Problem 3.1 The deflection y (m) of a cantilever beam under a uniform load can b

Question

Problem 3.1 The deflection y (m) of a cantilever beam under a uniform load can be calculated with the following equation: y = qx^2/24EI (x^2 - 4Lx + 6L^2) where q is the applied load (1.5 kN/m) x is the distance along the beam (m) E is the Young's modulus of the beam (25000 kPa) I is the Moment of Inertia of the beam (12 m^4) L is the length of the beam (100 m) Write a script to complete the following tasks: a) Define variables for each constant defined above. b) Define a vector x with at least 50 values between 0 and 100 m. c) Calculate the deflection y (m) of the beam for each distance along the beam x. The deflection for ALL distances should be calculated in one equation HINT: You will need to use the dot operator. d) Use the appropriate built-in MATLAB function to calculate the minimum and maximum deflection values and assign the values to variables. e) Display an output message of your choice and the minimum and maximum deflection values to the command window using the built-in MATLAB disp function. Show the display messages in your diary file. Check your answers with the solutions below: Solution at x = 0m: y=0 Solution at x = 100m: y=62.5

Explanation / Answer

% part 1
q = 1.5;
E = 25000;
I = 12;
L = 100;

% part b
x = linspace(0,50,100);

y = zeros(1,100);
% part c
for i = 1:100
c = x(:,i);
y(:,i) = (q*c*c*(c*c - 4*L*c + 6*L*L))/(24*E*I);
end

% part 4
minimum = min(y)
maximum = max(y)

% part 5 for x = 100
x = 100;
y = (q*x*x*(x*x - 4*L*x + 6*L*L))/(24*E*I)

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