University of Florida/Eml4507/Team 7 Report 6

Problem 1
On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Find
Solve the general eigenvalue problem by first converting it to the standard eigenvalue problem for the spring-mass-damper system given on p.53-13 of 'Fead.s13.sec.53b'.

Given
$$ M = \begin{pmatrix} 3 & 0 \\ 0 & 2 \end{pmatrix} $$

$$ K = \begin{pmatrix} 30 & -20 \\ -20 & 35 \end{pmatrix} $$

Solution
Converting the general eigenvalue problem to the standard eigenvalue problem and solving it General eigenvalue form: $$ Kx = \lambda Mx $$ Standard eigenvalue form: $$ K^* x^* = \lambda x^* $$ Where, $$ K^* = M^{-1/2} K M^{-1/2} $$ $$ x^* = M^{1/2} x $$ $$ K^* = \begin{pmatrix} 10 & -8.16 \\ -8.16 & 17.5 \end{pmatrix} $$ $$ M^{1/2} = \begin{pmatrix} \sqrt{3} & 0 \\ 0 & \sqrt{2} \end{pmatrix} $$ $$ M^{-1/2} = \begin{pmatrix} 1 / \sqrt{3} & 0 \\ 0 & 1 / \sqrt{2} \end{pmatrix} $$ $$ K^* x^* = \lambda x^* $$ $$ K^* M^{1/2} x = \lambda M^{1/2} x $$ $$ \lambda M^{1/2} x - K^* M^{1/2} x = 0 $$ $$ ( \lambda M^{1/2} - K^* M^{1/2})x = 0 $$ $$ \lambda M^{1/2} - K^* M^{1/2} = \begin{pmatrix} \sqrt{3} \lambda - 17.3 & 11.5 \\ 14.1 & \sqrt{2} \lambda - 24.7 \end{pmatrix} $$ $$ det( \lambda M^{1/2} - K^* M^{1/2}) = 0 $$ Calculating the determinant $$ (\sqrt{3} \lambda - 17.3)(\sqrt{2} \lambda - 24.7) - 162.15 = 0 $$ $$ 2.4 \lambda^2 - 67.2 \lambda + 427.3 = 0 $$ Therefore, the Eigenvalues are: $$ \lambda_1 = 18.2, \lambda_2 = 9.8 $$ The next step is finding the Eigenvectors $$ \lambda_1 = 18.2 $$ $$ ( \lambda_1 M^{1/2} - K^* M^{1/2})X_1 = \begin{pmatrix} 14.2 & 11.5 \\ 14.1 & 1 \end{pmatrix} \begin{pmatrix} x_{11} \\ x_{21} \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$$

Letting $$ x_{21} = 1 $$ and calculating $$ x_{12} $$

$$ \begin{pmatrix} x_{11} \\ x_{21} \end{pmatrix} = \begin{pmatrix} -0.81 \\ 1 \end{pmatrix} $$ $$ \lambda_2 = 9.8 $$ $$ ( \lambda_2 M^{1/2} - K^* M^{1/2})X_1 = \begin{pmatrix} -0.326 & 11.5 \\ 14.1 & -10.8 \end{pmatrix} \begin{pmatrix} x_{12} \\ x_{22} \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$$

Letting $$ x_{12} = 1 $$ and calculating $$ x_{22} $$

$$ \begin{pmatrix} x_{12} \\ x_{22} \end{pmatrix} = \begin{pmatrix} 1 \\ 1.3 \end{pmatrix} $$

$$ \mathbf{|X_1 X_2|}=\begin{bmatrix} x_{11} & x_{12}\\ x_{21} & x_{22}\\ \end{bmatrix} = \begin{bmatrix} -0.81 & 1\\ 1 & 1.3\\ \end{bmatrix} $$ These results compare favorably with those from problem 5.6 using CALFEM. Mass Orthogonality: $$ x_i^T M_{xj} = 0 $$ The eigenvectors are therefore proven to be mass-orthogonal.

Problem 2
On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Find
The Lowest 3 eigenpairs $$(\omega_j,\phi_j) for j=1,2,3$$ by transforming the generalized eigenvalue problem into a standard eigenvalue problem and plot the 3 lowest mode shapes in a gif image.

Given
$$E=100 GPa, A=1.0 cm^2, L=0.3m, \rho=5000 \frac{kg}{m^3}$$

Solution
clear clc

%GIVENS L=0.3; E=100e9; A=1e-4; rho=5000; ep=[E A];

%ELEMENT DOF Edof=zeros(25,5); for i=1:6 j=2*(i-1); Edof(i,:)=[i,1+j,2+j,3+j,4+j]; end for i=7:12 j=2*(i+1); Edof(i,:)=[i,j-1,j,j+1,j+2]; end for i=13:19 j=2*(i-13); Edof(i,:)=[i,1+j,2+j,15+j,16+j]; end for i=20:25 j=2*(i-20); Edof(i,:)=[i,1+j,2+j,17+j,18+j]; end

