Marking a single point on a graph

This is my code for finding normal and shear stress:

sigma_x = 8;

sigma_y = -12;

tau_xy = -6;

theta = [-90:.05:90];

%Normal Stress

sigma_x1 = ((sigma_x + sigma_y)/2)+(((sigma_x - sigma_y)/2)*(cosd(2*theta)))+(tau_xy*(sind(2*theta)));

sigma_y1 = ((sigma_x + sigma_y)/2)-(((sigma_x - sigma_y)/2)*(cosd(2*theta)))-(tau_xy*(sind(2*theta)));

%Shear Stress

tau_x1y1 = -(((sigma_x - sigma_y)/2)*(sind(2*theta)))+(tau_xy*(cosd(2*theta)));

%plot

plot(theta, tau_x1y1),xlabel('Degree of Rotation'), ylabel('Shear Stress'),title('Shear Stress Based on Rotation')

grid on, axis equal

I need to know how to just mark the points where shear stress = 0.

Thank you.

Answer 1

[Star Strider]

This first finds the approximate indices for the zero-crossings, then interpolates to find the exact values:

sigma_x = 8;
sigma_y = -12;
tau_xy = -6;
theta = [-90:.05:90];
%Normal Stress
sigma_x1 = ((sigma_x + sigma_y)/2)+(((sigma_x - sigma_y)/2)*(cosd(2*theta)))+(tau_xy*(sind(2*theta)));
sigma_y1 = ((sigma_x + sigma_y)/2)-(((sigma_x - sigma_y)/2)*(cosd(2*theta)))-(tau_xy*(sind(2*theta)));
%Shear Stress
tau_x1y1 = -(((sigma_x - sigma_y)/2)*(sind(2*theta)))+(tau_xy*(cosd(2*theta)));

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
tauzix = zci(tau_x1y1);                                                 % Approximate Zero-Crossing Indices
for k = 1:numel(tauzix)
    xval(k) = interp1(tau_x1y1(tauzix(k)-1:tauzix(k)+1), theta(tauzix(k)-1:tauzix(k)+1), 0);    % ‘Theta’ Values At Zero-Crossings
end


%plot
plot(theta, tau_x1y1)
hold on
plot(xval, zeros(size(xval)), 'pg')
hold off
xlabel('Degree of Rotation'), ylabel('Shear Stress'),title('Shear Stress Based on Rotation')
grid on, axis equal

[Paul Bradford]

Worked very well. Thank you.

[Star Strider]

As always, my pleasure.