Plot_20P.m

%Plot of central_diff20P code for P =0,100,200,300 and for q=1,10,20,30,50
b=0.1; %width of beam
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
E=70E9; %Modulus of Elasticity
n=20; %Number of segments 
x=1/n; %segment equivalent 
%For loop for P=0
i=0;
P=0; 
w0=zeros(1,5); %Vector of zeros for displacement when P=0 
w100=zeros(1,5); %Vector of zeroes for displacement when P=100
w200=zeros(1,5); %Vector of zeroes for displacement when P=200
w300=zeros(1,5); %Vector of zeroes for displacement when P=300
for q=[1,10,20,30,50]
    i=i+1;
    z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement

    Off_Diag=-4-(((P*(1/(n^2)))/(E*I))); %Off Diagonal value 
    Diag=6+((P*(2*(1/(n^2))))/(E*I)); %Diagonal value
    ODV = ones((n-2),1)*Off_Diag; %Off Diagonal vector
    DV = ones(n-1,1)*Diag; %Diagonal vector
    OOD = ones((n-3),1); %Off off diagonal vector 

%Generate Matrix X
    X=diag(ODV,-1)+diag(DV)+diag(ODV,1)+diag(OOD,2)+diag(OOD,-2);
    X(1,1)= 5+((P*(2*(1/(n^2))))/(E*I));
    X((n-1),(n-1))=5+((P*(2*(1/(n^2))))/(E*I));

%Generate  Matrix Y
    Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];

%Solve for deflection Matrix 
    W=X\Y;
    maxw=max(-W);
    w0(i)=-maxw;
end
q=[1,10,20,30,50];
plot(q,w0)


%For loop for P=100
i=0;
P=100;
for q=[1,10,20,30,50]
    i=i+1;
    z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement
    Off_Diag=-4-(((P*(1/(n^2)))/(E*I))); %Off Diagonal value 
    Diag=6+((P*(2*(1/(n^2))))/(E*I)); %Diagonal value
    ODV = ones((n-2),1)*Off_Diag; %Off Diagonal vector
    DV = ones(n-1,1)*Diag; %Diagonal vector
    OOD = ones((n-3),1); %Off off diagonal vector 

%Generate Matrix X
    X=diag(ODV,-1)+ diag(DV)+diag(ODV,1)+diag(OOD,2)+diag(OOD,-2);
    X(1,1)= 5+((P*(2*(1/(n^2))))/(E*I));
    X((n-1),(n-1))=5+((P*(2*(1/(n^2))))/(E*I));

%Generate  Matrix Y
    Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];

%Solve for deflection Matrix 
    W=X\Y;
    maxw=max(-W);
    w100(i)=-maxw;
end 
q=[1,10,20,30,50];
hold on 
plot(q,w100)

%For loop for P=200
i=0;
P=200;
for q=[1,10,20,30,50]
    i=i+1;
    z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement
    Off_Diag=-4-(((P*(1/(n^2)))/(E*I))); %Off Diagonal value 
    Diag=6+((P*(2*(1/(n^2))))/(E*I)); %Diagonal value
    ODV = ones((n-2),1)*Off_Diag; %Off Diagonal vector
    DV = ones(n-1,1)*Diag; %Diagonal vector
    OOD = ones((n-3),1); %Off off diagonal vector 

%Generate Matrix X
    X=diag(ODV,-1)+ diag(DV)+diag(ODV,1)+diag(OOD,2)+diag(OOD,-2);
    X(1,1)= 5+((P*(2*(1/(n^2))))/(E*I));
    X((n-1),(n-1))=5+((P*(2*(1/(n^2))))/(E*I));

%Generate  Matrix Y
    Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];

%Solve for deflection Matrix 
    W=X\Y;
    maxw=max(-W);
    w200(i)=-maxw;
end 
q=[1,10,20,30,50];
plot(q,w200)

%For loop for P=300
i=0;
P=300;
for q=[1,10,20,30,50]
    i=i+1;
    z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement
    Off_Diag=-4-(((P*(1/(n^2)))/(E*I))); %Off Diagonal value 
    Diag=6+((P*(2*(1/(n^2))))/(E*I)); %Diagonal value
    ODV = ones((n-2),1)*Off_Diag; %Off Diagonal vector
    DV = ones(n-1,1)*Diag; %Diagonal vector
    OOD = ones((n-3),1); %Off off diagonal vector 

%Generate Matrix X
    X=diag(ODV,-1)+ diag(DV)+diag(ODV,1)+diag(OOD,2)+diag(OOD,-2);
    X(1,1)= 5+((P*(2*(1/(n^2))))/(E*I));
    X((n-1),(n-1))=5+((P*(2*(1/(n^2))))/(E*I));

%Generate  Matrix Y
    Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];

%Solve for deflection Matrix 
    W=X\Y;
    maxw=max(-W);
    w300(i)=-maxw;
end 
q=[1,10,20,30,50];

plot(q,w300)
title('Distributed Loading versus Max Beam Deflection for 20 Segment Beam')
xlabel('Loading q (N/m)')
ylabel('Deflection dx')
legend('P=0', 'P=100', 'P=200', 'P=300')