How can I SOLVE THIS PROJECT

[anas khalid]

Case 1: Uniform beam under distributed load.

In the shown Figure, a uniform beam subject to a linearly increasing distributed load. The deflection y (m) can be expressed by

y=w_o/120EIL (-x^5+2L^2 x^3-L^4 x)

Where E is the modulus of elasticity and I is the moment of inertia (m4), L length of beam. Use the following parameters L=600 cm, E=50,000 kN/cm2, I= 30.000 cm4, wo=2.5 kN/cm, to find the requirements

Develop MATLAB code to determine the point of maximum deflection by using numerical method (bisection, false position method,….). Hint(The value of x where dy/dx=0). Plot the point of maximum deflection versus iteration number. Plot the values of the relative approximate error of the point of maximum deflection (ϵ_(a,x)) versus iteration number.

Plot the following quantities versus distance along the beam Displacement (y). Slope θ(x)=dy/dx. Moment M(x)=EId^2 y/dx^2. Shear V(x)=EId^3 y/dx^3. Loading w(x)=-EId^4 y/dx^4.

[Ashik Mahamud]

I'm new, i Don't understand how to solve it. Plz help me to solve the project

Answer 1

[raymond keen]

w0 = 2.5 ;     
E = 50000; 
I = 30000; 
L=600; 
 
t = 0; 
v = 599; 
 
 
while (abs(t-v)>0.0000001) 
    z = (t+v)/2; 
     
    
    ydiff = (w0)/(120*E*I*L)*(-5*z^4+6*L^2*z^2-L^4); 
    t_val = (w0)/(120*E*I*L)*(-5*t^4+6*L^2*t^2-L^4); 
    v_val = (w0)/(120*E*I*L)*(-5*v^4+6*L^2*v^2-L^4); 
     
    if (sign(ydiff) ~= sign(v_val))      
        t = z;      
    else 
 
        v = z;       
    end 
end 
 
x = (t+v)/2 
 
ydiff = (w0)/(120*E*I*L)*(-5*x^4+6*L^2*x^2-L^4)