Required information The figure below shows a pinned-fixed beam subject to a uni
ID: 2074378 • Letter: R
Question
Required information
The figure below shows a pinned-fixed beam subject to a uniform load.
The equation for the resulting deflections is
y=w48EI(2x43Lx3+L3x)y=-w48EI2x4-3Lx3+L3x
Use the following parameter values in your computation (making sure that you use consistent units): L = 400 cm, E = 52,000 kN/cm2, I = 32,000 cm4, and w = 4 kN/cm.
Develop a MATLAB script that plots the function dy/dx versus x (with appropriate labels) and use bisectnew to determine the point of maximum deflection (i.e., the value of x where dy/dx = 0). Then substitute this value into the deflection equation to determine the value of the maximum deflection.
Employ initial guesses of xl = 0 and xu = 0.9 L.
In addition, use Ead = 0.0000001 m. Also, set format long in your script so you display 15 significant digits for your results.
Explanation / Answer
clc
clear all
close all
syms x
l= 400; E=52000; I=32000; w=4;
y=w*((2*x^4)+(3*l*x^3)+(l^3*x))/E*I ; % equation of deflection
dydx1= diff(y);
dydx= double(subs(dydx1,x,0:1:l)); % slope
plot(0:l,dydx) % plot
xlabel('x');
ylabel('dy/dx')
x1= double(solve(dydx1,x)); % dy/dx=0
ymax=double(subs(y,x,x1(1))); % ymax
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