%COORDINATES ex=zeros(14,2); ey=zeros(14,2); for i=1:25 if i<7 ex(i,:)=[L*(i-1),L*i]; ey(i,:)=[0,0]; elseif i>6&&i<13 ex(i,:)=[L*(i-7),L*(i-6)]; ey(i,:)=[L,L]; elseif i>12&&i<20 ex(i,:)=[L*(i-13),L*(i-13)]; ey(i,:)=[0,L]; else ex(i,:)=[L*(i-20),L*(i-19)]; ey(i,:)=[0,L]; end end

%STIFFNESS AND MASS MATRIX K=zeros(28); M=zeros(28); for i=1:25 E=ep(1);A=ep(2); xt=ex(i,2)-ex(i,1); yt=ey(i,2)-ey(i,1); L=sqrt(xt^2+yt^2); l=xt/L; m=yt/L; ke=E*A/L*[l^2 l*m -l^2 -l*m; l*m m^2 -l*m -m^2; -l^2 -l*m l^2 l*m; -l*m -m^2 l*m m^2;]; m=L*A*rho; me=[m/2 0 0 0; 0 m/2 0 0; 0 0 m/2 0; 0 0 0 m/2]; edoft=Edof(i,2:5); K(edoft,edoft)=K(edoft,edoft)+ke; M(edoft,edoft)=M(edoft,edoft)+me; end

%FIND THE EIGEN VALUES AND VECTORS ndof=size(K,1); freedof=[1:ndof]'; fixdof=[1 15 16]'; freedof(fixdof)=[]; Kred=K(freedof,freedof); Mred=M(freedof,freedof);

Ks=Mred^(-1/2)*Kred*Mred^(-1/2); [X1,D1]=eig(Ks); X2=Mred^(-1/2)*X1; for j=1:size(X2) d=sqrt(X2(:,j)'*X2(:,j)); X3(:,j)=X2(:,j)/d; end [D1,i]=sort(diag(D1)); X4=X3(:,i); eigenval=D1; eigenvec=zeros(size(K,1),size(X4,1)); eigenvec(freedof,:)=X4;

%PLOT THE GIF for kk=1:3 eigenvalx=eigenval(kk); eigenvecx=eigenvec(:,kk); w=sqrt(eigenvalx); T=2*pi/w dt=T/100; t=0:dt:T; figure(kk) if kk==1; filename = 'mode1 r5p2.gif'; elseif kk==2; filename = 'mode2 r5p2.gif'; elseif kk==3; filename = 'mode3 r5p2.gif'; end for jj = 1:100 tt=t(jj); d=eigenvecx*sin(w*tt); d=d'; rr=Edof(:,2:5); ed=zeros(25,4); for i=1:25; ed(i,1:4)=d(rr(i,:)); end xd=(ex+ed(:,[1 3]))'; yd=(ey+ed(:,[2 4]))'; s1=['-', 'k']; axis manual plot(xd,yd,s1) set(gca, 'ylim', [-1.5 1.5], 'xlim', [0 3]); drawnow frame = getframe(1); im = frame2im(frame); [imind,cm] = rgb2ind(im,256); if jj == 1; imwrite(imind,cm,filename,'gif', 'Loopcount',inf); else imwrite(imind,cm,filename,'gif','WriteMode','append'); end end end

The resulting egienpairs are:

\displaystyle \begin{align} &\omega_1=1.6890 \times 10^5 \phi_1=\begin{bmatrix} 0\\ -0.0082\\ -0.0279\\ -0.0757\\ -0.0479\\ -0.1982\\ -0.0605\\ -0.3581\\ -0.0670\\ -0.5384\\ -0.0690\\ -0.7244\\ -0.0690\\ -0.9052\\ 0\\ 0\\ 0.0364\\ -0.0677\\ 0.0645\\ -0.1906\\ 0.0847\\ -0.3514\\ 0.0974\\ -0.5332\\ 0.1038\\ -0.7213\\ 0.1058\\ -0.9045 \end{bmatrix}\\ &\omega_2= 2.6676 \times 10^6 \phi_2=\begin{bmatrix} 0\\ -0.0745\\ 0.0227\\ -0.4176\\ 0.0973\\ -0.6512\\ 0.1884\\ -0.6252\\ 0.2603\\ -0.3137\\ 0.2941\\ 0.1825\\ 0.2976\\ 0.6937\\ 0\\ 0\\ 0.0732\\ -0.3541\\ 0.0714\\ -0.6149\\ 0.0153\\ -0.6228\\ -0.0603\\ -0.3368\\ -0.1201\\ 0.1553\\ -0.1455\\ 0.6853 \end{bmatrix}\\ &\omega_3=7.0219 \times 10^6 \phi_3=\begin{bmatrix} 0\\ -0.0352\\ -0.2178\\ -0.0416\\ -0.3907\\ -0.1023\\ -0.5191\\ -0.1283\\ -0.6115\\ -0.0751\\ -0.6722\\ 0.0253\\ -0.6941\\ 0.0971\\ 0\\ 0\\ -0.1204\\ -0.0089\\ -0.2656\\ -0.0780\\ -0.4221\\ -0.1195\\ -0.5663\\ -0.0809\\ -0.6710\\ 0.0154\\ -0.7178\\ 0.0940 \end{bmatrix}\\ \end{align} $$

The mode shapes for the previous eigenpairs are"

Problem 3
'''On our honor, the solution to this problem was generated by referring to the solution to Problem 3.1 at these locations: Eml4507 Team7 Report3, Team Negative Damping (3): Report 3, Eml4507.s13.team2/Report3, and EML4507.s13.team4ever.R3. Their solutions were not copied, but consulted.'''

