmn,Smax_ang, ...
  Smin_ang,Tmax_ang,Tmin_ang]= ...
  prstress(Sigma_x,Sigma_y,Tau_xy);

%...Find properties for rotated axes
theta=linspace(-180,180,No_angs+1);
for i=1:No_angs+1
  [Sxtheta(i),Sytheta(i),Sxytheta(i)]= ...
    strangle(theta(i),Sigma_x,Sigma_y,Tau_xy);
end

%...Output results
fprintf ...
  ('\n\nDetermination of Principal Stresses');
fprintf ...
  ('\n-----------------------------------\n');
fprintf('\n  Sigma-x: %g',Sigma_x);
fprintf('\n  Sigma-y: %g',Sigma_y);
fprintf('\n  Tau-xy:  %g\n',Tau_xy);
if Key == 1
  fprintf('\n  -----------------------------');
  fprintf('\n   ALL axes are principal axes');
  fprintf('\n  -----------------------------');
  fprintf('\n  Sigma-max: %g',Smax);
  fprintf('\n  Sigma-min: %g',Smin);
  fprintf('\n  Tau-max:   %g',Tmxmn);
else
  fprintf('\n  Sigma-max: %g at %g', ...
    Smax,Smax_ang);
  fprintf('\n  Sigma-min: %g at %g', ...
    Smin,Smin_ang);
  fprintf('\n  Sigma-avg: %g at %g', ...
    Savg,Tmax_ang);
  fprintf('\n  Tau-max:   %g at %g', ...
    Tmxmn,Tmax_ang);
  fprintf('\n  Tau-min:   %g at %g', ...
    -Tmxmn,Tmin_ang);
end
fprintf('\n\n');

%...Plot the results
prplot(Smax,Smin,Savg,Tmxmn,Smax_ang, ...
  Tmax_ang,Sigma_x,Sigma_y,Tau_xy)
% genprint('prstress');
  disp('Press a key to continue'); pause;

clf;
plot(theta,Sxtheta,'-',theta,Sytheta,'--', ...
     theta,Sxytheta,':');
  title('Transformation of Stress');
  xlabel('Angle (degrees)');
  ylabel('Stress'); 
  h=legend(' Sx',' Sy',' Tau','Location','Best'); 
  axes(h); drawnow;
% genprint('rotstr')
  disp('Press a key to continue'); pause;

tit=['Polar Diagram for Transformation ', ...
     'of Stress'];
theta=theta*degrad;
clf;
  polarstr(theta,Sxtheta,'w-'); hold on;
  polarstr(theta,Sytheta,'c--');
  polarstr(theta,Sxytheta,'g-.');
  title(tit); axis('equal'); axis('off');
  h=legend(' Sx',' Sy',' Tau','Location','Best'); 
  hold off; axes(h); drawnow;
% genprint('polar')