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.

Answer 1

%%% MATLAB CODE

clear all
clc

%%% Input the parameters %%%
L = input('Enter beam length: ');
FR = input('Enter flexural rigidity: ');
F = input('Enter force: ');
M = input('Enter beam moment: ');

%%% Deflection and slope calculation %%%
c1 = F/(6*FR);
c2 = M/(2*FR);
p = [c1 (c2-(3*c1*L)) 0 0]; %Deflection polynomial
x = linspace(0,L,100);
y = polyval(p,x);
indexy = find(y==0);
sp = polyder(p); %Slope polynomial
s = polyval(sp,x);
indexs = find(s==0);
plot(x,y,'-.b')
hold on
plot(x,s,'--r')
plot(x(indexy),y(indexy),'g*');
plot(x(indexs),y(indexs),'bX');
xlabel('Length')
legend('Deflection','Slope','Zero deflection','Zero slope')

----Deflection -- --Slope Zero deflection x Zero slope o* ---------- 0 0.2 0.4 0.8 1 0.6 Length

In case of any queries feel free to comment, I will be happy to help you