Find
Using FE matlab code, with non-zero prescribed displacement degrees-of-freedom, using the same "connectivity array" given in the same problem statement, provide all of the unknown global displacement degrees-of-freedom, force components(reactions), and member forces. Plot the deformed shape superposed on the undeformed shape. Verify the results with CALFEM.

Compare the reactions in the case of non-zero prescribed disp dofs with the reactions in the case of zero prescribed disp dofs.

Given
In the non-zero prescribed case: $$d_1 = ? cm$$ $$d_2 = ? cm$$ $$d_3 = 2 cm$$ $$d_4 = -1 cm$$ $$d_5 = -3 cm$$ $$d_6 = 5 cm$$ $$d_7 = 0 cm$$ $$d_8 = 0 cm$$

In the zero prescribed case: $$d_1 = ? cm$$ $$d_2 = ? cm$$ $$d_3 = 0 cm$$ $$d_4 = 0 cm$$ $$d_5 = 0 cm$$ $$d_6 = 0 cm$$ $$d_7 = 0 cm$$ $$d_8 = 0 cm$$

Solution
MATLAB code:

%Displacements d3= 0.02; %in m d4= -0.01; d5= -0.03; d6= 0.05; d7 = 0; d8 = 0; ph1= 0; ph2 = 0; dsmall = [d3; d4; d5; d6;]; %ph =placeholder, displacement unknown theta=45; %Property Matrix= [element number; EA/L; angle;]; P = [1:3; 10^5*206 10^5*206 10^5*206; -pi/6 pi/2 -5*pi/6;]; %angles refer to 1->3, 1->2, 1->4 %Global Coordinate System

GNC = [ 0, 0; 0, 1;    .866, -.5;     -.866, -.5;];

lm = [.866, -.5; 0 ,    1;      -.866, -.5;];

%populate global force matrix dof = 8; %4 nodes, 2 directions reach F = zeros(dof,1); F(1) = 20000*cos(pi/4); F(2) = 20000*sin(pi/4);

%populate stiffness matrices lsq1 = (lm(1,1))^2; msq1 = (lm(1,2))^2; ltimesm1 = lm(1,1)*lm(1,2); Ke1 = [ lsq1, ltimesm1, 0, 0, -lsq1, -ltimesm1, 0, 0; ltimesm1, msq1, 0, 0 -ltimesm1, -msq1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0;            0, 0, 0, 0, 0, 0, 0, 0;             -lsq1, -ltimesm1, 0, 0, lsq1, ltimesm1, 0, 0; -ltimesm1, -msq1, 0, 0, ltimesm1, msq1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0;            0, 0, 0, 0, 0, 0, 0, 0;];     lsq2 = (lm(2,1))^2; msq2 = (lm(2,2))^2; ltimesm2 = lm(2,1)*lm(2,2); Ke2 = [ lsq2, ltimesm2, -lsq2, -ltimesm2, 0, 0, 0, 0; ltimesm2, msq2, -ltimesm2, -msq2, 0, 0, 0, 0; -lsq2, -ltimesm2, lsq2, ltimesm2, 0, 0, 0, 0; -ltimesm2, -msq2, ltimesm2, msq2, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0;            0, 0, 0, 0, 0, 0, 0, 0;             0, 0, 0, 0, 0, 0, 0, 0;             0, 0, 0, 0, 0, 0, 0, 0;];    lsq3 = (lm(3,1))^2; msq3 = (lm(3,2))^2; ltimesm3 = lm(3,1)*lm(3,2); Ke3 = [ lsq3, ltimesm3, 0, 0, 0, 0, -lsq3, -ltimesm3; ltimesm3, msq3, 0, 0, 0, 0, -ltimesm3, -msq3; 0, 0, 0, 0, 0, 0, 0, 0;            0, 0, 0, 0, 0, 0, 0, 0;             0, 0, 0, 0, 0, 0, 0, 0;             0, 0, 0, 0, 0, 0, 0, 0;             -lsq3, -ltimesm3, 0, 0, 0, 0, lsq3, ltimesm3; -ltimesm3, -msq3, 0, 0, 0, 0, ltimesm3, msq3;];

Kglobal = P(2,1)*(Ke1+Ke2+Ke3)

%find unknown displacements, after reducing Fsmall = [F(1) F(2)]'; Ksmall = zeros([2,6]);

for i=1:2 for j=1:6 Ksmall (i,j) = Kglobal((i+1),j); end end

unknownds = Ksmall\Fsmall d1 = unknownds(1); d2 = unknownds(2);

Ksmall2 = zeros([4,4]);

for i=1:4 for j=1:4 Ksmall2 (i,j) = Kglobal((i+1),j); end end

unknownFs = Ksmall2* dsmall

P1 = 10^5*206*.866*(d5-d1)-.5*(d6-d2) P2 = 10^10*206*0*(d3-d1)-1*(d4-d2) P3 = 10^10*206*-.866*(d7-d1)-.5*(d8-d2)

