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');
---------------------------------------------------------------------------
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');
---------------------------------------------------------------------------
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')
---------------------------------------------------------------------------
