indeterminate beam a calculate shear force diagram and bending moment diagram and deflection in matlab

To calculate the shear force diagram, bending moment diagram, and deflection of an indeterminate beam in Matlab, you can follow these general steps:

1. Define the beam properties such as length, supports, material properties, loads, etc.
2. Use the equilibrium equations and compatibility equations to set up the stiffness matrix and load matrix for the given beam.
3. Use matrix operations to solve for the unknown displacements and forces in the beam elements.
4. Calculate the shear forces, bending moments, and deflection along the beam length using the solved displacements and forces.

Here is a very simplified example to demonstrate the process for a statically determinate beam (simply supported beam) using finite element analysis:

main.m
% Beam properties
L = 5; % Length of the beam
E = 200e9; % Young's Modulus
I = 4.1667e-5; % Moment of Inertia
w = 10; % Distributed load

% Stiffness matrix
K = [12, 6*L, -12, 6*L; 
    6*L, 4*L^2, -6*L, 2*L^2; 
    -12, -6*L, 12, -6*L; 
    6*L, 2*L^2, -6*L, 4*L^2]*(E*I)/(L^3);

% Load matrix
F = [w*L/2; w*L^2/12; w*L/2; -w*L^2/12];

% Displacement and reaction forces
displacements = K\F;

% Shear force and bending moment calculations
x = 0:0.1:L;
V = zeros(size(x));
M = zeros(size(x));
for i = 1:length(x)
    N = [1, x(i), x(i)^2, x(i)^3]*displacements;
    dN = [0, 1, 2*x(i), 3*x(i)^2]*displacements;
    V(i) = N*w;
    M(i) = E*I*dN;
end

% Deflection calculation
deflection = [1, x, x.^2, x.^3]*displacements;

% Plotting the results
figure;
subplot(3,1,1);
plot(x,V);
title('Shear Force Diagram');

subplot(3,1,2);
plot(x,M);
title('Bending Moment Diagram');

subplot(3,1,3);
plot(x,deflection);
title('Deflection Diagram');
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This code computes the shear force diagram, bending moment diagram, and deflection diagram of a simply supported beam with a distributed load using finite element analysis in Matlab.

Please note that for indeterminate beams, a more complex approach like the Matrix Displacement Method or Finite Element Method should be employed depending on the degree of indeterminacy.