Resulting in:

Kglobal =

Columns 1 through 7

3.0898e+07           0            0            0  -1.5449e+07   8.9198e+06  -1.5449e+07 0    3.09e+07            0    -2.06e+07   8.9198e+06    -5.15e+06  -8.9198e+06 0           0            0            0            0            0            0            0    -2.06e+07            0     2.06e+07            0            0            0 -1.5449e+07  8.9198e+06            0            0   1.5449e+07  -8.9198e+06            0 8.9198e+06   -5.15e+06            0            0  -8.9198e+06     5.15e+06            0 -1.5449e+07 -8.9198e+06            0            0            0            0   1.5449e+07 -8.9198e+06   -5.15e+06            0            0            0            0   8.9198e+06

Column 8

-8.9198e+06 -5.15e+06 0           0            0            0   8.9198e+06 5.15e+06

unknownds =

0.00045767  0.00045767

unknownFs =

-1.339e+06 0   1.236e+06 -3.9818e+05

P1 =

-5.3519e+05

P2 =

1045.8

P3 =

22.884

In the zero case: In the zero prescribed case: $$d_1 = ? cm$$ $$d_2 = ? cm$$ $$d_3 = 0 cm$$ $$d_4 = 0 cm$$ $$d_5 = 0 cm$$ $$d_6 = 0 cm$$ $$d_7 = 0 cm$$ $$d_8 = 0 cm$$

Simply strike the rows and columns, resulting in:

unknownds =

0.00045767  0.00045767

All the outer node reactions are zero, since their displacements are zero.

P1 =

-0.34500e+05

P2 =

-0.94400e+05

P3 =

1.29000e+05

Problem 4
On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Find
Solve the initial truss structure using truss FEs

Solution
function FEAr6p4

nodelocation=[-1.5 0 8; 1.5 0 8;   -1.5 1.5 4;    1.5 1.5 4;    1.5 -1.5 4;    -1.5 -1.5 4;    -4 4 0;    4 4 0;    4 -4 0;    -4 -4 0];

%INPUT:  ex = [-1.5 1.5] %        ey = [0 0]         element node coordinates %        ez = [z1 z2] %   %         ep = [E A]           E: Young's modulus %                             A: cross section area % ex=[nodelocation(1,1) nodelocation(2,1); nodelocation(4,1) nodelocation(1,1); nodelocation(3,1) nodelocation(2,1); nodelocation(5,1) nodelocation(1,1); nodelocation(6,1) nodelocation(2,1); nodelocation(4,1) nodelocation(2,1); nodelocation(5,1) nodelocation(2,1); nodelocation(3,1) nodelocation(1,1); nodelocation(6,1) nodelocation(1,1); nodelocation(6,1) nodelocation(3,1); nodelocation(5,1) nodelocation(4,1); nodelocation(4,1) nodelocation(3,1); nodelocation(6,1) nodelocation(5,1); nodelocation(10,1) nodelocation(3,1); nodelocation(7,1) nodelocation(6,1); nodelocation(9,1) nodelocation(4,1); nodelocation(8,1) nodelocation(5,1); nodelocation(7,1) nodelocation(4,1); nodelocation(8,1) nodelocation(3,1); nodelocation(10,1) nodelocation(5,1); nodelocation(9,1) nodelocation(6,1); nodelocation(10,1) nodelocation(6,1); nodelocation(7,1) nodelocation(3,1); nodelocation(8,1) nodelocation(4,1); nodelocation(9,1) nodelocation(5,1);];

ey=[nodelocation(1,2) nodelocation(2,2); nodelocation(4,2) nodelocation(1,2); nodelocation(3,2) nodelocation(2,2); nodelocation(5,2) nodelocation(1,2); nodelocation(6,2) nodelocation(2,2); nodelocation(4,2) nodelocation(2,2); nodelocation(5,2) nodelocation(2,2); nodelocation(3,2) nodelocation(1,2); nodelocation(6,2) nodelocation(1,2); nodelocation(6,2) nodelocation(3,2); nodelocation(5,2) nodelocation(4,2); nodelocation(4,2) nodelocation(3,2); nodelocation(6,2) nodelocation(5,2); nodelocation(10,2) nodelocation(3,2); nodelocation(7,2) nodelocation(6,2); nodelocation(9,2) nodelocation(4,2); nodelocation(8,2) nodelocation(5,2); nodelocation(7,2) nodelocation(4,2); nodelocation(8,2) nodelocation(3,2); nodelocation(10,2) nodelocation(5,2); nodelocation(9,2) nodelocation(6,2); nodelocation(10,2) nodelocation(6,2); nodelocation(7,2) nodelocation(3,2); nodelocation(8,2) nodelocation(4,2); nodelocation(9,2) nodelocation(5,2);];

