Question

Need help!!

1. (25 Points) In the figure below, figure (a) shows a uniform beam subject to a linearly increasing distributed load which starts a 0 at the left end and increases to Wo on the right end. As depicted in (b), the beam deflection can be computed with 4 120EIL where E is the modulus of elasticity [kN/cm2] and I is the moment of inertia [cm]. Calculate each of thee following quantities (take the derivatives by hand) and plot them versus distance along the beam using Matlab (a) Displacement y, (b) Slope )dyld] (c) Moment [M) EId'y/d*], (d) Shear V) Eld'y/d:'] Use the following parameters f L-500[cm, E- 35,000 [kN/cm2], 1- 35,000 [cm, Wo 2.75 [kN/cm]. Calculate the deflection every 20 [cm] Use the "subplot" function to display the plots in a 2x2 array in the or your computation: the same figure in the order (a) to (d). Type "help subplot at the Matlab prompt to learn how to use it. Include a title and axis labels (with units in square brackets) for each subplot. Plot the displacement with a solid blue line with dots at the data points, slope with a red dashed line, moment with a green dash-dot line, and shear with a magenta dotted line

Answer 1

MATLAB CODE

clc
clear all
%Given
L=500;
E=35000;
I=35000;
wo=2.75;
x=0:20:500;
Y=(wo./(120*E*I*L)).*(2*L.^2.*x.^3-x.*L^4-x.^5); %Given deflection eq.
S=(wo./(120*E*I*L)).*(6*L^2.*x.^2-L^2-5*x.^4); %Slope equation hand calculation
M=(wo./(120*E*I*L)).*(12*L^2.*x-20*x.^3); %Moment equation hand calculation
SF=(wo./(120*E*I*L)).*(12*L^2-60*x.^2); %Shear equation force hand calculation

subplot(2,2,1)
plot(x,Y)
axis([0 500 min(Y) max(Y)])
title('Deflection')

subplot(2,2,2)
plot(x,S)
axis([0 500 min(S) max(S)])
title('Slope')

subplot(2,2,3)
plot(x,M)
axis([0 500 min(M) max(M)])
title('Moment')

subplot(2,2,4)
plot(x,SF)
axis([0 500 min(SF) max(SF)])
title('Shear Force')

OUTPUT GRAPH