how do I build the a beam deflection graph ?

How do you do?

I was wondering if someone could help me with a problem I have been given. It is about deflection of beams in a course in college called numerical analysis.

Given: 𝑞0 = 1𝑁𝑚𝑚, E = 140MPa, L = 1000mm, v = -0.7mm.

1.Draw the x in front of I for 100∙ 10^6 mm^4 ≤ I ≤ 450∙10^6 mm^4. What conclusion can be physically deduced from the graph?

2. Find the value of I for which the beam does not decrease to the value given above.

Write down how you chose an initial guess.

The code that i wrote gives me an empty graph

[KSSV]

Copy and paste your code here. Image sniipet will not help us to help you.

[Netanel Malihi]

function graph_Ix = beamDeflection(v,q0,L,E)

 %for x=0:100:1000
     %I = -(q0*L)/(3*pi^4*E*v)*(48*L^3*cos((pi*x)/(2*L))-48*L^3+3*pi^3*L*x^2-pi^3*x^3)
 %end
 %plot(x,I)
 x=[0:1:1000]
 I = -(q0*L)/(3*pi^4*E*v)*(48*L^3*cos((pi*x)/(2*L))-48*L^3+3*pi^3*L*x.^2-pi^3*x.^3)
 plot(x,I)

[Netanel Malihi]

Of course excuse me

[VBBV]

The code that you wrote in snapshot (image) is not same as whats posted in OP.

Did you try with code in your OP ?

Note that reason why you dont see the plot is that you're trying to plot against one point in x vector. vs I

when the for loop is completed, value of x is just one point instead of vector as specified in OP.

Answer 1

[KSSV]

q0 = 1 ;
E = 140 ;
L = 1000 ; 
v = -0.7 ;

beamDeflection(v,q0,L,E) ; 

function beamDeflection(v,q0,L,E)

 %for x=0:100:1000
     %I = -(q0*L)/(3*pi^4*E*v)*(48*L^3*cos((pi*x)/(2*L))-48*L^3+3*pi^3*L*x^2-pi^3*x^3)
 %end
 %plot(x,I)
 x = 0:1:1000 ; 
 I = -(q0*L)/(3*pi^4*E*v)*(48*L^3*cos((pi*x)/(2*L))-48*L^3+3*pi^3*L*x.^2-pi^3*x.^3) ; 
 plot(x,I)
end

[Netanel Malihi]

thanks, how do i code the range condition: 100∙ 10^6 mm^4 ≤ I ≤ 450∙10^6 mm^4 in the graph?

[KSSV]

Read about axis and inequalitties i.e. <, >

Answer 2

[Talal]

function [X, y_true, y_num, error] = beam_deflection(x_initial,x_step, x_end,E, I, M)

% Calculates beam deflection using analytical and numerical integration methods

% Inputs:

% x_initial: starting value for x

% x_step: step size for x

% x_end: ending value for x

% E: modulus of elasticity

% I: moment of inertia

% M: function handle for moment as a function of x

% Outputs:

% X: array of x values

% y_true: array of true deflection values

% y_num: array of numerical deflection values

% error: array of errors between true and numerical deflection values

% Create array of x values

X = x_initial:x_step:x_end;

% Initialize arrays for y_true, y_num, and error

y_true = zeros(1, length(X));

y_num = zeros(1, length(X));

error = zeros(1, length(X));

% Calculate y_true for each x value using analytical integration

for i = 1:length(X)

x = X(i);

y_true(i) = integral(@(x) M(x)/(E*I), 0, x);

end

% Calculate y_num for each x value using numerical integration

for i = 2:length(X)

x = X(i);

x_prev = X(i-1);

theta_prev = M(x_prev)/(E*I);

theta = M(x)/(E*I);

y_num(i) = y_num(i-1) + ((x - x_prev)/2)*(theta +theta_prev);

end

% Calculate error for each x value

error = y_true - y_num;

end

% Input variables

x_initial = 0;

x_step = 0.01;

x_end = 5;

E = 200e9; % Pa

I = 8.333e-6; % m^4

wo = 1000; % N/m

% Moment as a function of x

M = @(x) (wo*x^2*(10-x)^2)/120;

% Call beam_deflection function

[X, y_true, y_num, error] = beam_deflection(x_initial, x_step, x_end, E, I, M);

% Plot results

figure

plot(X, y_true, 'r', X, y_num, 'b')

title('Beam Deflection')

xlabel('x (m)')

ylabel('y (m)')

legend('Analytical', 'Numerical')

I am not getting the plots, could anyone resolve this issue and rectidy the error

Answer 3

[NODIRABDUSHAKHIDOV]

check this out. Hope it solves your problem.

clear all

% Input variables

x_initial = 0;

x_step = 0.01;

x_end = 5;

E = 200e9; % Pa

I = 8.333e-6; % m^4

wo = 1000; % N/m

% Moment as a function of x

M = @(x) (wo*x.^2.*(10-x).^2)/120;

% Call beam_deflection function

[X, y_true, y_num, error] = beam_deflection(x_initial, x_step, x_end, E, I, M);

% Plot results

figure

plot(X, y_true, 'r', X, y_num, 'b');

xlabel('x');

ylabel('Deflection');

legend('True deflection', 'Numerical deflection');

title('Beam Deflection');

function [X, y_true, y_num, error] = beam_deflection(x_initial, x_step, x_end, E, I, M)

% Calculates beam deflection using analytical and numerical integration methods

% Inputs:

% x_initial: starting value for x

% x_step: step size for x

% x_end: ending value for x

% E: modulus of elasticity

% I: moment of inertia

% M: function handle for moment as a function of x

% Outputs:

% X: array of x values

% y_true: array of true deflection values

% y_num: array of numerical deflection values

% error: array of errors between true and numerical deflection values

% Create array of x values

X = x_initial:x_step:x_end;

% Initialize arrays for y_true, y_num, and error

y_true = zeros(1, length(X));

y_num = zeros(1, length(X));

error = zeros(1, length(X));

% Calculate y_true for each x value using analytical integration

for i = 1:length(X)

x = X(i);

y_true(i) = integral(@(x) M(x)/(E*I), 0, x);

end

% Calculate y_num for each x value using numerical integration

for i = 2:length(X)

x = X(i);

x_prev = X(i-1);

theta_prev = M(x_prev)/(E*I);

theta = M(x)/(E*I);

y_num(i) = y_num(i-1) + ((x - x_prev)/2)*(theta + theta_prev);

end

% Calculate error for each x value

error = abs(y_true - y_num); % Calculate absolute difference

end