Matlab code for cantilever beam with point load at free end

# * Item one
# * Item two

Answer 1

[Aman]

Hi Mamatha,

As per my understanding, the length of the cantilever beam (L) is 10 m and the point load (P) is 28 kN. So with the given information, we can say that the vertical reaction (RA) will be the same as P, and the moment reaction (MA) will be the product of P and L. Please find the code for the same below, which also includes the calculation of the deflectio (delta) at the free end:

L = 10;
P = 38 * 10^3;

RA = P;
MA = P * L;

E = 210 * 10^9;  % Young's modulus (N/m^2)
I = 0.1;  % Moment of inertia (m^4)
delta = (P * L^3) / (3 * E * I);

disp(['Vertical reaction at the fixed end (RA): ', num2str(RA), ' N'])
disp(['Moment reaction at the fixed end (MA): ', num2str(MA), ' N·m'])
disp(['Deflection at the free end (delta): ', num2str(delta), ' meters'])

I hope it helps!

Answer 2

[Umar]

Hi Mahamata,

Based on your query, it seems you are looking for a Matlab code to analyze the behavior of a cantilever beam with a point load at the free end. This type of analysis is commonly used in structural engineering and mechanics to understand the deflection and stress distribution in such beams. Here is a sample Matlab code that will help you with the screen shot provided and give you idea to help resolve your problem.

% Define beam properties L = 5; % Length of the beam (in meters) E = 200e9; % Young's modulus of the beam material (in Pascals) I = 1.2e-4; % Moment of inertia of the beam's cross-section (in meters^4)

% Define point load P = 1000; % Magnitude of the point load (in Newtons)

% Create a vector of positions along the beam x = linspace(0, L, 100); % Generating 100 points along the beam length

% Calculate the deflection at each position using the Euler-Bernoulli beam theory deflection = (P .* x.^2 .* (3*L - x)) / (6 * E * I);

% Plot the deflection profile plot(x, deflection); xlabel('Position along beam (m)'); ylabel('Deflection (m)'); title('Deflection of Cantilever Beam with Point Load');

% Calculate and plot the bending moment distribution moment = P * (L - x); figure; plot(x, moment); xlabel('Position along beam (m)'); ylabel('Bending Moment (Nm)'); title('Bending Moment Distribution in Cantilever Beam');

This code uses basic principles of structural mechanics to calculate and visualize the deflection and bending moment distribution in a cantilever beam subjected to a point load at its free end. The deflection is calculated using the Euler-Bernoulli beam theory, while the bending moment distribution is directly proportional to the distance from the free end.