Consider a cantilever beam under a concentrated force and moment as shown below.

Question

Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter, and its unit is force length2), force F, and moment M. Use MATLAB built-in polynomial functions to find and plot the beam's deflection y (which is the sum of y and y) and slope 0, and also to locate the places) along the beam where the deflection would be zero and where the slope would be zero, respectively, and to get the deflection and slope at the free end of the beam. Run your program and report the results with the following parameters: L-1 .2 m, El-6x105 N-m2, F-1 1000 N, and M-10000 N m.

Explanation / Answer

clear all;close all;clc;commandwindow;
F=input('enter the value for Force F :');
M=input('enter the value for Momentum M :');
L=input('enter the value for beam length L :');
EI=input('enter the value for flexural rigidity EI :');
i=1;
for x=0:0.1:1.2
y1(i)=-((F*x.^2)*((3*L)-x))/(6*EI);
y2(i)=(M*x.^2)/(2*EI);
y(i)=y1(i)+y2(i);
i=i+1;
end
plot(y);
% axis([0 1.2 0 0.0014])

syms x
y1=-((F*x.^2)*((3*L)-x))/(6*EI);
theta1=diff(y1,x)
y2=(M*x.^2)/(2*EI);
theta2=diff(y2,x)
theta=theta1+theta2

%deflection and slope will be zero at x=0;
%deflection and slope at free end is computed by substituting x=1.2 in y
%and theta..
x=1.2;
y1=-((F*x.^2)*((3*L)-x))/(6*EI);
y2=(M*x.^2)/(2*EI);
max_y=y1+y2;
max_theta=subs(theta,x);
display('deflection at free end is ');
display(max_y);
display('slope at free end (in radians )is ');
display(max_theta);

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