MATLAB coding for Plotting SFD's and BMD's for different cases in continuous beams

a)

% CONTINUOUS SPAN BEAMS

%- SFD

%- BMD

clear all

clc

fprintf('Title:continuous beam with half UDL and Moment\n');

%diamensions of beam

L=2000; %Total length of the beam

L1=1000;%Length of Span AB

L2=L1;%Length of span BC

B=200; %breath of the beam

D=200;  %depth of the beam

M20=20;%grade of concrete

w=2000; %load

E=5000*sqrt(M20);

a=1000;

b=1000;

L=L1+L2;

Ra=(7*w*L1)/16;

Rb=(5*w*L1)/8;

Rc=(w*L1)/16;

I= (B*D^3)/12;

j=0;

for x=0:1:L

    j=j+1;

    if x<L1

    sf(j)=Ra-w*x;

    sf1(j)=0;

    bm(j)=Ra*x-(w*x^2)/2;

    bm1(j)=0;

    else

    sf(j)=Rc;

    sf1(j)=0;

    bm(j)=Rc*(L-x);

    bm1(j)=0;

    end

end

x=0:1:L

subplot(3,1,1)

plot(x,sf,x,sf1,'linewidth',2);

title('shear force');

xlabel('length of the beam in mm');

ylabel('shear force in n');

subplot(3,1,2)

plot(x,bm,x,bm1,'linewidth',3);

title('bending moment');

xlabel('length of the beam in mm');

ylabel('bending moment in n-mm');

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b)

clear all   

clc

fprintf('Title:continuous beam with half UDL and Moment\n');

%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');

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c)

clear all

clc

fprintf('Title:continuous beam with point load\n');

% Dimensions of the Beam

L=input('length of the Beam in m: ');

%Load

w=input('Enter the Load in KN/m: ');

%Moments

Ma=w*L/6;

Mb=w*L/24;

Mc=-w*L/48;

%Reactions

Ra=((Ma-Mb)/L)+(w/2);

Rc=((Mc-Mb)/(2*L));

Rb=w-Ra-Rc;

i=0;

for X=0:0.002:(3*L)

    i=i+1;

   if X<L/2

       SF(i)=Ra;

       SF1(i)=0;

       BM(i)=(Ra*X)-Ma;

       BM1(i)=0;

   elseif X>=L/2&&X<=L

       SF(i)=Ra-w;

       SF1(i)=0;

       BM(i)=(Ra*X)-w*(X-(L/2))-Ma;

       BM1(i)=0;

   else

       SF(i)=Ra+Rb-w;

       SF1(i)=0;

       BM(i)=(Ra*X)+(Rb*(X-L))-(w/2*(2*X-L))-Ma;

       BM1(i)=0;

   end

end

X=0:0.002:(3*L);

% ploting the SF,&BM

subplot(2,1,1)

plot(X,SF,X,SF1)

xlabel('Length of the beam in m')

ylabel('Shear Force in KN')

title('Shear force diagram')

subplot(2,1,2)

plot(X,BM,X,BM1)

xlabel('Length of the beam in m')

ylabel('Bending Moment in KN-m')

title('Bending Moment diagram')

---------------------------------------------------------------------------

d)

clear all

clc

fprintf('Title:continuous beam with two point loads and UDL \n');

% Dimensions of the Beam

L=input('length of the Beam in m: ');

%Load

w1=input('Enter the UDL in KN/m: ');

w2=input('Enter the point load in KN/m: ');

%Moments

Ma=5*(w1*L^2)/48-1/32*w2*L;

Mb=(w1*(L^2)/24)+(w2*L/16);

Mc=5*(w2*L)/32-1/48*w1*(L^2);

%Reactions

Ra=((Ma-Mb)/L)+(w1*L/2);

Rc=((Mc-Mb)/L)+w2/2;

Rb=(w1*L)+w2-Ra-Rc;

i=0;

for X=0:0.002:(3*L)

    i=i+1;

   if X<L

       SF(i)=Ra-(w1*X);

       SF1(i)=0;

       BM(i)=(Ra*X)-Ma-(w1*(X^2)*0.5);

       BM1(i)=0;

   elseif X>=L&&X<1.5*L

       SF(i)=Ra-(w1*L)+Rb;

       SF1(i)=0;

       BM(i)=(Ra*X)+(Rb*(X-L))-w1*L*((0.5*L)+(X-L))-Ma;

       BM1(i)=0;

   else

       SF(i)=Ra+Rb-(w1*L)-w2;

       SF1(i)=0;

       BM(i)=(Ra*X)+(Rb*(X-L))-w1*L*((0.5*L)+(X-L))-Ma-(w2*(X-1.5*L));

       BM1(i)=0; 

   end

  

end

X=0:0.002:(3*L);

% ploting the SF,&BM

subplot(2,1,1)

plot(X,SF,X,SF1)

xlabel('Length of the beam in m)')

ylabel('Shear Force in KN')

title('Shear force diagram')

subplot(2,1,2)

plot(X,BM,X,BM1)

xlabel('Length of the beam in m)')

ylabel('Bending Moment in KN-m')

title('Bending Moment diagram')

---------------------------------------------------------------------------

e)

clear all

clc

fprintf('Title:continuous beam with UDL at centre and two points loads at some distance from free end\n');

%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');

---------------------------------------------------------------------------

f)

clear all

clc

fprintf('Title: continuous beam with UDL at centre and point loads at some distance from left end\n');

% Dimensions of the Beam

l=input('length of the Beam in m: ');

%Load

w=input('Enter the UDL in KN/m: ');

w1=input('Enter the PointLoad in KN/m: ');

%Moments

Ma=((-3*w1*l^2)/104)+((3*w*l)/208);

Mb=(-2*Ma);

Mc=((5*w1*(l^2))/104)+((21*w*l)/208);

%Reactions

Ra=(Ma-Mb)/l;

Rb=((Ma-Mc)/l)-(2*Ra)+((w1*l)/2);

Rd=(-Mc/l)+(w/2);

Rc=(-Mb/l)-(2*Rd)+(3*w/2)+(w1*l/2);

i=0;

for X=0:0.02:(3*l);

    i=i+1;

    if(X<l)

        SF(i)=Ra;

        SF1(i)=0;

        BM(i)=(Ra*X)-Ma;

        BM1(i)=0;

    elseif(X>=l&&X<2*l)

        SF(i)=Ra+Rb-(w1*(X-l));

        SF1(i)=0;

        BM(i)=(Ra*X)+Rb*(X-l)-(w1*((X-l)^2)*0.5)-Ma

        BM1(i)=0;

    elseif(X>=2*l&&X<2.5*l)

        SF(i)=-Rd+w;

        SF1(i)=0;

        BM(i)=(Ra*X)+Rb*(X-l)-Ma-w1*l*((l*0.5)+(X-(2*l)))+(Rc*(X-(2*l)));

        BM1(i)=0;

       

    else

        SF(i)=-Rd;

        SF1(i)=0;

        BM(i)=Rd*((3*l)-X);

        BM1(i)=0;

    end

end

X=0:0.02:(3*l);

subplot(2,1,1);

plot(X,SF,X,SF1)

xlabel('Length of the beam in m')

ylabel('Shear Force in KN')

title('Shear force diagram')

subplot(2,1,2)

plot(X,BM,X,BM1)

xlabel('Length of the beam in m')

ylabel('Bending Moment in KN-m')

title('Bending Moment diagram')

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