ez=[nodelocation(1,3) nodelocation(2,3); nodelocation(4,3) nodelocation(1,3); nodelocation(3,3) nodelocation(2,3); nodelocation(5,3) nodelocation(1,3); nodelocation(6,3) nodelocation(2,3); nodelocation(4,3) nodelocation(2,3); nodelocation(5,3) nodelocation(2,3); nodelocation(3,3) nodelocation(1,3); nodelocation(6,3) nodelocation(1,3); nodelocation(6,3) nodelocation(3,3); nodelocation(5,3) nodelocation(4,3); nodelocation(4,3) nodelocation(3,3); nodelocation(6,3) nodelocation(5,3); nodelocation(10,3) nodelocation(3,3); nodelocation(7,3) nodelocation(6,3); nodelocation(9,3) nodelocation(4,3); nodelocation(8,3) nodelocation(5,3); nodelocation(7,3) nodelocation(4,3); nodelocation(8,3) nodelocation(3,3); nodelocation(10,3) nodelocation(5,3); nodelocation(9,3) nodelocation(6,3); nodelocation(10,3) nodelocation(6,3); nodelocation(7,3) nodelocation(3,3); nodelocation(8,3) nodelocation(4,3); nodelocation(9,3) nodelocation(5,3);];

E=3*10^7; A=0.0218; B=zeros(3, 25); Kefinal=zeros(25,1); for i=1:25 B(1,i)=ex(i,2)-ex(i,1) ; B(2,i)= ey(i,2)-ey(i,1); B(3,i)=ez(i,2)-ez(i,1) ; for i=1:25 l=B(:,i); L=sqrt(l'*l); Kle=E*A/L*[1 -1; -1 1]; n=l'/L G=[  n   zeros(size(n)); zeros(size(n))  n   ];

Ke=G'*Kle*G end end % b=B*B' % L=sqrt(b) % Kle=E*A/L*[1 -1; %            -1  1]; % %   n=B'/L; %  G=[   n   zeros(size(n)); %    zeros(size(n))   n   ] % % Ke=G'*Kle*G;

OUTPUT:

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640   -3.7823   -5.2007   -2.3640    1.0745    1.7192    2.3640   -3.7823    1.7192    2.7508    3.7823   -5.2007    2.3640    3.7823    5.2007    2.3640   -1.0745   -1.7192   -2.3640    3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640   3.7823   -1.0745   -1.7192   -1.7192   -2.7508   -2.3640   -3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640   -3.7823   -5.2007   -2.3640    1.0745    1.7192    2.3640   -3.7823    1.7192    2.7508    3.7823   -5.2007    2.3640    3.7823    5.2007    2.3640   -1.0745   -1.7192   -2.3640    3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640   3.7823   -1.0745   -1.7192   -1.7192   -2.7508   -2.3640   -3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865    4.2984   -2.6865    2.6865    2.6865    4.2984   -2.6865    4.2984    4.2984    6.8775   -4.2984   -2.6865   -2.6865   -4.2984    2.6865   -2.6865   -2.6865   -4.2984    2.6865   -4.2984   -4.2984   -6.8775    4.2984

Columns 5 through 6

-2.6865  -4.2984   -2.6865   -4.2984   -4.2984   -6.8775    2.6865    4.2984    2.6865    4.2984    4.2984    6.8775

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640   -3.7823   -5.2007   -2.3640    1.0745    1.7192    2.3640   -3.7823    1.7192    2.7508    3.7823   -5.2007    2.3640    3.7823    5.2007    2.3640   -1.0745   -1.7192   -2.3640    3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640   3.7823   -1.0745   -1.7192   -1.7192   -2.7508   -2.3640   -3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865    4.2984   -2.6865    2.6865    2.6865    4.2984   -2.6865    4.2984    4.2984    6.8775   -4.2984   -2.6865   -2.6865   -4.2984    2.6865   -2.6865   -2.6865   -4.2984    2.6865   -4.2984   -4.2984   -6.8775    4.2984

Columns 5 through 6

-2.6865  -4.2984   -2.6865   -4.2984   -4.2984   -6.8775    2.6865    4.2984    2.6865    4.2984    4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865  -2.6865    4.2984   -2.6865   -2.6865    2.6865   -4.2984    2.6865    4.2984   -4.2984    6.8775   -4.2984   -2.6865    2.6865   -4.2984    2.6865    2.6865   -2.6865    4.2984   -2.6865   -4.2984    4.2984   -6.8775    4.2984

Columns 5 through 6

2.6865  -4.2984   -2.6865    4.2984    4.2984   -6.8775   -2.6865    4.2984    2.6865   -4.2984   -4.2984    6.8775

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640   -3.7823   -5.2007   -2.3640    1.0745    1.7192    2.3640   -3.7823    1.7192    2.7508    3.7823   -5.2007    2.3640    3.7823    5.2007    2.3640   -1.0745   -1.7192   -2.3640    3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640   3.7823   -1.0745   -1.7192   -1.7192   -2.7508   -2.3640   -3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865    4.2984   -2.6865    2.6865    2.6865    4.2984   -2.6865    4.2984    4.2984    6.8775   -4.2984   -2.6865   -2.6865   -4.2984    2.6865   -2.6865   -2.6865   -4.2984    2.6865   -4.2984   -4.2984   -6.8775    4.2984

