A beam is subjected to a linearly increasing distributed load. The elastic curve

Question

A beam is subjected to a linearly increasing distributed load. The elastic curve (deflection) is shown in the figure. The equation to find the maximum deflection is given below. Create a matlab code where you can calculate the maximum deflection (dy/dx=0) using the bisection method.
Use initial guesses of 0 and 8, L = 6.27 m, E = 97000 kN/cm2, I =35000 cm4, and w0= 2.5 kN/cm.
What will be the value of x (location of maximum deflection) after 6 bisection iteration?


Choices a 2.8125 b 4.2188 c 2.5313 d 1.4063 Wo Y=+' - 120EIT 2LT L'r)

Explanation / Answer

Matlab function Bisection.m

function Root = Bisection(f,a,b,Max_Iter) % The function definition bisect.m
xplus = b;
xminus = a;
Iter = 0; % iteration counter
xnew=(xplus+xminus)*0.5; % new point in the intervel
while Iter<Max_Iter % iterate loop unitil Iter > Max_iter
   fnew=f(xnew); % function evaluating at newly computed x value
    if(fnew>0) % determin the sign of f at new x value
        xplus=xnew; % if f is positive replave x+ with new x
    else
        xminus=xnew; % if f is negative replace x- with new x
    end
    Iter = Iter +1; % Increment Iteration counter
   xnew=(xplus+xminus)*0.5; % new x value
end
Root = xnew; % after the iterations the approximated root will be in xnew
end

Calling the function

clc; clear; % clearing command window and workspace
x0 = 0; x1 = 8; % initial guesses
L = 6.27; % L in m
E = 97000; %E in kN/cm2
I = 35000; % I in cm4
Wo = 2.5; % Wo in kN/cm
f = @(x) (Wo/(120*E*I*L))*(-5*x.^4+6*L^2*x.^2-L^4); % RHS od dy/dx
itr = 6; % Number of iteration
Root = Bisection(f,x0,x1,itr)% Function call

OUTPUT

Root =

    2.8125

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.