Question

 Figure P5.13a shows a uniform beam subject to a linearly increasing distributed load. The equation for the resulting elastic curve is (see Fig. P5.135) 

Use bisection to determine the point of maximum deflection (that is, the value of x where dy/dx = 0). Then substitute this value into Eq. (P5.13) to determine the value of the maximum deflection. Use the following parameter values in your com- putation: L = 600 cm, E = 50,000 kN/cm², I = 30,000 cm, and w₀ = 2.5 kN/cm.  

Answer 1

clc
clear all
close all
L=600;
E=50000;
I=30000;
w0=2.5;
g=@(x) (w0/(120*E*I*L))*(- x*L^4 + 2*L^2*x^3 - x^5);
f=@(x) (w0/(120*E*I*L))*(- L^4 + 6*L^2*x^2 - 5*x^4);
e=1e-6;
a=0;
b=500;
iter = 0;
  
if f(a)*f(b)>=0

disp('No Root')

else

prev = (a+b)/2;
p=a;
while (abs(f(p))>e)
prev=p;

iter =iter+ 1;

p = (a+b)/2;

if f(p) == 0
p
q=1
break;

end

if f(a)*f(p)<0

b = p;

else

a = p;

end
if(iter==100)
disp('the required accuracy is not reached in 50 iterations');
end
end

end
fprintf('The maximum deflection is %f which happens at x=%f\n',abs(g(p)),p);