Columns 5 through 6

-2.6865  -4.2984   -2.6865   -4.2984   -4.2984   -6.8775    2.6865    4.2984    2.6865    4.2984    4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865  -2.6865    4.2984   -2.6865   -2.6865    2.6865   -4.2984    2.6865    4.2984   -4.2984    6.8775   -4.2984   -2.6865    2.6865   -4.2984    2.6865    2.6865   -2.6865    4.2984   -2.6865   -4.2984    4.2984   -6.8775    4.2984

Columns 5 through 6

2.6865  -4.2984   -2.6865    4.2984    4.2984   -6.8775   -2.6865    4.2984    2.6865   -4.2984   -4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865   -4.2984   -2.6865    2.6865    2.6865   -4.2984   -2.6865   -4.2984   -4.2984    6.8775    4.2984   -2.6865   -2.6865    4.2984    2.6865   -2.6865   -2.6865    4.2984    2.6865    4.2984    4.2984   -6.8775   -4.2984

Columns 5 through 6

-2.6865   4.2984   -2.6865    4.2984    4.2984   -6.8775    2.6865   -4.2984    2.6865   -4.2984   -4.2984    6.8775

Ke =

NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN NaN  NaN   NaN   NaN   NaN   NaN

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689   -5.5171   -4.1378    2.0689    1.0345   -2.7585   -2.0689   -5.5171   -2.7585    7.3561    5.5171   -4.1378   -2.0689    5.5171    4.1378   -2.0689   -1.0345    2.7585    2.0689    5.5171    2.7585   -7.3561   -5.5171

Columns 5 through 6

-2.0689   5.5171   -1.0345    2.7585    2.7585   -7.3561    2.0689   -5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689    5.5171   -4.1378   -2.0689    1.0345   -2.7585    2.0689    5.5171   -2.7585    7.3561   -5.5171   -4.1378    2.0689   -5.5171    4.1378    2.0689   -1.0345    2.7585   -2.0689   -5.5171    2.7585   -7.3561    5.5171

Columns 5 through 6

2.0689  -5.5171   -1.0345    2.7585    2.7585   -7.3561   -2.0689    5.5171    1.0345   -2.7585   -2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378  -2.0689   -5.5171   -4.1378   -2.0689    1.0345    2.7585    2.0689   -5.5171    2.7585    7.3561    5.5171   -4.1378    2.0689    5.5171    4.1378    2.0689   -1.0345   -2.7585   -2.0689    5.5171   -2.7585   -7.3561   -5.5171

Columns 5 through 6

2.0689   5.5171   -1.0345   -2.7585   -2.7585   -7.3561   -2.0689   -5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+004 *

Columns 1 through 4

4.1378   2.0689    5.5171   -4.1378    2.0689    1.0345    2.7585   -2.0689    5.5171    2.7585    7.3561   -5.5171   -4.1378   -2.0689   -5.5171    4.1378   -2.0689   -1.0345   -2.7585    2.0689   -5.5171   -2.7585   -7.3561    5.5171

Columns 5 through 6

-2.0689  -5.5171   -1.0345   -2.7585   -2.7585   -7.3561    2.0689    5.5171    1.0345    2.7585    2.7585    7.3561

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887   -0.5033         0         0   -0.5033    1.3422         0         0         0         0         0         0   -0.1887    0.5033         0         0    0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887    0.5033    0.5033   -1.3422         0         0    0.1887   -0.5033   -0.5033    1.3422

Ke =

1.0e+005 *

Columns 1 through 4

0        0         0         0         0    0.1887    0.5033         0         0    0.5033    1.3422         0         0         0         0         0         0   -0.1887   -0.5033         0         0   -0.5033   -1.3422         0

Columns 5 through 6

0        0   -0.1887   -0.5033   -0.5033   -1.3422         0         0    0.1887    0.5033    0.5033    1.3422

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

0          0           0           0      218000           0           0           0           0           0           0           0           0     -218000           0           0           0           0

Columns 4 through 6

0          0           0           0     -218000           0           0           0           0           0           0           0           0      218000           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

Columns 1 through 3

218000          0           0           0           0           0           0           0           0     -218000           0           0           0           0           0           0           0           0

Columns 4 through 6

-218000          0           0           0           0           0           0           0           0      218000           0           0           0           0           0           0           0           0

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640    1.7192   -1.0745    2.3640    5.2007    3.7823   -2.3640    1.7192    3.7823    2.7508   -1.7192   -1.0745   -2.3640   -1.7192    1.0745   -2.3640   -5.2007   -3.7823    2.3640   -1.7192   -3.7823   -2.7508    1.7192

Columns 5 through 6

-2.3640  -1.7192   -5.2007   -3.7823   -3.7823   -2.7508    2.3640    1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640    1.7192   -1.0745   -2.3640    5.2007   -3.7823    2.3640    1.7192   -3.7823    2.7508   -1.7192   -1.0745    2.3640   -1.7192    1.0745    2.3640   -5.2007    3.7823   -2.3640   -1.7192    3.7823   -2.7508    1.7192

Columns 5 through 6

2.3640  -1.7192   -5.2007    3.7823    3.7823   -2.7508   -2.3640    1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745  -2.3640   -1.7192   -1.0745   -2.3640    5.2007    3.7823    2.3640   -1.7192    3.7823    2.7508    1.7192   -1.0745    2.3640    1.7192    1.0745    2.3640   -5.2007   -3.7823   -2.3640    1.7192   -3.7823   -2.7508   -1.7192

