Plotting cantilever and beam plots using Matlab - matlab

Question

Problem
I have to plot a beam/cantilever using Matlab. Where my inputs are:
Length of the beam
Position of the loads (input is a vector)
Forces of the load (input is a vector)
Whether is it a cantilever or not. Because I have different equations for calculating the displacement.
My Solution
I have come to an idea on how I can actually plot the cantilever, but I can not formulate it into a code in MATLAB. I have spent hours trying to write something on Matlab but I have gotten nowhere. (I am a novice to Matlab)
My solution is as follow: I have the formula for the displacement from starting position.
I can define a vector using loop for x coordinates until the given beam length. Hence,
x=[0 ... L]
Then I want to define another vector where the difference is calculated (this is where I can't figure out Matlab)
y = [h, h - y(x1), h - y(x2), .... h - y(L)]
where h is the starting height, which I have thought to be defined as (y(x1) - y(L)) + 1, so that the graph then doesn't go into the negative axes. y(x) is the function which will calculate the displacement or fall of the beam.
Once that is done, then I can simply plot(x,y) and that would give me a graph of a shape of deflected beam for the given range from 0 to beam length. I have tested my theory on excel and it works as per the graph is concerned but I can not figure out implementation on Matlab.
My incomplete code
%Firstly we need the inputs
%Length of the beam
l = str2double(input('Insert the length of your beam: ', 's'));
%Now we need a vector for the positions of the load
a = [];
while 1
a(end+1) = input('Input the coordinate for the position of your load: ');
if length(a)>1; break; end
end
%Now we need a vector for the forces of the load
W = [];
while 1
W(end+1) = input('Input the forces of your load: ');
if length(W)>1; break; end
end
%
%
%
%Define the formula
y = ((W * (l - a) * x)/(6*E*I*l)) * (l^2 - x^2 - (l - a)^2);
%Where
E = 200*10^9;
I = 0.001;
%
%
%
%Now we try to plot
%Define a vector with the x values
vectx = [];
for i = 1:l
vectx = [vectx i];
end
%Now I want to calculate displacement for each x value from vectx
vecty = [];
for i=1:l
vecty=[10 - y(x(i)) i];
end
%Now I can plot all the information
plot(vectx, vecty)
hold on
%Now I plot the coordinate of the positions of the load
plot(load)
end
Really need some help/guidance. Would be truly grateful if someone can help me out or give me a hint :)
I have edited the question with further details

Answer 1

There are several things that do not work in your example.
For instance, parameters should be defined BEFORE you use them, so E and I should be defined before the deflection equation. And you should define x.
I do not understand why you put your inputs whithin a while loop, if you stop it at length(a)>1;. You can remove the loop.
You do not need a loop to calculate displacements, you can just use a substraction between vectors, like displacement = 10 - y. However, I do not understand what is H in your example; since your beam is initially at position 0, your displacement is just -y.
Finally, your equation to calculate the deformed shape is wrong; it only accounts for the first part of the beam.
Here, try if this code works:
%Length of the beam
l = input('Insert the length of your beam: ');
%Now we need a vector for the positions of the load
a = input('Input the coordinate for the position of your load: ');
%Now we need a vector for the forces of the load
W = input('Input the forces of your load: ');
%Define the formula
E = 200*10^9;
I = 0.001;
% x Position along the beam
x = linspace(0,l,100);
b = l - a;
% Deflection before the load position
pos = x <= a;
y(pos) = ((W * b .* x(pos))/(6*E*I*l)) .* (l^2 - x(pos).^2 - b^2);
% Cantilever option
% y(pos) = W*x(pos).^2/(6*E*I).*(3*a-x(pos));
% Deflection after the load position
pos = x > a;
y(pos) = ((W * b )/(6*E*I*l)) .* (l/b*(x(pos)-a).^3 + (l^2 - b^2)*x(pos) - x(pos).^3);
% Cantilever option
% y(pos) = W*a^2/(6*E*I).*(3*x(pos)-a);
displacement = 10 - y; % ???
% Plot beam
figure
plot(x , x .* 0 , 'k-')
hold on;
% Plot deflection
plot(x , y , '--')
% Plot load position
% Normalize arrow size as 1/10 of the beam length
quiver(a , 0 , 0 , sign(W) .* max(abs(y))/2)