%Modal Analysis of a 16 story building

%stiffness (KK) and mass (M) matrices for a 16 story bldg
%the units: kips, inches, and second.
KK=[683.45 -390.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
   -390.25 976.15 -585.9 0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 -585.9 1171.8 -585.9 0 0 0 0 0 0 0 0 0 0 0 0;
   0 0 -585.9  1003.7 -417.8 0 0 0 0 0 0 0 0 0 0 0;  
   0 0 0 -417.8 835.6 -417.8 0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 -417.8 835.4 -417.8 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 -417.8 719.3 -301.5 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 -301.5 603 -301.5 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 -301.5 603 -301.5 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 -301.5 499.23 -197.73 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 -197.73 395.46 -197.73 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0 -197.73 395.46 -197.73 0 0 0;
   0 0 0 0 0 0 0 0 0 0 0 -197.73 300.53 -102.8 0 0;
   0 0 0 0 0 0 0 0 0 0 0 0 -102.8 205.6 -102.8 0;
   0 0 0 0 0 0 0 0 0 0 0 0 0 -102.8 205.6 -102.8;
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 -102.8  102.8];  		%stiffness matrix
md=[.508*[1 1 1] .505*[1 1 1] .504*[1 1 1 1 1 1 1 1 1 1]];
ml=.244*[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];
m1=md+ml;
MM=diag(m1);
M=diag(m1);			% mass matrix

[VV,DD]=eig(KK,MM);	% solving the eigenvalue problem
[temp1,I]=sort(diag(DD));	%sorting the eigenvalues in ascending order
om2=diag(temp1);				% digonalizing the sorted eigenvalues 
Phi=zeros(16,16);				% a 16x16 zero matrix that will be filled by eigenvectors
for j=1:16,
Phi(:,j)=VV(:,I(j));	% sorting the Phi (eigenvectors) accordingly
end

om=sqrt(om2);			% natural frequencies diagonal matrix
for i=1:16,				%mass normalizing the eigenvectors
Phi(:,i)=Phi(:,i)/sqrt(Phi(:,i)'*MM*Phi(:,i));	
end
% om is the diagonal matrix of natural frequencies and
% phi is the matrix of eigenvectors; each column of phi
% matrix correspond to one of the mode shapes

plot(Phi(:,2));	% plot the 2nd mode shape; by changin 2 to any number between 
						% 1 and 16, the corresponding mode shape will be plotted