Columns 5 through 6

2.3640   1.7192   -5.2007   -3.7823   -3.7823   -2.7508   -2.3640   -1.7192    5.2007    3.7823    3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

1.0745   2.3640   -1.7192   -1.0745    2.3640    5.2007   -3.7823   -2.3640   -1.7192   -3.7823    2.7508    1.7192   -1.0745   -2.3640    1.7192    1.0745   -2.3640   -5.2007    3.7823    2.3640    1.7192    3.7823   -2.7508   -1.7192

Columns 5 through 6

-2.3640   1.7192   -5.2007    3.7823    3.7823   -2.7508    2.3640   -1.7192    5.2007   -3.7823   -3.7823    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640    3.7823   -5.2007   -2.3640    1.0745   -1.7192    2.3640    3.7823   -1.7192    2.7508   -3.7823   -5.2007    2.3640   -3.7823    5.2007    2.3640   -1.0745    1.7192   -2.3640   -3.7823    1.7192   -2.7508    3.7823

Columns 5 through 6

2.3640  -3.7823   -1.0745    1.7192    1.7192   -2.7508   -2.3640    3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640   -3.7823   -5.2007    2.3640    1.0745   -1.7192   -2.3640   -3.7823   -1.7192    2.7508    3.7823   -5.2007   -2.3640    3.7823    5.2007   -2.3640   -1.0745    1.7192    2.3640    3.7823    1.7192   -2.7508   -3.7823

Columns 5 through 6

-2.3640   3.7823   -1.0745    1.7192    1.7192   -2.7508    2.3640   -3.7823    1.0745   -1.7192   -1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007   2.3640    3.7823   -5.2007    2.3640    1.0745    1.7192   -2.3640    3.7823    1.7192    2.7508   -3.7823   -5.2007   -2.3640   -3.7823    5.2007   -2.3640   -1.0745   -1.7192    2.3640   -3.7823   -1.7192   -2.7508    3.7823

Columns 5 through 6

-2.3640  -3.7823   -1.0745   -1.7192   -1.7192   -2.7508    2.3640    3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

5.2007  -2.3640   -3.7823   -5.2007   -2.3640    1.0745    1.7192    2.3640   -3.7823    1.7192    2.7508    3.7823   -5.2007    2.3640    3.7823    5.2007    2.3640   -1.0745   -1.7192   -2.3640    3.7823   -1.7192   -2.7508   -3.7823

Columns 5 through 6

2.3640   3.7823   -1.0745   -1.7192   -1.7192   -2.7508   -2.3640   -3.7823    1.0745    1.7192    1.7192    2.7508

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865    4.2984   -2.6865    2.6865    2.6865    4.2984   -2.6865    4.2984    4.2984    6.8775   -4.2984   -2.6865   -2.6865   -4.2984    2.6865   -2.6865   -2.6865   -4.2984    2.6865   -4.2984   -4.2984   -6.8775    4.2984

Columns 5 through 6

-2.6865  -4.2984   -2.6865   -4.2984   -4.2984   -6.8775    2.6865    4.2984    2.6865    4.2984    4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865  -2.6865    4.2984   -2.6865   -2.6865    2.6865   -4.2984    2.6865    4.2984   -4.2984    6.8775   -4.2984   -2.6865    2.6865   -4.2984    2.6865    2.6865   -2.6865    4.2984   -2.6865   -4.2984    4.2984   -6.8775    4.2984

Columns 5 through 6

2.6865  -4.2984   -2.6865    4.2984    4.2984   -6.8775   -2.6865    4.2984    2.6865   -4.2984   -4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865   2.6865   -4.2984   -2.6865    2.6865    2.6865   -4.2984   -2.6865   -4.2984   -4.2984    6.8775    4.2984   -2.6865   -2.6865    4.2984    2.6865   -2.6865   -2.6865    4.2984    2.6865    4.2984    4.2984   -6.8775   -4.2984

Columns 5 through 6

-2.6865   4.2984   -2.6865    4.2984    4.2984   -6.8775    2.6865   -4.2984    2.6865   -4.2984   -4.2984    6.8775

Ke =

1.0e+004 *

Columns 1 through 4

2.6865  -2.6865   -4.2984   -2.6865   -2.6865    2.6865    4.2984    2.6865   -4.2984    4.2984    6.8775    4.2984   -2.6865    2.6865    4.2984    2.6865    2.6865   -2.6865   -4.2984   -2.6865    4.2984   -4.2984   -6.8775   -4.2984

Columns 5 through 6

2.6865   4.2984   -2.6865   -4.2984   -4.2984   -6.8775   -2.6865   -4.2984    2.6865    4.2984    4.2984    6.8775

Problem 5
On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Find
Vibration analysis of 3-D truss system in R6.4

