Plotting deflection of beam using macaulay functions

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I am trying to plot the deflection of a beam under bending forces. My understanding is to use the heaviside function but i am having trouble plotting these points. An example of this function would be: slope=(1/(E*I))*(146.5*<x>^2+315<x-0.12>^2-70.24*,x.^3)
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Benjamin
Benjamin 2024-7-30
This code does not allow for the macaulay function to be considered, I managed to plot my shear force and bending moment diagrams fine but not the deflection and slope diagrams. What I plan to do is derive equations for each section of the beam on the same set if axes so the macaula functions wont be needed however to plot this in one plot function would be way preffered.
Umar
Umar 2024-7-30
@Benjamin, if you still have any further questions, please let me know.

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回答(1 个)

William Rose
William Rose 2024-8-18
You wrote:
"An example of this function would be: slope=(1/(E*I))*(146.5*<x>^2+315<x-0.12>^2-70.24*,x.^3)"
I interpret that to mean
I am not sure where you want to apply the heaviside function, and I do not know the range for x.
Example: A beam of length 1 is supported at x=0, x=0.4, and x=1. The deflection is given by
y=(x-0.2)^2-0.04 for x=0 to 0.4
and by
y=2*(x-0.7)^2-0.09 for x=0.4 to 1.0.
Plot the deflection (y) versus position (x), the easy way, and using heaviside functions.
Easy way:
x1=0:.01:.4;
y1=(x1-0.2).^2-0.04;
x2=0.4:0.01:1.0;
y2=(x2-0.7).^2-0.09;
figure;
subplot(211), plot(x1,y1,'-r.',x2,y2,'-b.'); xlabel('x'); ylabel('y'); grid on
Heaviside way:
x=0:.01:1;
y=heaviside(0.4-x).*((x-0.2).^2-0.04)+heaviside(x-0.4).*((x-0.7).^2-0.09);
subplot(212); plot(x,y,'-g.'); xlabel('x'); ylabel('y'); grid on
Good luck.
  1 个评论
William Rose
William Rose 2024-8-18
The basic idea for using heaviside functions is:
Suppose for , and for .
Then we can write a single function for y(x) using the heaviside function, h():
which we implement in matlab with
y=fR(x).*heaviside(xc-x)+fL(x).*heaviside(x-xc);
where x is a vector covering the full range of x.
If y has three functions, which apply in three different regions, then proceed as above, and use two heaviside functions in the middle region, to turn on and turn off the middle function at the appropriate values of x.
For example, if is the active function from , and fL and fR apply on the left and right sides, then multiply by two heaviside functions:
y=fR(x).*heaviside(xc1-x)+...
fmid(x).*heaviside(x-xc1).*heaviside(xc2-x)+...
fL(x).*heaviside(x-xc2);
Good luck.

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