calculate shear force and bending moment and deflection by using intgertion in matlab

To calculate shear force, bending moment, and deflection of a beam using integration in MATLAB, you can follow these steps:

  1. Define the loading and boundary conditions for the beam.
  2. Use the integration method to calculate shear force, bending moment, and deflection equations based on the loading and boundary conditions.
  3. Plot the shear force, bending moment, and deflection diagrams.

Here is an example MATLAB code snippet to calculate and plot shear force, bending moment, and deflection of a simply supported beam with a point load at the center:

main.m
% Define beam parameters
L = 5; % Length of the beam
P = 10; % Point load at the center of the beam
E = 200e9; % Young's modulus
I = 1e-4; % Moment of inertia
x = 0:0.01:L; % Define the range of x-coordinate

% Calculate the shear force equation
V = @(x) P/2 - P*(x>L/2); % Shear force equation

% Calculate the bending moment equation
M = @(x) P/2*x - P*(x>L/2).*(x-L/2); % Bending moment equation

% Calculate the deflection equation
w = @(x) (P*x.^2).*(x<L/2)/24/E/I - (P*(x-L/2).^2).*(x>L/2)/24/E/I; % Deflection equation

% Integrate to get the actual values
V_values = arrayfun(V, x);
M_values = arrayfun(M, x);
w_values = arrayfun(w, x);

% Plot the diagrams
figure;
subplot(3,1,1);
plot(x, V_values, 'r', 'LineWidth', 2);
xlabel('x');
ylabel('Shear Force');
title('Shear Force Diagram');

subplot(3,1,2);
plot(x, M_values, 'b', 'LineWidth', 2);
xlabel('x');
ylabel('Bending Moment');
title('Bending Moment Diagram');

subplot(3,1,3);
plot(x, w_values, 'g', 'LineWidth', 2);
xlabel('x');
ylabel('Deflection');
title('Deflection Diagram');
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You can modify the beam parameters, loading conditions, and equations based on your specific beam problem.

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