Solution
clear clc

E=3*10^7; A=0.0218; rho= 7.3*10^(-4); Edof=[1 1 2 3 4 5 6; 2 1 2 3 10 11 12 ;    3 4 5 6 7 8 9;     4 1 2 3 13 14 15;     5 4 5 6 16 17 18;     6 4 5 6 10 11 12;     7 4 5 6 13 14 15;     8 1 2 3 7 8 9;     9 1 2 3 16 17 18;     10 7 8 9 16 17 18;     11 10 11 12 13 14 15;     12 7 8 9 10 11 12;     13 13 14 15 16 17 18;     14 7 8 9 28 29 30;     15 16 17 18 19 20 21;     16 10 11 12 25 26 27;     17 13 14 15 22 23 24;     18 10 11 12 19 20 21;     19 7 8 9 22 23 24;     20 13 14 15 28 29 30;     21 16 17 18 25 26 27;     22 16 17 18 28 29 30;     23 7 8 9 19 20 21;     24 10 11 12 22 23 24;     25 13 14 15 25 26 27]; coord=[-1.5   0   8; 1.5   0   8;        -1.5  1.5  4;        1.5   1.5  4;        1.5  -1.5  4;        -1.5 -1.5  4;        -4     4   0;         4     4   0;         4    -4   0;        -4    -4   0]; ex=zeros(25,2); ey=zeros(25,2); ez=zeros(25,2); for i=1:25 ex(i,1)=coord((Edof(i,2)+2)/3,1); ex(i,2)=coord((Edof(i,5)+2)/3,1); ey(i,1)=coord((Edof(i,3)+1)/3,2); ey(i,2)=coord((Edof(i,6)+1)/3,2); ez(i,1)=coord(Edof(i,4)/3,3); ez(i,2)=coord(Edof(i,7)/3,3); end

K=zeros(75,75); M=zeros(75); for i=1:25 dx=ex(i,2)-ex(i,1) ; dy= ey(i,2)-ey(i,1); dz=ez(i,2)-ez(i,1) ;

L=sqrt(dx^2+dy^2+dz^2); Kle=E*A/L*[1 -1; -1 1]; l=dx/L; m=dy/L; n=dz/L; G=[l m n 0 0 0; 0 0 0 l m n]; mass=L*A*rho; me=[mass/2 0 0 0 0 0; 0 mass/2 0 0 0 0; 0 0 mass/2 0 0 0; 0 0 0 mass/2 0 0; 0 0 0 0 mass/2 0; 0 0 0 0 0 mass/2]; Ke=G'*Kle*G; S=Edof(i,2:7); K(S,S)=K(S,S)+Ke; M(S,S)=M(S,S)+me; end nd=size(K,1); fdof=[1:nd]'; bc=[25 26 22 24 19 21 28 30 ]'; fdof(bc)=[]; [X,D]=eig(K(fdof,fdof),M(fdof,fdof)); nfdof=size(X,1); eigenval=diag(D); eigenvec=zeros(nd,nfdof); eigenvec(fdof,:)=X; %top for kk=1:3 eigenvalx=eigenval(kk); eigenvecx=eigenvec(:,kk); w=sqrt(eigenvalx); T=2*pi/w; dt=T/100; t=0:dt:T; figure(kk)

if kk==1; filename = 'mode1_top.gif'; elseif kk==2; filename = 'mode2_top.gif'; elseif kk==3; filename = 'mode3_top.gif'; end

for jj = 1:100 tt=t(jj); d=eigenvecx*sin(w*tt); d=d'; rr=Edof(:,2:7); ed=zeros(25,6); for i=1:25; ed(i,1:6)=d(rr(i,:)); end xd=(ex+ed(:,[1 4]))'; yd=(ey+ed(:,[2 5]))'; zd=(ez+ed(:,[3 6]))'; s1=['-', 'k']; axis manual plot(xd,zd,s1) set(gca, 'ylim', [-12 12], 'xlim', [-12 12]); drawnow frame = getframe(1); im = frame2im(frame); [imind,cm] = rgb2ind(im,256); if jj == 1; imwrite(imind,cm,filename,'gif', 'Loopcount',inf); else imwrite(imind,cm,filename,'gif','WriteMode','append'); end end end %side for kk=1:3 eigenvalx=eigenval(kk); eigenvecx=eigenvec(:,kk) w=sqrt(eigenvalx) T=2*pi/w; dt=T/100 t=0:dt:T; figure(kk) if kk==1; filename = 'mode1_side.gif' elseif kk==2; filename = 'mode2_side.gif' elseif kk==3; filename = 'mode3_side.gif' end for jj = 1:100 tt=t(jj); d=eigenvecx*sin(w*tt); d=d'; rr=Edof(:,2:7); ed=zeros(25,6); for i=1:25; ed(i,1:6)=d(rr(i,:)); end xd=(ex+ed(:,[1 4]))'; yd=(ey+ed(:,[2 5]))'; zd=(ez+ed(:,[3 6]))'; s1=['-', 'k']; axis manual plot(xd,yd,s1) set(gca, 'ylim', [-12 12], 'xlim', [-12 12]); drawnow frame = getframe(1); im = frame2im(frame); [imind,cm] = rgb2ind(im,256); if jj == 1; imwrite(imind,cm,filename,'gif', 'Loopcount',inf); else imwrite(imind,cm,filename,'gif','WriteMode','append'); end end end

Top and Side view for Mode 1:

Top and Side view for Mode 2:

Top and Side view for Mode 3:

Contributing Team Members
On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.