Using singularity functions write the equations for the shea

Using singularity functions, write the equations for the shear and bending moment for the beam and loading shown. Use MATLAB to write a code to plot the shear and bending moment diagrams. Determine the maximum value of the bending moment in the beam from your MATLAB plot. Using singularity functions, write the equations for the shear and bending moment for the beam and loading shown. Use MATLAB to write a code to plot the shear and bending moment diagrams. Determine the maximum value of the bending moment in the beam from your MATLAB plot.

Solution

1)

clear all
clc
fprintf(\'Title:beam with UVL at one end and point load at some distance from end\ \');

%Dimensions
L=input(\'Length of the beam in m: \');
%Loads
w=input(\'Enter the Load in KN : \');
w1=input(\'Enter the Load in KN/m : \');
%Moments
Mc=((58*w*L)/(1215))+((11*w1*L^2)/(180));
Md=((10*w*L)/(54))-((Mc)/(2));
Mb=((w1*L^2)/(4))+((10*w*L)/(54))-((7*Mc)/(2));
Ma=((10*w)/(54))-((Mb)/(2));
%Reactions
Ra=((Ma-Mb)/(L))+((2*w)/(3));
Rd=((Md-Mc)/(L))+(w/3);
Rb=((Ma-Mc)/(L))-(2*Ra)+((5*w)/(3))+((w1*L)/(2));
Rc=((Md-Mb)/(L))-(2*Rd*L)-((4*w)/(3))+((w1*L)/(2));
i=0;
for X=0:0.01:(3*L)
    i=i+1;
    if X<(L/3)
        SF(i)=Ra;
        SF1(i)=0;
        BM(i)=(Ra*X)-(Ma);  
        BM1(i)=0;   
    elseif X>=(L/3)&&X<=L
        SF(i)=Ra-(w);
        SF1(i)=0;
        BM(i)=(Ra*X)-(w*(X-(L/3)))-(Ma);
        BM1(i)=0;
    elseif X>=L&&X<=(2*L)
        SF(i)=Ra-(w)+Rb-(w1*(X-L));
        SF1(i)=0;
        BM(i)=(Ra*X)-(w*(X-(L/3)))-(Ma)+(Rb*(X-L))-(w1*((X-L)^2)*0.5);
        BM1(i)=0;
    elseif X>=(2*L)&&X<=((7/3)*L)
        SF(i)=-Rd+w;
        SF1(i)=0;
        BM(i)=(Rd*((3*L)-X))-Md-(w*((2.33*L)-X));
        BM1(i)=0;
    else
       
        SF(i)=-Rd;
        SF1(i)=0;
        BM(i)=(Rd*((3*L)-X))-Md;
        BM1(i)=0;
   
    end
    end

X=0:0.01:(3*L)
%Plot Shear Force
subplot(2,1,1);
plot(X,SF,X,SF1);
title(\'Shear Force Diagram\');
xlabel(\'Length of the Beam in m\');
ylabel(\'Shear Force in KN\');

%Plot Bending Moment
subplot(2,1,2);
plot(X,BM,X,BM1);
title(\'Bending Moment Diagram\');
xlabel(\'Length of the Beam in m\');
ylabel(\'Bending Moment in KN-m\');

2)

clear all   
clc
fprintf(\'Title:continuous beam with half UDL and Moment\ \');

%Dimensions
L=input(\'Length of the beam in m: \');
%Loads
w=input(\'Enter the Load in KN/m : \');
M=input(\'Enter the Moment in KN-m : \');
%Moments
Mb=((-w*L^2)/(24))-((24*M)/(150));
Ma=((w*L^2)/(8))-((Mb)/(2));
Mc=((-2*M)/(50))-((Mb)/(2));
%Reactions
Ra=((Ma-Mb)/(L))+((w*L)/(2));
Rc=((Mc-Mb)/(L))+(M/L);
Rb=(w*L)-(Ra)-(Rc);
i=0;
for X=0:0.02:(2*L);
    i=i+1;
    if X<=L
        SF(i)=Ra-(w*X);  
        SF1(i)=0;
        BM(i)=(Ra*X)-((w*X^2)*0.5)-Ma;  
        BM1(i)=0;   
    elseif X>=L&&X<=(1.6*L)
        SF(i)=Ra+Rb-(w*L);
        SF1(i)=0;
        BM(i)=(Rc*((2*L)-X))-Mc-M;
        BM1(i)=0;
    else
        SF(i)=Ra+Rb-(w*L);
        SF1(i)=0;
        BM(i)=-Mc+(Rc*((2*L)-X));
        BM1(i)=0;
    end
end
X=0:0.02:(2*L);
% ploting the SF,&BM

subplot(2,1,1);
plot(X,SF,X,SF1);
title(\'Shear Force Diagram\');
xlabel(\'Length of the Beam in m\');
ylabel(\'Shear Force in KN\');

% ploting the SF,&BM

subplot(2,1,2);
plot(X,BM,X,BM1);
title(\'Bending Moment Diagram\');
xlabel(\'Length of the Beam in m\');
ylabel(\'Bending Moment in KN-m\');