Shear force and Bending Moment diagrams using Matlab

Matlab program prob6_3 below shows how to generate

shear force and bending moment diagrams for a beam.
Problem 6.3 of Hibbeler’s textbook,
‘Mechanics of Materials’, 8^th. edition,
using US system of customary units.

% prob6_3.m

% Daniel A. Landeros Rojas / Ricardo E. Avila Montoya  
% Mechanics of Materials / August 30, 2013
% ricardo_avila@hotmail.com
% Chihuahua, Mexico

clc

clear
disp(' ')
disp('Problem 6.3, Hibbeler, 8th. edition')

% Data input section

% The units of the problem are US customary, not SI
% A crane lifts a 1200 Lb load applied at its end, with the 
% power of a hydraulic cylinder. Length of beam is 8 feet.

delta_x = .5;           % Increment for discretization of x axis.

x = (0: delta_x: 96)';  % Generate column array for x-axis. 

FAy = -2000;    % Vertical force at point A

FBy = 3200;     % Vertical force at point B
FCy = -1200;    % Applied load at point C

N = size(x, 1); % Size of the x-axis discretization

V = zeros(N, 1);    % Shear force function of x.
M = V;              % Bending moment function of x.

% Data processing section

for index = 1: N;   % For every discrete point along x.

   % First portion of the beam, 0 < x < 36 (inch)

   V(index) = FAy;
   M(index) = FAy*x(index);

   % Second portion of the beam, 36 < x < 96 (inch)

   if(x(index)>=36)
        V(index) = V(index) + FBy;
        M(index) = M(index) + FBy*(x(index)-36);
   end

end

V(N) = V(N) + FCy;  % Shear force for last point of diagram

% Data post-processing section

% Shear force diagram

figure(1)
plot(x,V, 'b', 'linewidth', 2.5)
grid
xlabel('x, inch')
ylabel('Shear force, Lb')
title('Shear force diagram')
axis tight

% Bending moment diagram

figure(2)
plot(x,M, 'r', 'linewidth', 2.5)
grid
xlabel('x, inch')
ylabel('Bending moment, Lb-in')
title('Bending Moment diagram')
axis tight

disp(' ')

disp('*** Successful execution of program ***')
% end of Matlab program

figure(1)

figure(2)

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