Question

Implement the working of a mohr circle in matlab. ask user to enter the stresses in x and y direction. take the inputs to a stress tensor. then use formulations to find the eigen value and vectors.

MATLAB

Answer 1

% Center of Mohr Circle

sigma_x =input('Enter value of stress in x direction in N/mm2: ');

sigma_y = input('Enter value of stress in y direction in N/mm2: ');

sigma_c = (sigma_x+sigma_y)/2;

% Center = (sigma_c,0)

shear_t = input('Enter value of shear stress in N/mm2: ');

% Radius of Mohr Circle

r = sqrt(((sigma_x-sigma_y)/2)^2+shear_t^2);

twotheta = atan(shear_t/((sigma_x-sigma_y)/2));

theta = twotheta/2;

theta_2 = 0:1:360;

theta_2 = theta_2.*pi/180;

x = r*cos(theta_2)+sigma_c;

y = r*sin(theta_2);

sigma_1 = max(x);

sigma_2 = min(x);

Sx = [sigma_x shear_t];

Sy = [sigma_y -shear_t];

% all points together

allpoints = [sigma_c 0; sigma_1 0; sigma_2 0; sigma_x shear_t; sigma_y -shear_t];

plot(sigma_1,0,'o','LineWidth',2,'color','k')

hold on

plot(sigma_2,0,'o','LineWidth',2,'color','k')

plot(sigma_c,0,'o','LineWidth',2,'color','k')

plot([Sx(:,1) Sy(:,1)],[Sx(:,2) Sy(:,2)],'LineWidth',2,'color','k')

plot(x,y)

labels = {'C','P Str','P Str','B','A'};

labelpoints(allpoints(:,1), allpoints(:,2),labels,'SE',0.5,1)

grid on

axis equal

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