Displacement of cantilevered beam matlab

[DODGEVIPER13]

Homework Statement

Write a Matlab function to plot the displacement of a cantilevered beam under a point load. Annotate the figure’s axes and title the figure. In addition to creating the plot, the function should report (in the figure’s title!) the maximum deflection and angle between the horizontal and the surface of the beam at its tip. The geometry of the beam is shown below:
The formulas for the displacement y and tip angle θ are
y=-((Wx^2)/6EI)(3a-x) for 0<X<a
y=-((Wa^2)/6EI)(3x-a) for a<x<L
theta=0.5*((Wa^2)/EI)

where W is the point load, E is the Young’s modulus for the beam, I is the moment of inertia for the beam, and L is the length of the beam. Test your function with E = 30 Mpsi, I = 0.163 in4, L = 10 in, a = 3 in, W = 1,000 lbf. Report both your code and the plot for the given values.

Homework Equations

The Attempt at a Solution

function[ymax,theta]=displacement(E,I,L,a,W)


for x=linspace(0,a);
y=-(W*x.^2*(3*a-x))/(6*E*I);
end
for x=linspace(a,L);
y=-(W*a.^2*(3*x-a))/(6*E*I);
end

theta=0.5*((W*a.^2)/(E*I));
plot(y,x);
xlabel('Pos');
ylabel('disp');
title(sprintf('ymax=%g, theta=%5.3f',ymax,theta));

This is what I get:

ans =

8.2822e+003

The plot shows nothing so I am confused, what should I do?

 

[SteamKing]

For one thing, E = 30 Mpsi = 30 * 10^6 psi, or 30,000,000 psi. This accounts for the discrepancy in the deflection calculation. It doesn't explain why to slope wasn't output.

 

[DODGEVIPER13]

>> displacement(30*10.^6,0.163,10,3,1000) ok this is what I entered and I still didn't get a plot any more hints?

 

[DODGEVIPER13]

hey appreciate the help man I got it figure out

 

[rezeew]

Your attempt at a solution is on the right track, but there are a few things that need to be corrected in order for your code to work correctly. First, you need to define your variables and constants, such as E, I, L, a, and W. Without these values, your code won't be able to calculate the displacement and angle correctly. Also, your code currently only calculates the displacement at a single point, rather than along the entire length of the beam. You need to use a loop to calculate the displacement at multiple points along the beam's length.

Additionally, your code for the second part of the beam (x > a) is incorrect. It should be y=-(W*a^2*(3*x-a))/(6*E*I), without the dot after the "a". This is causing an error in your code.

Here is a corrected version of your code:

% Define variables and constants
E = 30*10^6; % Young's modulus in psi
I = 0.163; % moment of inertia in in^4
L = 10; % length of beam in inches
a = 3; % distance from support to point load in inches
W = 1000; % point load in lbf

% Define arrays for x and y values
x = linspace(0,L); % create an array of x values from 0 to L
y = zeros(size(x)); % create an array of the same size as x, filled with zeros

% Calculate displacement at each point along the beam's length
for i = 1:length(x)
if x(i) <= a % for x values less than or equal to a, use first formula
y(i) = -(W*x(i)^2*(3*a-x(i)))/(6*E*I);
else % for x values greater than a, use second formula
y(i) = -(W*a^2*(3*x(i)-a))/(6*E*I);
end
end

% Calculate maximum displacement and angle
ymax = max(y); % maximum displacement is the largest value in the y array
theta = 0.5*((W*a^2)/(E*I)); % angle in radians

% Plot displacement vs. position
plot(x,y);
xlabel('Position (in)');
ylabel('Displacement (in)');
title(sprintf('Maximum displacement = %g in, Angle = %5