Shear Force and Bending Moment Diagram for simply supported beam软件

This Matlab code can be used for finding Support reaction, Maximum Bending Moment, SFD and BMD

软件应用简介

Shear Force and Bending Moment Diagram for simply supported beam软件

% This Matlab code can be used for simply supported beam with single point

% load or uniformly distributed to find the

% * Support reaction

% * Maximum Bending Moment

% * Shear force diagram

% * Bending Moment daigram

clc; clear; close all

disp(‘Simply Supported Beam’);

% Data input section

disp(‘ ‘);

L = input(‘Length of beam in meter = ‘);

disp(‘ ‘);disp(‘Type 1 for point load, Type 2 for udl’)

Type = input(‘Load case = ‘);

if Type == 1

disp(‘ ‘);

W = input(‘Load applied in kN = ‘);

disp(‘ ‘);

a = input(‘Location of Load from left end of the beam in meter = ‘);

c = L-a;

R1 = W*(L-a)/L; % Left Support Reaction.

R2 = W*a/L; % Right Support Reaction.

else

disp(‘ ‘);

W = input(‘Uniformly distributed load in kN/m = ‘);

disp(‘ ‘);

b = input(‘Length of udl in meter = ‘);

disp(‘ ‘);

cg = input(‘C.G of udl from left end of the beam in meter = ‘);

a = (cg-b/2);

c = L-a-b;

R1 = W*b*(b+2*c)/(2*L); % Left Support Reaction.

R2 = W*b*(b+2*a)/(2*L); % Right Support Reaction.

end

% Discretization of x axis.

n = 1000; % Number of discretization of x axis.

delta_x = L/n; % Increment for discretization of x axis.

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

V = zeros(size(x, 1), 1); % Shear force function of x.

M = zeros(size(x, 1), 1); % Bending moment function of x.

% Data processing section

if Type == 1

for ii = 1:n+1

% First portion of the beam, 0 < x < b

V(ii) = R1;

M(ii) = R1*x(ii);

% Second portion of the beam, b < x < L

if x(ii) >= a

V(ii) = R1-W;

M(ii) = R1*x(ii)-W*(x(ii)-a);

end

end

x1 = a;

Mmax = W*a*(L-a)/L;

else

for ii = 1:n+1

% First portion of the beam, 0 < x < a

if x(ii) < a

V(ii) = R1;

M(ii) = R1*x(ii);

elseif a <= x(ii) && x(ii)< a+b

% Second portion of the beam, a < x < a+b

V(ii) = R1-W*(x(ii)-a);

M(ii) = R1*x(ii)-W*((x(ii)-a)^2)/2;

elseif x(ii) >= (a+b)

% Second portion of the beam, a+b < x < L

V(ii) = -R2;

M(ii) = R2*(L-x(ii));

end

end

x1 = a+b*(b+2*c)/(2*L);

Mmax = W*b*(b+2*c)*(4*a*L+2*b*c+b^2)/(8*L^2);

end

disp(‘ ‘);disp ([‘Left support Reaction’ ‘ = ‘ num2str(R1) ‘ ‘ ‘kN’])

disp(‘ ‘);disp ([‘Left support Reaction’ ‘ = ‘ num2str(R2) ‘ ‘ ‘kN’])

disp(‘ ‘);disp ([‘Maximum bending moment’ ‘ = ‘ num2str(Mmax) ‘ ‘ ‘kNm’])

figure

subplot(2,1,1);

plot(x, V, ‘r’,’linewidth’,1.5); % Grafica de las fuerzas cortantes.

grid

line([x(1) x(end)],[0 0],’Color’,’k’);

line([0 0],[0 V(1)],’Color’,’r’,’linewidth’,1.5);

line([x(end) x(end)],[0 V(end)],’Color’,’r’,’linewidth’,1.5);

title(‘Shear Force Diagram’,’fontsize’,16)

text(a/2,V(1),num2str(V(1)),’HorizontalAlignment’,’center’,’FontWeight’,’bold’,’fontsize’,16)

text((L-c/2),V(end),num2str(V(end)),’HorizontalAlignment’,’center’,’FontWeight’,’bold’,’fontsize’,16)

axis off

subplot(2,1,2);

plot(x, M, ‘r’,’linewidth’,1.5); % Grafica de momentos flectores;

grid

line([x(1) x(end)],[0 0],’Color’,’k’);

line([x1 x1],[0 Mmax],’LineStyle’,’–‘,’Color’,’b’);

title(‘Bending Moment Diagram’,’fontsize’,16)

text(x1+1/L,Mmax/2,num2str(roundn(Mmax,-2)),’HorizontalAlignment’,’center’,’FontWeight’,’bold’,’fontsize’,16)

text(x1,0,[num2str(roundn(x1,-2)) ‘ m’],’HorizontalAlignment’,’center’,’FontWeight’,’bold’,’fontsize’,16)

axis off