Design of beam: diagrams using Matlab, Hibbeler's F1.7 problem, page 38.

Matlab program to plot the mechanical diagrams for Hibbeler's
"Mechanics of Materials",
8th. edition, problem F1.7, page 38.

For this problem we assume a maximum distributed load
w = 12000 N/m.

The resulting forces in the vertical supporting rods are:
Rod AB force = 12000 N.
Rod CD force = 24000 N.
_________________________________________________________________
 
% hibbeler_f1_7.m
% Joel Aguinaga / Ricardo Avila, 18 Aug. 2014
% Fundamental Problem F1.7, Hibbeler's
% "Mechanics of Materials", 8th. edition, page 38

clc

clear

disp(' ')

disp('Hibbeler''s Fundamental problem F7.1 ')
disp('"Mechanics of Materials", 8th. edition, p.38 ')
disp('******************************************** ')
disp(' ')

% Data pre-processing

delta_x = .01;  % Define step of discretization for x-axis
x = [ 0: delta_x: 6]';  % Generate x-axis discretization.

N = size(x, 1);  % Calculate size of the discretization

V = zeros(N, 1); % Fill with zeros variable in memory: shear force. 
M = V;           % Memory required to store Bending Moment.
y = V;           % Memory to store elastic curve information.

% Material and Geometric Constants:

E = 200E9;  % Assume a steel beam, for Elastic Modulus
I = 1;      % Moment of inertia is not determined, use unit value
EI = E * I; % Multiply those values

% Data processing section of program: 

% ____________________________________________________________
V = -1000* x.^2 + 12000;    % Equation for Shear Force curve
M = -333.3333* x.^3 + 12000*x;  % Bending Moment equation.

% The elastic curve resulting from double integration,

% following Euler's method: EI * (d2y/dx2) = M(x).
y = -16.6666* x.^5 + 2000 *x.^3 - 50400 *x;

% Divide elastic curve by EI

y = y / EI;

% Post-processing section of program:

%_____________________________________________________________

% Plot the Shear Force Diagram

figure(1)
plot(x, V, 'r', 'linewidth', 3)
grid
title(' Shear Force Diagram')
xlabel('x, m')
ylabel('V, N')

% Plot the Bending Moment Diagram

figure(2)
plot (x, M, 'b', 'linewidth', 3)
grid
title('Bending Moment Diagram')
xlabel('x, m')
ylabel('M, N-m')

% Plot the Elastic Curve Diagram

figure(3)
plot (x, y, 'k', 'linewidth', 3)
grid
title('Elastic Curve Diagram')
xlabel('x, m')
ylabel('y, m')

% Find and display the minimum value of elastic curve

y_min = min(y)

% Find and display the maximum value of bending moment
M_max = max(M)

disp(' ')

disp('**********************')
disp('Successful Program Run')


Figure 1. Shear Force Diagram:

 

 

 

Figure 2. Bending Moment Diagram:

 

Figure 3. Elastic Curve Diagram: