User:Uf.team.wiki/HW7

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Contents

Model Frame Problem[edit]

Problem Setup[edit]

Shown below is the Frame element that consists of a truss element (axial deformation) and a beam element (transverse deformation)

Figure 1:Frame Element Layout

General Frame Breakdown with Local DOF's[edit]

In general, (generalized forces)

e=1,2 i=1,2,...6

Here, represent rotational degrees of freedom and correspond to DOF's that are bending moments


Figure 2: Frame Element with Global DOF's

Frame with Global Degrees of Freedom[edit]

Figure 3: Entire Frame Element with Global DOF's
  • 2 element stiffness matrices:
  • Global stiffness matrix:
File:K Topography.JPG
Figure 4: Global stiffness matrix block diagram

Local DOF's shown with Element 1[edit]

Figure 5: Single Element 1 with Local DOF's


Note,

Dimensional Analysis[edit]

Here we are analyzing the dimensions of the force displament relationship. We are loking to see how the units will emerge in the element stiffness matrix.

Arc Length[edit]

  • [x] = square brackets represent a dimensiokn

(rotational degree of freedom, no dimension)




Figure 6: Arc Length AB

Dimensional Analysis on Other Useful Parameters[edit]







Force Displacement Relationship Proofs[edit]

The matrix is discussed above and shown below

The transfer matrix, is given as:

The transpose of the transfer matrix, is given as:



The preceding matricies will be beneficial in developing the following relationship between the element force-displacement relationship in global coordinates from the element force-displacement relationship in local coordinates and is represented as:




  • where


  • knowing




Where

Looking at Deformed Truss Elements and Interpolations of Applied Forces[edit]

PVW for Beams[edit]

Motivation: find displacement V(ʎ) of element given deformed shape of truss

 for all W(x)

Integration by parts for the first term yields:



Now, looking at the figure below, focus on the stiffness term to derive the beam stiffness matrix and to identify the beam shape functions:

Figure 7: Displacements of General Element

Recall: \

Knowing the following interpolations shown below, their modal shapes are shown in the figure that follows.

Figure 8: Applied Force Interpolation

Determination of Applied Forces[edit]

The other applied internal forces and are illustrated in figure 9 below.

Figure 9:Interpolations for further applied forces

Determining the Displacement Vector[edit]

Looking at the equation for a vector[edit]

Recall: when determining beam shape functions


Compute:

Figure 10: Working with the displacement vector from the element

In order to compute we use the following equations:





The following relationship can be established and represent both vectors as:

Further simplifying this result, we take the following:


Using Dimensional Analysis with the Shape Functions[edit]

(displacement translational)


(rotational)


(displacement translational)


(rotational)

Deriving Beam Shape Functions[edit]

From the m\ddot{v} for the static case:

"EI" is a constant so the above equation becomes:


Use the following boundary conditions to solve for C1, C2, C3

Solving for C1, C2, C3:




Looking at Vibrations using FEA[edit]

General Cases: The Simple Form[edit]

In general,

With i,j = 2,3,5,6

Elastodynamics (trusses, 2-D frames, 3-D elasticity)[edit]

Looking at the Modal problem (lecture 31), we use the discrete Principle of Virtual Work:

It is important to note the following:

  • the boundary conditions are already applied
  • K matrix represents the reduced stiffness matrix.

The above equation is true for all .

Equations (1), (2), and (3) complete the ordinary differential equations (ODEs). These differential equations are second order in time, and have their initial conditions governed by the elastodynamics of the discretized continuous problem.

Equations (1), (2), and (3) are solved by taking the following steps:

Step 1: Using the unforced vibrations problem[edit]

This equation is equal to zero because there are no fores acting on the system. This equation will be referred as (4).

Assuming:

Where,

  • the phi matrix is not dependent on time

Therefore:

This means equation (4) translates into:

Concluding that,

Which is the generalized eigenvalue problem that was looked at in HW 4 and HW 5, as has the general form:

Where lambda represents an eigen value.

Setting the B matrix to zero corresponds to a general eigen value problem and is equal to the identity matrix. After this transformation the equation becomes:

Indicating that one of the eigenvalue is:

Using,

to represent the eigen pairs, i = 1 through n

Step 2: Modal Superposition Method[edit]

Knowing the orthogonal properties of the eigen pairs, we can calculate the following:

The delta is taken to be known as the Kronecker delta.

This simplification is made possible due to the mass orthogonality properties of eigenvectors.

This is now applied to equations (1), (2), (3), and (4) and results:

Here, the left hand side of the equation is equal to the Kronecker delta.

Therefore,

Equations (1)-(3) simplify to:

Looking at the equation above, the first parenthesis term is equal to the second derivative of the d matrix, while the second parenthesis term is equal to the d matrix itself.

Looking at this next equation above, the first parenthesis term is equal to the Kronecker delta, while the second parenthesis term is equal to the product of an eigenvalue and the Kronecker delta. Therefore, it is known that this equation can be simplified into an ordinary differential equation (ODE) shown below:

with i ranges from 1 to n.

Wikiversity vs. E-learning Comparison[edit]

In concluding this semester, this team agrees that there are both drawbacks and benefits of using MediaWiki and WebCT. The comparisons made are in the areas of collaboration, layout and privacy.

As a means of collaboration, Mediawiki is far superior. When working in terms of collaboration, it is known for its purpose in collaboration. It benefits from common internet accessibility, the history of edits and a common document. When all group members are able to see the same document real time and edit as necessary, it makes things much smoother. The ability to track user edits was very useful for assessing team member contributions and correcting mistakes. WebCT uses discussion boards for collaboration, which severely limits the scope of projects capable. Since there is no common document is established, it is very hard to understand edits rather than constantly exchanging a master document via email or messaging. Ultimately, for this class, the scope of collaboration did not extend as far as was perhaps intended. In general, the assignment was divided based on lecture days and each person made their own posts with little editing. In particular, collaboration across groups was very limited, and hardly existed.

The file structure is very straightforward for WebCT when compared to MediaWiki. The layout of WebCT lends itself to a more logical repository of common files, such as syllabus, homework assignments, solutions, grades, etc. The file structure is very straightforward and easily located for WebCT. However, Mediawiki doesn't have as good a hierarchical structure. This can be confusing and circular at times.

Because WebCT requires an individual login and provides the ability to privately upload individual assignments, it outperforms Mediawiki in terms of privacy due to this "double wall". WebCT is a much more individualized platform as compared to Mediawiki. Also, the universal accessibility of Mediawiki reduces the problems of limited bandwidth often encountered during high traffic periods by WebCT.

Regardless of the platform, we feel that submitting homework and notes as was done in this class is not the most effective use of time. It was often frustrating to type out the Latex code for equations, taking far longer than just writing it by hand. Furthermore, drawing figures by means of Visio or Inkscape was also troublesome and frustrating and extremely time consuming. The return on investment for this time was very small. It served more to frustrate and waste time than to reinforce learning. Mediawiki certainly represents a great resource, but may be better used for presenting a final report or project rather than day-to-day homework assignments in a class such as this one.

Analysis of the 2-Element System[edit]

This section analyzes the 2-Element System found in HW2. Various frame/truss and boundary conditions will be explored.

2-Bar Truss[edit]

This part is a recap of the 2-Bar Truss System found in HW3

Required MATLAB Functions[edit]

Before running the 2-Bar Truss System program, the following three MATLAB program functions must be in the same directory. They are obtained from the textbook website (See HW1 for textbook information). Matlab Truss Files

PlaneTrussElement.m[edit]

This function takes the Modulus of Elasticity (e), the Cross-Sectional Area (A) and the Nodal Coordinates (coord) of the element and generates the local stiffness matrix.

function k = PlaneTrussElement(e, A, coord)
% PlaneTrussElement(e, A, coord)
% Generates stiffness matrix for a plane truss element
% e = modulus of elasticity
% A = area of cross-section
% coord = coordinates at the element ends
 
x1=coord(1,1); y1=coord(1,2);
x2=coord(2,1); y2=coord(2,2);
L=sqrt((x2-x1)^2+(y2-y1)^2);
ls=(x2-x1)/L; ms=(y2-y1)/L;
k = e*A/L*[ls^2, ls*ms,-ls^2,-ls*ms;
ls*ms, ms^2,-ls*ms,-ms^2;
-ls^2,-ls*ms,ls^2,ls*ms;
-ls*ms,-ms^2,ls*ms,ms^2];
NodalSoln.m[edit]

This function takes the Global Stiffness Matrix (K), the Global Force vector (R), and two inputs that are the boundary conditions. The output is an array of the displacement and reaction forces.

function [d, rf] = NodalSoln(K, R, debc, ebcVals)
% [nd, rf] = NodalSoln(K, R, debc, ebcVals)
% Computes nodal solution and reactions
% K = global coefficient matrix
% R = global right hand side vector
% debc = list of degrees of freedom with specified values
% ebcVals = specified values
dof = length(R);
df = setdiff(1:dof, debc);
Kf = K(df, df);
Rf = R(df) - K(df, debc)*ebcVals;
dfVals = Kf\Rf;
d = zeros(dof,1);
d(debc) = ebcVals;
d(df) = dfVals;
rf = K(debc,:)*d - R(debc);
PlaneTrussResults.m[edit]

This function inputs the Modulus of Elasticity (e), Cross-Sectional Area (A), Nodes of Each Element (coord), and the Displacement calculated in the previous function (disps). The output are the Strain, Stress, and Axial Force of each element.

function results = PlaneTrussResults(e, A, coord, disps)
% results = PlaneTrussResults(e, A, coord, disps)
% Compute plane truss element results
% e = modulus of elasticity
% A = Area of cross-section
% coord = coordinates at the element ends
% disps = displacements at element ends
% The output quantities are eps = axial strain
% sigma = axial stress and force = axial force.

x1=coord(1,1); y1=coord(1,2);
x2=coord(2,1); y2=coord(2,2);
L=sqrt((x2-x1)^2+(y2-y1)^2);
ls=(x2-x1)/L; ms=(y2-y1)/L;
T=[ls,ms,0,0; 0,0,ls,ms];
d = T*disps;
eps= (d(2)-d(1))/L;
sigma = e.*eps;
force = sigma.*A;
results=[eps, sigma, force];

Main MATLAB Function[edit]

The following is the main MATLAB function (bar2.m) to solve for the 2-Bar Truss System

e = [3 5]; 
A = [1 2]; 
P = 7;
L=[4 2];
theta = [30 45]*pi/180;
nodes = [0, 0; L(1)*cos(theta(1)), L(1)*sin(theta(1)); L(1)*cos(theta(1))+L(2)*cos(theta(1)), L(1)*sin(theta(1))-L(2)*sin(theta(2))];
dof=2*length(nodes);
conn=[1,2; 2,3];
lmm = [1, 2, 3, 4; 3, 4, 5, 6];
elems=size(lmm,1);
K=zeros(dof);
debc = [1, 2, 5, 6];
ebcVals = zeros(length(debc),1);
 
%load vector
R = zeros(dof,1); 
R(4) = P;
 
% Assemble global stiffness matrix
K=zeros(dof);
for i=1:elems
lm=lmm(i,:);
con=conn(i,:);
k=PlaneTrussElement(e(i), A(i), nodes(con,:));
K(lm, lm) = K(lm, lm) + k;
end
K
R
% Nodal solution and reactions
[d1, reactions] = NodalSoln(K, R, debc, ebcVals)
results=[];
for i=1:elems
results = [results; PlaneTrussResults(e(i), A(i), nodes(conn(i,:),:), d1(lmm(i,:)))];
end
format short g
results

Results[edit]

The following are the results to bar2.m

K =

       0.5625      0.32476      -0.5625     -0.32476            0            0
      0.32476       0.1875     -0.32476      -0.1875            0            0
      -0.5625     -0.32476       3.2458      -1.8661      -2.6833       2.1909
     -0.32476      -0.1875      -1.8661       1.9764       2.1909      -1.7889
            0            0      -2.6833       2.1909       2.6833      -2.1909
            0            0       2.1909      -1.7889      -2.1909       1.7889


R =

     0
     0
     0
     7
     0
     0


d1 =

            0
            0
       4.4547
       7.7482
            0
            0


reactions =

      -5.0221
      -2.8995
       5.0221
      -4.1005


results =

        1.933        5.799        5.799
      0.64835       3.2417       6.4835

2-Element Frame[edit]

The following analyzes the 2-Element Frame System. The properties of the frame system is the same as the bar truss system. The cross-sectional area is assumed to be square.

Required MATLAB Functions[edit]

Before running the 2-Bar Truss System program, the following three MATLAB program functions must be in the same directory. They are obtained from the textbook website (See HW1 for textbook information). Matlab Truss Files

PlaneFrameElement.m[edit]
function [ke, rq] = PlaneFrameElement(modulus, inertia, A, qs, qt, coord)
% [ke, rq] = PlaneFrameElement(modulus, inertia, A, qs, qt, coord)
% Generates equations for a plane frame element
% modulus = modulus of elasticity
% inertia = moment of inertia
% A = area of cross-section
% qs = distributed load along the element axis
% qt = distributed load normal to the element axis
% coord = coordinates at the element ends

EI=modulus*inertia; EA = modulus*A;
x1=coord(1,1); y1=coord(1,2);
x2=coord(2,1); y2=coord(2,2);
L=sqrt((x2-x1)^2+(y2-y1)^2);
ls=(x2-x1)/L; ms=(y2-y1)/L;

ke = [(EA*L^2*ls^2 + 12*EI*ms^2)/L^3, ((-12*EI + EA*L^2)*ls*ms)/L^3, ...
        (-6*EI*ms)/L^2, -((EA*L^2*ls^2 + 12*EI*ms^2)/L^3), ...
        ((12*EI - EA*L^2)*ls*ms)/L^3, (-6*EI*ms)/L^2;
    ((-12*EI + EA*L^2)*ls*ms)/L^3, (12*EI*ls^2 + EA*L^2*ms^2)/L^3, ...
        (6*EI*ls)/L^2, ((12*EI - EA*L^2)*ls*ms)/L^3, ...
        -((12*EI*ls^2 + EA*L^2*ms^2)/L^3), (6*EI*ls)/L^2;
    (-6*EI*ms)/L^2, (6*EI*ls)/L^2, (4*EI)/L, ...
        (6*EI*ms)/L^2, (-6*EI*ls)/L^2,(2*EI)/L;
    -((EA*L^2*ls^2 + 12*EI*ms^2)/L^3), ((12*EI -EA*L^2)*ls*ms)/L^3, ...
        (6*EI*ms)/L^2, (EA*L^2*ls^2 + 12*EI*ms^2)/L^3, ...
        ((-12*EI + EA*L^2)*ls*ms)/L^3, (6*EI*ms)/L^2;
    ((12*EI - EA*L^2)*ls*ms)/L^3, -((12*EI*ls^2 + EA*L^2*ms^2)/L^3),...
        (-6*EI*ls)/L^2, ((-12*EI + EA*L^2)*ls*ms)/L^3, ...
        (12*EI*ls^2 + EA*L^2*ms^2)/L^3, (-6*EI*ls)/L^2;
    (-6*EI*ms)/L^2, (6*EI*ls)/L^2, (2*EI)/L, (6*EI*ms)/L^2, ...
        (-6*EI*ls)/L^2, (4*EI)/L];
rq = [(L*(ls*qs - ms*qt))/2; (L*(ms*qs + ls*qt))/2;(L^2*qt)/12; 
    (L*(ls*qs - ms*qt))/2; (L*(ms*qs + ls*qt))/2; -(L^2*qt)/12];
NodalSoln.m[edit]

NodalSoln.m

PlaneFrameResults.m[edit]
function [f, bm, V] = PlaneFrameResults(modulus, inertia, A, ...
    qs, qt, coord, dn)
% [f, bm, V] = PlaneFrameResults(modulus, inertia, A, ...
%    qs, qt, coord, dn)
% Generates frame element results
% modulus = modulus of elasticity
% inertia = moment of inertia
% A = area of cross-section
% qs = distributed load along the element axis
% qt = distributed load normal to the element axis
% coord = coordinates at the element ends
% dn = nodal solution
% [f, bm, V] = [axial force, bending moment, shear]

EI=modulus*inertia; EA = modulus*A;
x1=coord(1,1); y1=coord(1,2);
x2=coord(2,1); y2=coord(2,2);
L=sqrt((x2-x1)^2+(y2-y1)^2);
ls=(x2-x1)/L; ms=(y2-y1)/L;

u = dn([1,4]);
v = dn([2,3,5,6]);

f=[]; bm=[]; V=[];
% Change increment to get results at more points
for s=0:L/2:L
    x = x1 + s*ls; y = y1+ s*ms;
    f = [f; [x,y,EA*(u(2)-u(1))/L]];
    dn2 = [(12*s)/L^3 - 6/L^2, (6*s)/L^2 - 4/L, 6/L^2 - (12*s)/L^3, ...
            (6*s)/L^2 - 2/L];
    bm = [bm; [x, y, EI*dn2*v+(qt*(L^2 - 6*s*L + 6*s^2))/(12)]];
    dn3 = [12/L^3, 6/L^2, -(12/L^3), 6/L^2];
    V = [V; [x, y, EI*dn3*v+((qt*(12*s - 6*L))/(12))]];
end

Main MATLAB Function[edit]

The following is the main MATLAB function, frame2.m

e = [3 5];
a = [1 2];
s = [sqrt(a(1)) sqrt(a(2))];
inertia = [(s(1)^4)/12 (s(2)^4)/12];
L = [4 2];
P = 7;
theta = [30 45]*pi/180;
nodes = [0, 0; L(1)*cos(theta(1)), L(1)*sin(theta(1)); L(1)*cos(theta(1))+L(2)*cos(theta(1)), L(1)*sin(theta(1))-L(2)*sin(theta(2))];
conn=[1,2; 2,3];
lmm=[1,2,3,4,5,6; 4,5,6,7,8,9];
n=3*length(nodes);
debc=[1,2,7,8]; 
ebcVals=zeros(length(debc),1);
K=zeros(n); 
R = zeros(n,1);
R(5) = P;

% Generate equations for each element and assemble them.
for i=1:2
    lm=lmm(i,:);
    con=conn(i,:);
    [ke, rq] = PlaneFrameElement(e(i), inertia(i), a(i), 0, 0, nodes(con,:));
    K(lm, lm) = K(lm, lm) + ke;
    R(lm) = R(lm) + rq;
end

K
R

% Nodal solution and reactions
d2 = NodalSoln(K, R, debc, ebcVals)
fa=[]; bma=[]; Va=[];
for i=1:2
    lm=lmm(i,:);
    con=conn(i,:);
    [f, bm, V]=PlaneFrameResults(e(i), inertia(i), a(i), 0, 0, nodes(con,:), d2(lm));
    fa = [fa; f]; bma = [bma; bm]; Va = [Va; V];
end
fa
bma
Va

Results[edit]

The following are the results of frame2.m

K =

  Columns 1 through 6

      0.57422      0.30446    -0.046875     -0.57422     -0.30446    -0.046875
      0.30446      0.22266      0.08119     -0.30446     -0.22266      0.08119
    -0.046875      0.08119         0.25     0.046875     -0.08119        0.125
     -0.57422     -0.30446     0.046875        3.973      -1.0101       1.3118
     -0.30446     -0.22266     -0.08119      -1.0101       3.0848        1.468
    -0.046875      0.08119        0.125       1.3118        1.468       3.2314
            0            0            0      -3.3988       1.3145      -1.2649
            0            0            0       1.3145      -2.8622      -1.5492
            0            0            0       1.2649       1.5492       1.4907

  Columns 7 through 9

            0            0            0
            0            0            0
            0            0            0
      -3.3988       1.3145       1.2649
       1.3145      -2.8622       1.5492
      -1.2649      -1.5492       1.4907
       3.3988      -1.3145      -1.2649
      -1.3145       2.8622      -1.5492
      -1.2649      -1.5492       2.9814


R =

     0
     0
     0
     0
     7
     0
     0
     0
     0


d2 =

            0
            0
        3.198
       4.0789
       7.1629
      -3.2732
            0
            0
      -3.8159


fa =

            0            0       3.0592
       1.7321            1       3.0592
       3.4641            2       3.0592
       3.4641            2      -18.241
       4.3301       1.2929      -18.241
       5.1962      0.58579      -18.241


bma =

            0            0      0.28116
       1.7321            1     -0.40445
       3.4641            2      -1.0901
       3.4641            2       1.1215
       4.3301       1.2929     -0.40445
       5.1962      0.58579      -1.9304


Va =

            0            0     -0.34281
       1.7321            1     -0.34281
       3.4641            2     -0.34281
       3.4641            2      -1.3648
       4.3301       1.2929      -1.3648
       5.1962      0.58579      -1.3648

2-Element Frame/Truss Hybrid[edit]

The following analyzes the 2-element frame/truss. Element 1 is a frame element and element 2 is a truss element.

Required MATLAB Functions[edit]

Before running the 2-Bar Truss System program, the following three MATLAB program functions must be in the same directory. They are obtained from the textbook website (See HW1 for textbook information). Matlab Truss Files

PlaneFrameElement.m[edit]

PlaneFrameElement.m

PlaneTrussElement.m[edit]

PlaneTrussElement.m

NodalSoln.m[edit]

NodalSoln.m

Main MATLAB Function[edit]

The following is the main MATLAB function, hybrid.m

e = [3 5];
a = [1 2];
s = [sqrt(a(1)) sqrt(a(2))];
inertia = [(s(1)^4)/12 (s(2)^4)/12];
L = [4 2];
P = 7;
theta = [30 45]*pi/180;
nodes = [0, 0; L(1)*cos(theta(1)), L(1)*sin(theta(1)); L(1)*cos(theta(1))+L(2)*cos(theta(1)), L(1)*sin(theta(1))-L(2)*sin(theta(2))];
conn=[1,2; 2,3];
lmm=[1,2,3,4,5,6; 4,5,6,7,8,9];
n=3*length(nodes);
debc=[1,2,3,7,8]; 
ebcVals=zeros(length(debc),1);
K=zeros(n); 
R = zeros(n,1);
R(5) = P;

% Generate equations for each element and assemble them.
% Frame Element
lm=lmm(1,:);
con=conn(1,:);
[ke, rq] = PlaneFrameElement(e(1), inertia(1), a(1), 0, 0, nodes(con,:));
K(lm, lm) = K(lm, lm) + ke;
R(lm) = R(lm) + rq;
%Truss Element
lm=lmm(2,:);
con=conn(2,:);
k=PlaneTrussElement(e(2), a(2), nodes(con,:));
k1=[];
for i=1:4
    k1 = [k1;k(i,:) 0 0];
end
k1 = [k1; 0 0 0 0 0 0; 0 0 0 0 0 0];
K(lm, lm) = K(lm, lm) + k1;

K
R

% Nodal solution
d3 = NodalSoln(K, R, debc, ebcVals)

Results[edit]

The following is the results of hybrid.m. The NaN results are unknown and ignored in the next step

K =

  Columns 1 through 6

      0.57422      0.30446    -0.046875     -0.57422     -0.30446    -0.046875
      0.30446      0.22266      0.08119     -0.30446     -0.22266      0.08119
    -0.046875      0.08119         0.25     0.046875     -0.08119        0.125
     -0.57422     -0.30446     0.046875       3.2575      -1.8864      -2.6364
     -0.30446     -0.22266     -0.08119      -1.8864       2.0115       2.1097
    -0.046875      0.08119        0.125      -2.6364       2.1097       2.9333
            0            0            0       2.1909      -1.7889      -2.1909
            0            0            0            0            0            0
            0            0            0            0            0            0

  Columns 7 through 9

            0            0            0
            0            0            0
            0            0            0
       2.1909            0            0
      -1.7889            0            0
      -2.1909            0            0
       1.7889            0            0
            0            0            0
            0            0            0


R =

     0
     0
     0
     0
     7
     0
     0
     0
     0

d3 =

            0
            0
            0
      -0.1556
       14.169
       -10.33
            0
            0
          NaN

Plot[edit]

The following is a plot of the undeformed 2-element, deformed 2-bar truss deformed 2-frame, and 2-element truss/frame hybrid systems. The frames are incomplete since the moment displacement are not taken into account.

File:Twoelement.jpg

The following is the MATLAB code used to plot.

clear all
close all

bar2;
frame2;
hybrid;

% Number of DOFs (Total of 2 for x and y displacement)
   dof = 2;

% Nodal Coordinates
   n_node = 3; % # of Nodes
   n_elem = 2; % # of Elements
   total_dof = dof * n_node; % Total DOFs of System

   L1 = 4; % Length of Element 1
   L2 = 2; % Length of Element 2
   theta1 = 30*pi/180; % Angle of Element 1 wrt x-axis in rad
   theta2 = 45*pi/180; % Angle of Element 2 wrt x-axis in rad

   % Initial conditions of Truss System
   position(:,1) = [0; 0];
   position(:,2) = [L1*cos(theta1); L1*sin(theta1)];
   position(:,3) = [(L1*cos(theta1))+(L2*cos(theta2)); (L1*sin(theta1))-(L2*sin(theta2))];
   
   % Deformed locations of Truss System
   position2(:,1) = position(:,1); % Node Location Fixed (Boundary Condtion)
   position2(:,2) = position(:,2)+[d1(3);d1(4)]; % Solved in HW2
   position2(:,3) = position(:,3); % Node Location Fixed (Boundary Condtion)
   
   % Deformed locations of Frame System
   position3(:,1) = position(:,1); % Node Location Fixed (Boundary Condtion)
   position3(:,2) = position(:,2)+[d2(4);d2(5)];
   position3(:,3) = position(:,3); % Node Location Fixed (Boundary Condtion)
   
   % Deformed locations of Hybrid System
   position4(:,1) = position(:,1); % Node Location Fixed (Boundary Condtion)
   position4(:,2) = position(:,2)+[d3(4);d3(5)];
   position4(:,3) = position(:,3); % Node Location Fixed (Boundary Condtion)

   % Set Up Nodal Loccatons
   for i = 1 : n_node
      x(i) = position(1,i);
      y(i) = position(2,i);
      x2(i) = position2(1,i);
      y2(i) = position2(2,i);
      x3(i) = position3(1,i);
      y3(i) = position3(2,i);
      x4(i) = position4(1,i);
      y4(i) = position4(2,i);
   end
   
% Connect the Nodes
   node_connect(1, 1) = 1; % Element 1
   node_connect(2, 1) = 2;
   node_connect(1, 2) = 2; % Element 2
   node_connect(2, 2) = 3;

   % Plot The Truss System
   for i =  1 : n_elem  
      node_1 = node_connect(1,i);
      node_2 = node_connect(2,i);
      xx = [x(node_1),x(node_2)];
      yy = [y(node_1),y(node_2)];
      xx2 = [x2(node_1),x2(node_2)];
      yy2 = [y2(node_1),y2(node_2)];
      xx3 = [x3(node_1),x3(node_2)];
      yy3 = [y3(node_1),y3(node_2)];
      xx4 = [x4(node_1),x4(node_2)];
      yy4 = [y4(node_1),y4(node_2)];
      plot(xx,yy,'--',xx2,yy2,xx3,yy3,'-r',xx4,yy4,'-g')
      hold on % Hold the current figure for the next element
   end
   
   legend('Undeformed','Deformed Truss','Deformed Frame','Deformed Frame/Truss',2)
   
   % Add Global Nodes and Element Numbers
   text(0.2,0.7,'1','EdgeColor','black'); % Node 1
   text(3.4,2.3,'2','EdgeColor','black'); % Node 2 (Initial)
   text(4.8,1.1,'3','EdgeColor','black'); % Node 3
   text(2.0,0.8,'1'); % Element 1 (Initial)
   text(4.0,1.0,'2'); % Element 2 (Initial)

   % Label the Graphs and Axies
   title('Two-Element System')
   xlabel('x')
   ylabel('y')

Analysis of the Electric Pylon System[edit]

This section analyzes the Electric Pylon System found in HW6

Electric Pylon Truss System[edit]

Analysis of the Electric Pylon truss system was solved in the last homework and can be found here

Electric Pylon Frame System[edit]

The Electric Pylon frame system is similar to the truss system, but the analysis is different. The cross-sectional area is assumed to be square

Required MATLAB Functions[edit]

Before running the 2-Bar Truss System program, the following three MATLAB program functions must be in the same directory. They are obtained from the textbook website (See HW1 for textbook information). Matlab Truss Files

PlaneFrameElement.m[edit]

PlaneFrameElement.m

NodalSoln.m[edit]

NodalSoln.m

PlaneFrameResults.m[edit]

PlaneFrameResults.m

Main MATLAB Function[edit]

The following is the main MATLAB Function to analyze the Electric Pylon Frame, electricframe.m

a = 400; % Cross-sectional area (mm^2)
e = 200000; % Modulus (MPa)
P = 1000; % Applied load (N)
s = sqrt(a);
I = (s^4)/12;
 
% Node locations
   position(:, 1) = [ 1.5; 0; 0]; % Left Leg
   position(:, 2) = [ 4.53; 0; 0]; % Right Leg
   position(:, 3) = [ 1.88; 1.18; 0];
   position(:, 4) = [ 3.03; 1.18; 0];
   position(:, 5) = [ 4.17; 1.18; 0];
   position(:, 6) = [ 2.2; 2.181; 0];
   position(:, 7) = [ 3.03; 2.181; 0];
   position(:, 8) = [ 3.85; 2.181; 0];
   position(:, 9) = [ 2.53; 3.181; 0];
   position(:, 10) = [ 3.53; 3.181; 0];
   position(:, 11) = [ 2.34; 3.681; 0];
   position(:, 12) = [ 3.03; 3.681; 0];
   position(:, 13) = [ 3.71; 3.681; 0];
   position(:, 14) = [ 2.16; 4.181; 0];
   position(:, 15) = [ 2.62; 4.181; 0];
   position(:, 16) = [ 3.44; 4.181; 0];
   position(:, 17) = [ 3.89; 4.181; 0];
   position(:, 18) = [ 2.36; 4.5; 0];
   position(:, 19) = [ 3.7; 4.5; 0];
   position(:, 20) = [ 1.8; 5.172; 0];
   position(:, 21) = [ 4.25; 5.172; 0];
   position(:, 22) = [ 0; 6; 0]; % Left Arm
   position(:, 23) = [ 1.06; 6; 0];
   position(:, 24) = [ 1.5; 6; 0];
   position(:, 25) = [ 1.82; 6; 0];
   position(:, 26) = [ 2.22; 6; 0];
   position(:, 27) = [ 2.71; 6; 0];
   position(:, 28) = [ 3.34; 6; 0];
   position(:, 29) = [ 3.84; 6; 0];
   position(:, 30) = [ 4.23; 6; 0];
   position(:, 31) = [ 4.55; 6; 0];
   position(:, 32) = [ 5; 6; 0];
   position(:, 33) = [ 6.05; 6; 0]; % Right Arm
   position(:, 34) = [ .8; 6.23; 0];
   position(:, 35) = [ 5.25; 6.23; 0];
   position(:, 36) = [ 1.24; 6.355; 0];
   position(:, 37) = [ 4.82; 6.355; 0];
   position(:, 38) = [ 1.5; 6.43; 0];
   position(:, 39) = [ 2; 6.43; 0];
   position(:, 40) = [ 2.48; 6.43; 0];
   position(:, 41) = [ 3.03; 6.43; 0];
   position(:, 42) = [ 3.58; 6.43; 0];
   position(:, 43) = [ 4.05; 6.43; 0];
   position(:, 44) = [ 4.55; 6.43; 0];
   position(:, 45) = [ 1.5; 7.43; 0];
   position(:, 46) = [ 4.55; 7.43; 0];
 
   % Scale to 60m
   positionM = max(position,[],2);
   xmax = positionM(1);
   ymax = positionM(2);
   position(1,:) = position(1,:)/xmax*60;
   position(2,:) = position(2,:)/ymax*60;
   % No need to scale the z-axis since all values are Zero
 
   % Convert from m to mm
   position = position*1000;
 
   % Change position array to work in this function
   nodes = position';
 
   % Build the conn Array
   node_connect(1, 1) = 1;   % element 1
   node_connect(2, 1) = 3;
 
   node_connect(1, 2) = 1;   % element 2
   node_connect(2, 2) = 4;
 
   node_connect(1, 3) = 3;   % element 5
   node_connect(2, 3) = 4;
 
   node_connect(1, 4) = 4;   % element 3
   node_connect(2, 4) = 2;
 
   node_connect(1, 5) = 4;   % element 6
   node_connect(2, 5) = 5;
 
   node_connect(1, 6) = 2;   % element 4
   node_connect(2, 6) = 5;
 
   node_connect(1, 7) = 3;   % element 8
   node_connect(2, 7) = 7;
 
   node_connect(1, 8) = 5;   % element 9
   node_connect(2, 8) = 7;
 
   node_connect(1, 9) = 3;   % element 7
   node_connect(2, 9) = 6;
 
   node_connect(1, 10) = 5;   % element 10
   node_connect(2, 10) = 8;
 
   node_connect(1, 11) = 6;   % element 11
   node_connect(2, 11) = 7;
 
   node_connect(1, 12) = 7;   % element 12
   node_connect(2, 12) = 8;
 
   node_connect(1, 13) = 6;   % element 13
   node_connect(2, 13) = 9;
 
   node_connect(1, 14) = 7;   % element 14
   node_connect(2, 14) = 9;
 
   node_connect(1, 15) = 7;   % element 15
   node_connect(2, 15) = 10;
 
   node_connect(1, 16) = 8;   % element 16
   node_connect(2, 16) = 10;
 
   node_connect(1, 17) = 9;   % element 17
   node_connect(2, 17) = 10;
 
   node_connect(1, 18) = 9;   % element 18
   node_connect(2, 18) = 11;
 
   node_connect(1, 19) = 9;   % element 19
   node_connect(2, 19) = 12;
 
   node_connect(1, 20) = 10;   % element 20
   node_connect(2, 20) = 12;
 
   node_connect(1, 21) = 10;   % element 21
   node_connect(2, 21) = 13;
 
   node_connect(1, 22) = 11;   % element 22
   node_connect(2, 22) = 12;
 
   node_connect(1, 23) = 12;   % element 23
   node_connect(2, 23) = 13;
 
   node_connect(1, 24) = 11;   % element 24
   node_connect(2, 24) = 14;
 
   node_connect(1, 25) = 11;   % element 25
   node_connect(2, 25) = 15;
 
   node_connect(1, 26) = 12;   % element 26
   node_connect(2, 26) = 15;
 
   node_connect(1, 27) = 12;   % element 27
   node_connect(2, 27) = 16;
 
   node_connect(1, 28) = 13;   % element 28
   node_connect(2, 28) = 16;
 
   node_connect(1, 29) = 13;   % element 29
   node_connect(2, 29) = 17;
 
   node_connect(1, 30) = 14;   % element 30
   node_connect(2, 30) = 15;
 
   node_connect(1, 31) = 15;   % element 31
   node_connect(2, 31) = 16;
 
   node_connect(1, 32) = 16;   % element 32
   node_connect(2, 32) = 17;
 
   node_connect(1, 33) = 14;   % element 33
   node_connect(2, 33) = 20;
 
   node_connect(1, 34) = 14;   % element 34
   node_connect(2, 34) = 18;
 
   node_connect(1, 35) = 15;   % element 35
   node_connect(2, 35) = 18;
 
   node_connect(1, 36) = 16;   % element 36
   node_connect(2, 36) = 19;
 
   node_connect(1, 37) = 17;   % element 37
   node_connect(2, 37) = 19;
 
   node_connect(1, 38) = 17;   % element 38
   node_connect(2, 38) = 21;
 
   node_connect(1, 39) = 18;   % element 39
   node_connect(2, 39) = 20;
 
   node_connect(1, 40) = 19;   % element 40
   node_connect(2, 40) = 21;
 
   node_connect(1, 41) = 20;   % element 41
   node_connect(2, 41) = 24;
 
   node_connect(1, 42) = 20;   % element 42
   node_connect(2, 42) = 26;
 
   node_connect(1, 43) = 21;   % element 43
   node_connect(2, 43) = 29;
 
   node_connect(1, 44) = 21;   % element 44
   node_connect(2, 44) = 31;
 
   node_connect(1, 45) = 22;   % element 45
   node_connect(2, 45) = 23;
 
   node_connect(1, 46) = 23;   % element 46
   node_connect(2, 46) = 24;
 
   node_connect(1, 47) = 24;   % element 47
   node_connect(2, 47) = 25;
 
   node_connect(1, 48) = 25;   % element 48
   node_connect(2, 48) = 26;
 
   node_connect(1, 49) = 26;   % element 49
   node_connect(2, 49) = 27;
 
   node_connect(1, 50) = 27;   % element 50
   node_connect(2, 50) = 28;
 
   node_connect(1, 51) = 28;   % element 51
   node_connect(2, 51) = 29;
 
   node_connect(1, 52) = 29;   % element 52
   node_connect(2, 52) = 30;
 
   node_connect(1, 53) = 30;   % element 53
   node_connect(2, 53) = 31;
 
   node_connect(1, 54) = 31;   % element 54
   node_connect(2, 54) = 32;
 
   node_connect(1, 55) = 32;   % element 55
   node_connect(2, 55) = 33;
 
   node_connect(1, 56) = 22;   % element 56
   node_connect(2, 56) = 34;
 
   node_connect(1, 57) = 23;   % element 57
   node_connect(2, 57) = 34;
 
   node_connect(1, 58) = 23;   % element 58
   node_connect(2, 58) = 36;
 
   node_connect(1, 59) = 24;   % element 59
   node_connect(2, 59) = 36;
 
   node_connect(1, 60) = 24;   % element 60
   node_connect(2, 60) = 38;
 
   node_connect(1, 61) = 25;   % element 61
   node_connect(2, 61) = 38;
 
   node_connect(1, 62) = 25;   % element 62
   node_connect(2, 62) = 39;
 
   node_connect(1, 63) = 26;   % element 63
   node_connect(2, 63) = 39;
 
   node_connect(1, 64) = 26;   % element 64
   node_connect(2, 64) = 40;
 
   node_connect(1, 65) = 27;   % element 65
   node_connect(2, 65) = 40;
 
   node_connect(1, 66) = 27;   % element 66
   node_connect(2, 66) = 41;
 
   node_connect(1, 67) = 28;   % element 67
   node_connect(2, 67) = 41;
 
   node_connect(1, 68) = 28;   % element 68
   node_connect(2, 68) = 42;
 
   node_connect(1, 69) = 29;   % element 69
   node_connect(2, 69) = 42;
 
   node_connect(1, 70) = 29;   % element 70
   node_connect(2, 70) = 43;
 
   node_connect(1, 71) = 30;   % element 71
   node_connect(2, 71) = 43;
 
   node_connect(1, 72) = 30;   % element 72
   node_connect(2, 72) = 44;
 
   node_connect(1, 73) = 31;   % element 73
   node_connect(2, 73) = 44;
 
   node_connect(1, 74) = 31;   % element 74
   node_connect(2, 74) = 37;
 
   node_connect(1, 75) = 32;   % element 75
   node_connect(2, 75) = 37;
 
   node_connect(1, 76) = 32;   % element 76
   node_connect(2, 76) = 35;
 
   node_connect(1, 77) = 33;   % element 77
   node_connect(2, 77) = 35;
 
   node_connect(1, 78) = 34;   % element 78
   node_connect(2, 78) = 36;
 
   node_connect(1, 79) = 35;   % element 79
   node_connect(2, 79) = 37;
 
   node_connect(1, 80) = 36;   % element 80
   node_connect(2, 80) = 38;
 
   node_connect(1, 81) = 37;   % element 81
   node_connect(2, 81) = 44;
 
   node_connect(1, 82) = 38;   % element 82
   node_connect(2, 82) = 39;
 
   node_connect(1, 83) = 39;   % element 83
   node_connect(2, 83) = 40;
 
   node_connect(1, 84) = 40;   % element 84
   node_connect(2, 84) = 41;
 
   node_connect(1, 85) = 41;   % element 85
   node_connect(2, 85) = 42;
 
   node_connect(1, 86) = 42;   % element 86
   node_connect(2, 86) = 43;
 
   node_connect(1, 87) = 43;   % element 87
   node_connect(2, 87) = 44;
 
   node_connect(1, 88) = 38;   % element 88
   node_connect(2, 88) = 45;
 
   node_connect(1, 89) = 39;   % element 89
   node_connect(2, 89) = 45;
 
   node_connect(1, 90) = 43;   % element 90
   node_connect(2, 90) = 46;
 
   node_connect(1, 91) = 44;   % element 91
   node_connect(2, 91) = 46;
 
   % Adjust the node_connect array to work on this function
   conn = node_connect';
 
   % Build the lmm array
 
   % Create dof for each node
   dofs=[];
   j = 1;
   for i=1:size(nodes,1)
       dofs = [dofs;j j+1 j+2];
       j = j + 3;
   end
 
   % Add the dofs to the lmm array in right order
   lmm=[];
   for i=1:size(conn,1)
       lmm = [lmm;dofs(conn(i,1),:) dofs(conn(i,2),:)];
   end
 
dof=3*length(nodes); % Total number of DOFs
debc = [1:6]; % Boundary Conditions on the Legs
ebcVals = zeros(length(debc),1);
 
%load vector
R = zeros(dof,1); 
R(dofs(33,2)) = -P; % Applies on Right Arm
 
% Assemble global stiffness matrix
K=zeros(dof);
for i=1:size(conn,1)
    lm=lmm(i,:);
    con=conn(i,:);
    [ke, rq] = PlaneFrameElement(e, I, a, 0, 0, nodes(con,:));
    K(lm, lm) = K(lm, lm) + ke;
    R(lm) = R(lm) + rq;
end

K
R
 
% Nodal solution and reactions
[d2, reactions] = NodalSoln(K, R, debc, ebcVals)
fa=[];
bma=[];
Va=[];
for i=1:size(conn,1)
    lm=lmm(i,:);
    con=conn(i,:);
    [f, bm, V]=PlaneFrameResults(e, I, a, 0, 0, nodes(con,:), d2(lm));
    fa = [fa; f]; bma = [bma; bm]; Va = [Va; V];
end
fa
bma
Va

Results[edit]

The following are the results to eletricframe.m

K =

  Columns 1 through 6

       4258.1       4680.9       -168.2            0            0            0
       4680.9         8014       98.246            0            0            0
       -168.2       98.246  1.6363e+006            0            0            0
            0            0            0       4178.7      -4639.8      -172.35
            0            0            0      -4639.8       8211.5      -97.383
            0            0            0      -172.35      -97.383   1.652e+006
        -1056        -2670        141.7            0            0            0
        -2670      -6751.1       -56.04            0            0            0
       -141.7        56.04  5.2047e+005            0            0            0
      -3202.1      -2010.9       26.505      -3210.9       2056.8       27.652
      -2010.9      -1262.8      -42.206       2056.8      -1317.5       43.169
      -26.505       42.206  2.9766e+005      -27.652      -43.169  3.0189e+005
            0            0            0      -967.81         2583        144.7
            0            0            0         2583        -6894       54.214
            0            0            0       -144.7      -54.214  5.2412e+005
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d2 =

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            0
            0
            0
     -0.24614
      0.21895
   1.417e-005
     -0.15703
   -0.0027938
 -2.4686e-005
       -0.211
     -0.34319
  1.6905e-005
     -0.21575
      0.38648
 -3.2663e-005
     -0.21762
     -0.14083
 -6.0656e-005
     -0.21753
     -0.62551
 -2.6214e-005
      0.30459
      0.35724
  -0.00011182
      0.33289
      -0.6888
  -0.00011361
      0.84792
      0.74728
  -0.00016371
      0.87753
      -0.2446
  -0.00012624
      0.91042
      -1.1024
   -0.0001487
       1.5418
       1.2099
  -0.00024631
       1.5409
      0.23912
  -0.00017152
         1.48
     -0.75545
  -0.00014212
       1.4796
      -1.4891
  -0.00017223
        2.174
       0.7244
  -0.00027969
       1.9197
      -1.1672
  -0.00018714
       4.5897
       2.8772
  -0.00034985
       3.4349
        -2.63
  -0.00032074
       6.0713
        6.519
  -0.00020147
       6.0713
        4.401
  -0.00020181
       6.0713
       3.5219
  -0.00019771
       6.0736
       2.8632
  -0.00020731
        6.086
       2.0637
  -0.00018169
        6.106
       1.2662
  -0.00017283
       6.0416
      0.11615
  -0.00022184
       5.9189
      -1.1413
  -0.00031855
       5.7851
      -2.4771
  -0.00038829
       5.6429
      -3.7847
  -0.00047491
       5.4055
      -6.3545
  -0.00069162
       4.8495
      -18.248
   -0.0014319
       6.4455
       4.9205
  -0.00020122
       6.7538
      -8.1535
  -0.00081383
       6.6489
       4.0414
  -0.00020254
       7.1971
      -5.2394
  -0.00056907
       6.7723
       3.5161
   -0.0002042
       6.7647
       2.4997
  -0.00019862
       6.7484
       1.6335
  -0.00017478
       6.7998
      0.71144
  -0.00018876
       6.9413
     -0.44373
  -0.00025705
       7.1234
      -1.8244
  -0.00036432
       7.3565
      -3.8516
  -0.00046347
       8.4199
       3.5161
  -0.00020588
       10.425
      -3.8516
  -0.00038093


reactions =

       183.78
      -501.65
      -51.164
      -183.78
       1501.7
      -52.192


fa =

        14876            0      -1921.6
        16760       4764.5      -1921.6
        18645       9528.9      -1921.6
        14876            0      -701.14
        22463       4764.5      -701.14
        30050       9528.9      -701.14
        18645       9528.9       625.03
        24347       9528.9       625.03
        30050       9528.9       625.03
        30050       9528.9       711.11
        37488       4764.5       711.11
        44926            0       711.11
        30050       9528.9       -381.9
        35702       9528.9       -381.9
        41355       9528.9       -381.9
        44926            0      -1658.9
        43140       4764.5      -1658.9
        41355       9528.9      -1658.9
        18645       9528.9        163.2
        24347        13571        163.2
        30050        17612        163.2
        41355       9528.9      -38.088
        35702        13571      -38.088
        30050        17612      -38.088
        18645       9528.9       279.92
        20231        13571       279.92
        21818        17612       279.92
        41355       9528.9      -60.131
        39769        13571      -60.131
        38182        17612      -60.131
        21818        17612      -18.156
        25934        17612      -18.156
        30050        17612      -18.156
        30050        17612      0.88143
        34116        17612      0.88143
        38182        17612      0.88143
        21818        17612       4777.5
        23455        21650       4777.5
        25091        25688       4777.5
        30050        17612       4408.6
        27570        21650       4408.6
        25091        25688       4408.6
        30050        17612       4647.5
        32529        21650       4647.5
        35008        25688       4647.5
        38182        17612         5075
        36595        21650         5075
        35008        25688         5075
        25091        25688       228.26
        30050        25688       228.26
        35008        25688       228.26
        25091        25688       9755.2
        24149        27707       9755.2
        23207        29725       9755.2
        25091        25688       7167.7
        27570        27707       7167.7
        30050        29725       7167.7
        35008        25688       6813.7
        32529        27707       6813.7
        30050        29725       6813.7
        35008        25688        10466
        35901        27707        10466
        36793        29725        10466
        23207        29725       346.15
        26628        29725       346.15
        30050        29725       346.15
        30050        29725       390.13
        33421        29725       390.13
        36793        29725       390.13
        23207        29725        12573
        22314        31744        12573
        21421        33763        12573
        23207        29725        11313
        24595        31744        11313
        25983        33763        11313
        30050        29725       9261.1
        28017        31744       9261.1
        25983        33763       9261.1
        30050        29725       8411.3
        32083        31744       8411.3
        34116        33763       8411.3
        36793        29725       9405.4
        35455        31744       9405.4
        34116        33763       9405.4
        36793        29725        10314
        37686        31744        10314
        38579        33763        10314
        21421        33763      -15.427
        23702        33763      -15.427
        25983        33763      -15.427
        25983        33763      -598.82
        30050        33763      -598.82
        34116        33763      -598.82
        34116        33763      -7.3223
        36347        33763      -7.3223
        38579        33763      -7.3223
        21421        33763        27825
        19636        37764        27825
        17851        41766        27825
        21421        33763        15557
        22413        35051        15557
        23405        36339        15557
        25983        33763        13897
        24694        35051        13897
        23405        36339        13897
        34116        33763       9651.2
        35405        35051       9651.2
        36694        36339       9651.2
        38579        33763        11032
        37636        35051        11032
        36694        36339        11032
        38579        33763        17850
        40364        37764        17850
        42149        41766        17850
        23405        36339        24888
        20628        39052        24888
        17851        41766        24888
        36694        36339        15754
        39421        39052        15754
        42149        41766        15754
        17851        41766        16196
        16364        45109        16196
        14876        48452        16196
        17851        41766        15196
        19934        45109        15196
        22017        48452        15196
        42149        41766        25393
        40116        45109        25393
        38083        48452        25393
        42149        41766        24136
        43636        45109        24136
        45124        48452        24136
            0        48452 -6.6526e-005
       5256.2        48452 -6.6526e-005
        10512        48452 -6.6526e-005
        10512        48452      0.00165
        12694        48452      0.00165
        14876        48452      0.00165
        14876        48452       59.344
        16463        48452       59.344
        18050        48452       59.344
        18050        48452       249.91
        20033        48452       249.91
        22017        48452       249.91
        22017        48452       328.99
        24446        48452       328.99
        26876        48452       328.99
        26876        48452      -825.09
        30000        48452      -825.09
        33124        48452      -825.09
        33124        48452      -1979.2
        35603        48452      -1979.2
        38083        48452      -1979.2
        38083        48452      -2768.3
        40017        48452      -2768.3
        41950        48452      -2768.3
        41950        48452      -3584.6
        43537        48452      -3584.6
        45124        48452      -3584.6
        45124        48452        -4255
        47355        48452        -4255
        49587        48452        -4255
        49587        48452      -4271.3
        54793        48452      -4271.3
        60000        48452      -4271.3
            0        48452       3673.9
       3966.9        49381       3673.9
       7933.9        50310       3673.9
        10512        48452       9420.5
       9223.1        49381       9420.5
       7933.9        50310       9420.5
        10512        48452        13682
        11405        49886        13682
        12298        51319        13682
        14876        48452        11984
        13587        49886        11984
        12298        51319        11984
        14876        48452        16149
        14876        50188        16149
        14876        51925        16149
        18050        48452        11881
        16463        50188        11881
        14876        51925        11881
        18050        48452        14159
        18942        50188        14159
        19835        51925        14159
        22017        48452        13239
        20926        50188        13239
        19835        51925        13239
        22017        48452        12251
        23306        50188        12251
        24595        51925        12251
        26876        48452        12369
        25736        50188        12369
        24595        51925        12369
        26876        48452        11798
        28463        50188        11798
        30050        51925        11798
        33124        48452        13078
        31587        50188        13078
        30050        51925        13078
        33124        48452        17097
        34314        50188        17097
        35504        51925        17097
        38083        48452        18911
        36793        50188        18911
        35504        51925        18911
        38083        48452        23797
        39124        50188        23797
        40165        51925        23797
        41950        48452        27421
        41058        50188        27421
        40165        51925        27421
        41950        48452        26724
        43537        50188        26724
        45124        51925        26724
        45124        48452        39480
        45124        50188        39480
        45124        51925        39480
        45124        48452        31697
        46463        49886        31697
        47802        51319        31697
        49587        48452        42442
        48694        49886        42442
        47802        51319        42442
        49587        48452        34819
        50826        49381        34819
        52066        50310        34819
        60000        48452        18696
        56033        49381        18696
        52066        50310        18696
       7933.9        50310       3632.6
        10116        50814       3632.6
        12298        51319       3632.6
        52066        50310       8093.3
        49934        50814       8093.3
        47802        51319       8093.3
        12298        51319       3726.7
        13587        51622       3726.7
        14876        51925       3726.7
        47802        51319       4643.8
        46463        51622       4643.8
        45124        51925       4643.8
        14876        51925      -121.95
        17355        51925      -121.95
        19835        51925      -121.95
        19835        51925       -274.4
        22215        51925       -274.4
        24595        51925       -274.4
        24595        51925       753.77
        27322        51925       753.77
        30050        51925       753.77
        30050        51925       2075.7
        32777        51925       2075.7
        35504        51925       2075.7
        35504        51925       3124.9
        37835        51925       3124.9
        40165        51925       3124.9
        40165        51925       3761.5
        42645        51925       3761.5
        45124        51925       3761.5
        14876        51925        16323
        14876        55962        16323
        14876        60000        16323
        19835        51925        13973
        17355        55962        13973
        14876        60000        13973
        40165        51925        27871
        42645        55962        27871
        45124        60000        27871
        45124        51925        30396
        45124        55962        30396
        45124        60000        30396


bma =

        14876            0       25.987
        16760       4764.5       3.6877
        18645       9528.9      -18.612
        14876            0       7.2088
        22463       4764.5       -3.674
        30050       9528.9      -14.557
        18645       9528.9      -28.985
        24347       9528.9      -9.0853
        30050       9528.9       10.814
        30050       9528.9       15.048
        37488       4764.5       3.7263
        44926            0      -7.5958
        30050       9528.9      -27.294
        35702       9528.9       9.8101
        41355       9528.9       46.914
        44926            0       -61.89
        43140       4764.5       4.4302
        41355       9528.9       70.751
        18645       9528.9      -17.129
        24347        13571      -14.274
        30050        17612      -11.419
        41355       9528.9       27.064
        35702        13571      -14.882
        30050        17612      -56.827
        18645       9528.9       38.198
        20231        13571      -14.381
        21818        17612      -66.961
        41355       9528.9      -64.564
        39769        13571      -13.241
        38182        17612       38.082
        21818        17612      -42.892
        25934        17612      -9.0686
        30050        17612       24.755
        30050        17612      -20.512
        34116        17612       11.294
        38182        17612         43.1
        21818        17612       102.27
        23455        21650      -24.226
        25091        25688      -150.72
        30050        17612       219.95
        27570        21650      -14.398
        25091        25688      -248.75
        30050        17612       34.583
        32529        21650      -14.902
        35008        25688      -64.387
        38182        17612       88.612
        36595        21650      -26.861
        35008        25688      -142.33
        25091        25688       11.202
        30050        25688     -0.48104
        35008        25688      -12.164
        25091        25688       777.99
        24149        27707      -31.054
        23207        29725       -840.1
        25091        25688       56.326
        27570        27707      -6.0118
        30050        29725      -68.349
        35008        25688        468.6
        32529        27707      -5.2657
        30050        29725      -479.13
        35008        25688       114.58
        35901        27707      -21.194
        36793        29725      -156.97
        23207        29725       14.661
        26628        29725       14.603
        30050        29725       14.544
        30050        29725        15.48
        33421        29725       -8.881
        36793        29725      -33.242
        23207        29725       1072.9
        22314        31744      -49.894
        21421        33763      -1172.7
        23207        29725       204.44
        24595        31744      -4.2486
        25983        33763      -212.93
        30050        29725       630.32
        28017        31744      -21.071
        25983        33763      -672.46
        30050        29725       118.34
        32083        31744      -7.3924
        34116        33763      -133.13
        36793        29725       720.33
        35455        31744       3.6185
        34116        33763      -713.09
        36793        29725       249.93
        37686        31744      -14.213
        38579        33763      -278.36
        21421        33763       30.105
        23702        33763        43.72
        25983        33763       57.335
        25983        33763       77.557
        30050        33763       9.6387
        34116        33763       -58.28
        34116        33763      -43.823
        36347        33763      -17.988
        38579        33763       7.8472
        21421        33763       860.16
        19636        37764      -31.508
        17851        41766      -923.17
        21421        33763       532.04
        22413        35051      -27.378
        23405        36339       -586.8
        25983        33763       1495.7
        24694        35051      -79.142
        23405        36339        -1654
        34116        33763        193.9
        35405        35051      -32.936
        36694        36339      -259.77
        38579        33763       1393.9
        37636        35051      -12.461
        36694        36339      -1418.8
        38579        33763       167.12
        40364        37764      -45.194
        42149        41766      -257.51
        23405        36339       1195.8
        20628        39052      -24.095
        17851        41766        -1244
        36694        36339       86.404
        39421        39052      -46.303
        42149        41766      -179.01
        17851        41766       846.56
        16364        45109       55.437
        14876        48452      -735.69
        17851        41766       386.98
        19934        45109       56.924
        22017        48452      -273.13
        42149        41766       1043.2
        40116        45109      0.74729
        38083        48452      -1041.7
        42149        41766       468.62
        43636        45109      -56.174
        45124        48452      -580.97
            0        48452      0.17061
       5256.2        48452    -0.085796
        10512        48452     -0.34221
        10512        48452        -3.78
        12694        48452       2.5092
        14876        48452       8.7983
        14876        48452       -33.49
        16463        48452       -8.073
        18050        48452       17.344
        18050        48452      -11.123
        20033        48452       17.226
        22017        48452       45.575
        22017        48452       48.122
        24446        48452       4.8617
        26876        48452      -38.399
        26876        48452        13.06
        30000        48452       -20.92
        33124        48452        -54.9
        33124        48452       1.5903
        35603        48452      -52.006
        38083        48452       -105.6
        38083        48452      -14.753
        40017        48452      -48.087
        41950        48452       -81.42
        41950        48452       25.811
        43537        48452      -72.779
        45124        48452      -171.37
        45124        48452      -102.82
        47355        48452      -129.49
        49587        48452      -156.17
        49587        48452      -313.11
        54793        48452      -189.57
        60000        48452      -66.037
            0        48452       10.244
       3966.9        49381     0.084684
       7933.9        50310      -10.074
        10512        48452       1838.2
       9223.1        49381      0.50096
       7933.9        50310      -1837.2
        10512        48452       452.72
        11405        49886     -0.57028
        12298        51319      -453.86
        14876        48452       1386.2
        13587        49886      -3.3391
        12298        51319      -1392.9
        14876        48452       913.27
        14876        50188      -4.9857
        14876        51925      -923.24
        18050        48452       1173.7
        16463        50188        1.766
        14876        51925      -1170.1
        18050        48452       456.17
        18942        50188       5.9411
        19835        51925      -444.28
        22017        48452       1145.6
        20926        50188      -11.007
        19835        51925      -1167.6
        22017        48452       295.65
        23306        50188       4.2567
        24595        51925      -287.14
        26876        48452       1008.6
        25736        50188      -1.2552
        24595        51925      -1011.1
        26876        48452        204.8
        28463        50188      -9.0334
        30050        51925      -222.87
        33124        48452       1170.1
        31587        50188        19.02
        30050        51925      -1132.1
        33124        48452        382.3
        34314        50188      -22.304
        35504        51925      -426.91
        38083        48452       1699.2
        36793        50188       37.914
        35504        51925      -1623.4
        38083        48452       652.44
        39124        50188      -30.142
        40165        51925      -712.72
        41950        48452       2243.5
        41058        50188       16.376
        40165        51925      -2210.8
        41950        48452        412.1
        43537        50188      -42.617
        45124        51925      -497.33
        45124        48452         2082
        45124        50188       8.7813
        45124        51925      -2064.4
        45124        48452        552.6
        46463        49886      -64.014
        47802        51319      -680.62
        49587        48452       4647.7
        48694        49886       96.765
        47802        51319      -4454.1
        49587        48452       783.27
        50826        49381       -105.2
        52066        50310      -993.66
        60000        48452       4839.7
        56033        49381       202.27
        52066        50310      -4435.1
       7933.9        50310       19.161
        10116        50814     -0.78544
        12298        51319      -20.732
        52066        50310       5101.3
        49934        50814       148.94
        47802        51319      -4803.4
        12298        51319       28.789
        13587        51622      -1.6753
        14876        51925      -32.139
        47802        51319       6057.5
        46463        51622       102.58
        45124        51925      -5852.4
        14876        51925       -8.493
        17355        51925       3.0026
        19835        51925       14.498
        19835        51925       29.296
        22215        51925        13.35
        24595        51925      -2.5968
        24595        51925       30.496
        27322        51925      -6.8345
        30050        51925      -44.165
        30050        51925     -0.74301
        32777        51925      -33.386
        35504        51925       -66.03
        35504        51925      -11.635
        37835        51925      -61.365
        40165        51925      -111.09
        40165        51925      -36.974
        42645        51925      -53.323
        45124        51925      -69.673
        14876        51925        405.7
        14876        55962      -0.5557
        14876        60000      -406.81
        19835        51925       520.53
        17355        55962      -2.0447
        14876        60000      -524.62
        40165        51925       263.27
        42645        55962      -4.6761
        45124        60000      -272.62
        45124        51925       863.78
        45124        55962       27.256
        45124        60000      -809.27


Va =

        14876            0   -0.0043524
        16760       4764.5   -0.0043524
        18645       9528.9   -0.0043524
        14876            0   -0.0012148
        22463       4764.5   -0.0012148
        30050       9528.9   -0.0012148
        18645       9528.9    0.0034897
        24347       9528.9    0.0034897
        30050       9528.9    0.0034897
        30050       9528.9   -0.0012818
        37488       4764.5   -0.0012818
        44926            0   -0.0012818
        30050       9528.9    0.0065637
        35702       9528.9    0.0065637
        41355       9528.9    0.0065637
        44926            0     0.013035
        43140       4764.5     0.013035
        41355       9528.9     0.013035
        18645       9528.9   0.00040842
        24347        13571   0.00040842
        30050        17612   0.00040842
        41355       9528.9    -0.006036
        35702        13571    -0.006036
        30050        17612    -0.006036
        18645       9528.9    -0.012109
        20231        13571    -0.012109
        21818        17612    -0.012109
        41355       9528.9      0.01182
        39769        13571      0.01182
        38182        17612      0.01182
        21818        17612    0.0082181
        25934        17612    0.0082181
        30050        17612    0.0082181
        30050        17612    0.0078221
        34116        17612    0.0078221
        38182        17612    0.0078221
        21818        17612    -0.029035
        23455        21650    -0.029035
        25091        25688    -0.029035
        30050        17612     -0.04946
        27570        21650     -0.04946
        25091        25688     -0.04946
        30050        17612    -0.010444
        32529        21650    -0.010444
        35008        25688    -0.010444
        38182        17612    -0.026617
        36595        21650    -0.026617
        35008        25688    -0.026617
        25091        25688   -0.0023561
        30050        25688   -0.0023561
        35008        25688   -0.0023561
        25091        25688     -0.36315
        24149        27707     -0.36315
        23207        29725     -0.36315
        25091        25688    -0.019497
        27570        27707    -0.019497
        30050        29725    -0.019497
        35008        25688     -0.14821
        32529        27707     -0.14821
        30050        29725     -0.14821
        35008        25688    -0.061511
        35901        27707    -0.061511
        36793        29725    -0.061511
        23207        29725 -1.7051e-005
        26628        29725 -1.7051e-005
        30050        29725 -1.7051e-005
        30050        29725   -0.0072246
        33421        29725   -0.0072246
        36793        29725   -0.0072246
        23207        29725     -0.50866
        22314        31744     -0.50866
        21421        33763     -0.50866
        23207        29725    -0.085171
        24595        31744    -0.085171
        25983        33763    -0.085171
        30050        29725     -0.22735
        28017        31744     -0.22735
        25983        33763     -0.22735
        30050        29725    -0.043885
        32083        31744    -0.043885
        34116        33763    -0.043885
        36793        29725     -0.29586
        35455        31744     -0.29586
        34116        33763     -0.29586
        36793        29725     -0.11966
        37686        31744     -0.11966
        38579        33763     -0.11966
        21421        33763    0.0059689
        23702        33763    0.0059689
        25983        33763    0.0059689
        25983        33763    -0.016704
        30050        33763    -0.016704
        34116        33763    -0.016704
        34116        33763     0.011578
        36347        33763     0.011578
        38579        33763     0.011578
        21421        33763     -0.20351
        19636        37764     -0.20351
        17851        41766     -0.20351
        21421        33763     -0.34413
        22413        35051     -0.34413
        23405        36339     -0.34413
        25983        33763     -0.86414
        24694        35051     -0.86414
        23405        36339     -0.86414
        34116        33763     -0.12447
        35405        35051     -0.12447
        36694        36339     -0.12447
        38579        33763     -0.88128
        37636        35051     -0.88128
        36694        36339     -0.88128
        38579        33763    -0.048457
        40364        37764    -0.048457
        42149        41766    -0.048457
        23405        36339     -0.31422
        20628        39052     -0.31422
        17851        41766     -0.31422
        36694        36339    -0.034495
        39421        39052    -0.034495
        42149        41766    -0.034495
        17851        41766      -0.2162
        16364        45109      -0.2162
        14876        48452      -0.2162
        17851        41766    -0.083795
        19934        45109    -0.083795
        22017        48452    -0.083795
        42149        41766     -0.26642
        40116        45109     -0.26642
        38083        48452     -0.26642
        42149        41766     -0.14342
        43636        45109     -0.14342
        45124        48452     -0.14342
            0        48452 -4.8782e-005
       5256.2        48452 -4.8782e-005
        10512        48452 -4.8782e-005
        10512        48452    0.0028825
        12694        48452    0.0028825
        14876        48452    0.0028825
        14876        48452     0.016018
        16463        48452     0.016018
        18050        48452     0.016018
        18050        48452     0.014293
        20033        48452     0.014293
        22017        48452     0.014293
        22017        48452    -0.017805
        24446        48452    -0.017805
        26876        48452    -0.017805
        26876        48452    -0.010877
        30000        48452    -0.010877
        33124        48452    -0.010877
        33124        48452    -0.021617
        35603        48452    -0.021617
        38083        48452    -0.021617
        38083        48452    -0.017236
        40017        48452    -0.017236
        41950        48452    -0.017236
        41950        48452    -0.062132
        43537        48452    -0.062132
        45124        48452    -0.062132
        45124        48452    -0.011954
        47355        48452    -0.011954
        49587        48452    -0.011954
        49587        48452     0.023727
        54793        48452     0.023727
        60000        48452     0.023727
            0        48452   -0.0024935
       3966.9        49381   -0.0024935
       7933.9        50310   -0.0024935
        10512        48452      -1.1566
       9223.1        49381      -1.1566
       7933.9        50310      -1.1566
        10512        48452     -0.26845
        11405        49886     -0.26845
        12298        51319     -0.26845
        14876        48452     -0.72075
        13587        49886     -0.72075
        12298        51319     -0.72075
        14876        48452     -0.52889
        14876        50188     -0.52889
        14876        51925     -0.52889
        18050        48452     -0.49823
        16463        50188     -0.49823
        14876        51925     -0.49823
        18050        48452     -0.23063
        18942        50188     -0.23063
        19835        51925     -0.23063
        22017        48452     -0.56408
        20926        50188     -0.56408
        19835        51925     -0.56408
        22017        48452     -0.13475
        23306        50188     -0.13475
        24595        51925     -0.13475
        26876        48452     -0.48615
        25736        50188     -0.48615
        24595        51925     -0.48615
        26876        48452    -0.090914
        28463        50188    -0.090914
        30050        51925    -0.090914
        33124        48452     -0.49639
        31587        50188     -0.49639
        30050        51925     -0.49639
        33124        48452     -0.19222
        34314        50188     -0.19222
        35504        51925     -0.19222
        38083        48452     -0.76823
        36793        50188     -0.76823
        35504        51925     -0.76823
        38083        48452     -0.33715
        39124        50188     -0.33715
        40165        51925     -0.33715
        41950        48452      -1.1409
        41058        50188      -1.1409
        40165        51925      -1.1409
        41950        48452     -0.19333
        43537        50188     -0.19333
        45124        51925     -0.19333
        45124        48452      -1.1941
        45124        50188      -1.1941
        45124        51925      -1.1941
        45124        48452     -0.31437
        46463        49886     -0.31437
        47802        51319     -0.31437
        49587        48452      -2.6951
        48694        49886      -2.6951
        47802        51319      -2.6951
        49587        48452      -0.5736
        50826        49381      -0.5736
        52066        50310      -0.5736
        60000        48452      -1.1382
        56033        49381      -1.1382
        52066        50310      -1.1382
       7933.9        50310   -0.0089071
        10116        50814   -0.0089071
        12298        51319   -0.0089071
        52066        50310      -2.2602
        49934        50814      -2.2602
        47802        51319      -2.2602
        12298        51319    -0.023003
        13587        51622    -0.023003
        14876        51925    -0.023003
        47802        51319      -4.3383
        46463        51622      -4.3383
        45124        51925      -4.3383
        14876        51925    0.0046365
        17355        51925    0.0046365
        19835        51925    0.0046365
        19835        51925   -0.0066998
        22215        51925   -0.0066998
        24595        51925   -0.0066998
        24595        51925    -0.013688
        27322        51925    -0.013688
        30050        51925    -0.013688
        30050        51925    -0.011969
        32777        51925    -0.011969
        35504        51925    -0.011969
        35504        51925    -0.021338
        37835        51925    -0.021338
        40165        51925    -0.021338
        40165        51925   -0.0065944
        42645        51925   -0.0065944
        45124        51925   -0.0065944
        14876        51925     -0.10062
        14876        55962     -0.10062
        14876        60000     -0.10062
        19835        51925     -0.11029
        17355        55962     -0.11029
        14876        60000     -0.11029
        40165        51925    -0.056551
        42645        55962    -0.056551
        45124        60000    -0.056551
        45124        51925     -0.20718
        45124        55962     -0.20718
        45124        60000     -0.20718

Plot[edit]

The following is the plot of the Electric Pylon with its undeformed shape, deformed truss, and deformed frame. The deformation is magnified by 1000 for better viewing.

File:Electrictf.jpg

The deformed truss and frame are very similar. The following is a zoomed portion of the right side. The differences are made clear.

File:Electrictfzoom.jpg

The following is the MATLAB function used to plot

close all
clear all
electric % Must be run to get the displacement array (d)
electricframe
 
% model with 3-D beam elements
   dof = 2;          % x and y displacement only
 
% obtain the coordinates of all nodes
   n_node = 46;             % number of nodes
   n_elem = 91;             % number of elements
   total_dof = dof * n_node;  % total dof of system
 
   position(:, 1) = [ 1.5; 0; 0];
   position(:, 2) = [ 4.53; 0; 0];
   position(:, 3) = [ 1.88; 1.18; 0];
   position(:, 4) = [ 3.03; 1.18; 0];
   position(:, 5) = [ 4.17; 1.18; 0];
   position(:, 6) = [ 2.2; 2.181; 0];
   position(:, 7) = [ 3.03; 2.181; 0];
   position(:, 8) = [ 3.85; 2.181; 0];
   position(:, 9) = [ 2.53; 3.181; 0];
   position(:, 10) = [ 3.53; 3.181; 0];
   position(:, 11) = [ 2.34; 3.681; 0];
   position(:, 12) = [ 3.03; 3.681; 0];
   position(:, 13) = [ 3.71; 3.681; 0];
   position(:, 14) = [ 2.16; 4.181; 0];
   position(:, 15) = [ 2.62; 4.181; 0];
   position(:, 16) = [ 3.44; 4.181; 0];
   position(:, 17) = [ 3.89; 4.181; 0];
   position(:, 18) = [ 2.36; 4.5; 0];
   position(:, 19) = [ 3.7; 4.5; 0];
   position(:, 20) = [ 1.8; 5.172; 0];
   position(:, 21) = [ 4.25; 5.172; 0];
   position(:, 22) = [ 0; 6; 0];
   position(:, 23) = [ 1.06; 6; 0];
   position(:, 24) = [ 1.5; 6; 0];
   position(:, 25) = [ 1.82; 6; 0];
   position(:, 26) = [ 2.22; 6; 0];
   position(:, 27) = [ 2.71; 6; 0];
   position(:, 28) = [ 3.34; 6; 0];
   position(:, 29) = [ 3.84; 6; 0];
   position(:, 30) = [ 4.23; 6; 0];
   position(:, 31) = [ 4.55; 6; 0];
   position(:, 32) = [ 5; 6; 0];
   position(:, 33) = [ 6.05; 6; 0];
   position(:, 34) = [ .8; 6.23; 0];
   position(:, 35) = [ 5.25; 6.23; 0];
   position(:, 36) = [ 1.24; 6.355; 0];
   position(:, 37) = [ 4.82; 6.355; 0];
   position(:, 38) = [ 1.5; 6.43; 0];
   position(:, 39) = [ 2; 6.43; 0];
   position(:, 40) = [ 2.48; 6.43; 0];
   position(:, 41) = [ 3.03; 6.43; 0];
   position(:, 42) = [ 3.58; 6.43; 0];
   position(:, 43) = [ 4.05; 6.43; 0];
   position(:, 44) = [ 4.55; 6.43; 0];
   position(:, 45) = [ 1.5; 7.43; 0];
   position(:, 46) = [ 4.55; 7.43; 0];
 
   % Scale to 60m
   positionM = max(position,[],2);
   xmax = positionM(1);
   ymax = positionM(2);
   position(1,:) = position(1,:)/xmax*60;
   position(2,:) = position(2,:)/ymax*60;
   % No need to scale the z-axis since all values are Zero
 
   % Convert from m to mm
   position = position*1000;
 
   % The displacement of nodes (electric.m must be run beforehand to get
   % the d array)
   d = d * 1000; %Magnification Factor to see displacement
   position2=position;
   j=1;
   for i=1:size(position2,2)
       position2(1,i)=position2(1,i)+d(j);
       position2(2,i)=position2(2,i)+d(j+1);
       j = j + 2;
   end
   
   % The displacement of nodes for the frame
   d2 = d2 * 1000; %Magnification Factor to see displacement
   position3=position;
   j=1;
   for i=1:size(position3,2)
       position3(1,i)=position3(1,i)+d2(j);
       position3(2,i)=position3(2,i)+d2(j+1);
       j = j + 3;
   end
 
   % print the node coord
   for i = 1 : n_node;
      x(i) = position(1,i);
      y(i) = position(2,i);
      z(i) = position(3,i);
      x2(i) = position2(1,i);
      y2(i) = position2(2,i);
      z2(i) = position2(3,i);
      x3(i) = position3(1,i);
      y3(i) = position3(2,i);
      z3(i) = position3(3,i);
   end
 
   node_connect(1, 1) = 1;   % element 1
   node_connect(2, 1) = 3;
 
   node_connect(1, 2) = 1;   % element 2
   node_connect(2, 2) = 4;
 
   node_connect(1, 3) = 3;   % element 5
   node_connect(2, 3) = 4;
 
   node_connect(1, 4) = 4;   % element 3
   node_connect(2, 4) = 2;
 
   node_connect(1, 5) = 4;   % element 6
   node_connect(2, 5) = 5;
 
   node_connect(1, 6) = 2;   % element 4
   node_connect(2, 6) = 5;
 
   node_connect(1, 7) = 3;   % element 8
   node_connect(2, 7) = 7;
 
   node_connect(1, 8) = 5;   % element 9
   node_connect(2, 8) = 7;
 
   node_connect(1, 9) = 3;   % element 7
   node_connect(2, 9) = 6;
 
   node_connect(1, 10) = 5;   % element 10
   node_connect(2, 10) = 8;
 
   node_connect(1, 11) = 6;   % element 11
   node_connect(2, 11) = 7;
 
   node_connect(1, 12) = 7;   % element 12
   node_connect(2, 12) = 8;
 
   node_connect(1, 13) = 6;   % element 13
   node_connect(2, 13) = 9;
 
   node_connect(1, 14) = 7;   % element 14
   node_connect(2, 14) = 9;
 
   node_connect(1, 15) = 7;   % element 15
   node_connect(2, 15) = 10;
 
   node_connect(1, 16) = 8;   % element 16
   node_connect(2, 16) = 10;
 
   node_connect(1, 17) = 9;   % element 17
   node_connect(2, 17) = 10;
 
   node_connect(1, 18) = 9;   % element 18
   node_connect(2, 18) = 11;
 
   node_connect(1, 19) = 9;   % element 19
   node_connect(2, 19) = 12;
 
   node_connect(1, 20) = 10;   % element 20
   node_connect(2, 20) = 12;
 
   node_connect(1, 21) = 10;   % element 21
   node_connect(2, 21) = 13;
 
   node_connect(1, 22) = 11;   % element 22
   node_connect(2, 22) = 12;
 
   node_connect(1, 23) = 12;   % element 23
   node_connect(2, 23) = 13;
 
   node_connect(1, 24) = 11;   % element 24
   node_connect(2, 24) = 14;
 
   node_connect(1, 25) = 11;   % element 25
   node_connect(2, 25) = 15;
 
   node_connect(1, 26) = 12;   % element 26
   node_connect(2, 26) = 15;
 
   node_connect(1, 27) = 12;   % element 27
   node_connect(2, 27) = 16;
 
   node_connect(1, 28) = 13;   % element 28
   node_connect(2, 28) = 16;
 
   node_connect(1, 29) = 13;   % element 29
   node_connect(2, 29) = 17;
 
   node_connect(1, 30) = 14;   % element 30
   node_connect(2, 30) = 15;
 
   node_connect(1, 31) = 15;   % element 31
   node_connect(2, 31) = 16;
 
   node_connect(1, 32) = 16;   % element 32
   node_connect(2, 32) = 17;
 
   node_connect(1, 33) = 14;   % element 33
   node_connect(2, 33) = 20;
 
   node_connect(1, 34) = 14;   % element 34
   node_connect(2, 34) = 18;
 
   node_connect(1, 35) = 15;   % element 35
   node_connect(2, 35) = 18;
 
   node_connect(1, 36) = 16;   % element 36
   node_connect(2, 36) = 19;
 
   node_connect(1, 37) = 17;   % element 37
   node_connect(2, 37) = 19;
 
   node_connect(1, 38) = 17;   % element 38
   node_connect(2, 38) = 21;
 
   node_connect(1, 39) = 18;   % element 39
   node_connect(2, 39) = 20;
 
   node_connect(1, 40) = 19;   % element 40
   node_connect(2, 40) = 21;
 
   node_connect(1, 41) = 20;   % element 41
   node_connect(2, 41) = 24;
 
   node_connect(1, 42) = 20;   % element 42
   node_connect(2, 42) = 26;
 
   node_connect(1, 43) = 21;   % element 43
   node_connect(2, 43) = 29;
 
   node_connect(1, 44) = 21;   % element 44
   node_connect(2, 44) = 31;
 
   node_connect(1, 45) = 22;   % element 45
   node_connect(2, 45) = 23;
 
   node_connect(1, 46) = 23;   % element 46
   node_connect(2, 46) = 24;
 
   node_connect(1, 47) = 24;   % element 47
   node_connect(2, 47) = 25;
 
   node_connect(1, 48) = 25;   % element 48
   node_connect(2, 48) = 26;
 
   node_connect(1, 49) = 26;   % element 49
   node_connect(2, 49) = 27;
 
   node_connect(1, 50) = 27;   % element 50
   node_connect(2, 50) = 28;
 
   node_connect(1, 51) = 28;   % element 51
   node_connect(2, 51) = 29;
 
   node_connect(1, 52) = 29;   % element 52
   node_connect(2, 52) = 30;
 
   node_connect(1, 53) = 30;   % element 53
   node_connect(2, 53) = 31;
 
   node_connect(1, 54) = 31;   % element 54
   node_connect(2, 54) = 32;
 
   node_connect(1, 55) = 32;   % element 55
   node_connect(2, 55) = 33;
 
   node_connect(1, 56) = 22;   % element 56
   node_connect(2, 56) = 34;
 
   node_connect(1, 57) = 23;   % element 57
   node_connect(2, 57) = 34;
 
   node_connect(1, 58) = 23;   % element 58
   node_connect(2, 58) = 36;
 
   node_connect(1, 59) = 24;   % element 59
   node_connect(2, 59) = 36;
 
   node_connect(1, 60) = 24;   % element 60
   node_connect(2, 60) = 38;
 
   node_connect(1, 61) = 25;   % element 61
   node_connect(2, 61) = 38;
 
   node_connect(1, 62) = 25;   % element 62
   node_connect(2, 62) = 39;
 
   node_connect(1, 63) = 26;   % element 63
   node_connect(2, 63) = 39;
 
   node_connect(1, 64) = 26;   % element 64
   node_connect(2, 64) = 40;
 
   node_connect(1, 65) = 27;   % element 65
   node_connect(2, 65) = 40;
 
   node_connect(1, 66) = 27;   % element 66
   node_connect(2, 66) = 41;
 
   node_connect(1, 67) = 28;   % element 67
   node_connect(2, 67) = 41;
 
   node_connect(1, 68) = 28;   % element 68
   node_connect(2, 68) = 42;
 
   node_connect(1, 69) = 29;   % element 69
   node_connect(2, 69) = 42;
 
   node_connect(1, 70) = 29;   % element 70
   node_connect(2, 70) = 43;
 
   node_connect(1, 71) = 30;   % element 71
   node_connect(2, 71) = 43;
 
   node_connect(1, 72) = 30;   % element 72
   node_connect(2, 72) = 44;
 
   node_connect(1, 73) = 31;   % element 73
   node_connect(2, 73) = 44;
 
   node_connect(1, 74) = 31;   % element 74
   node_connect(2, 74) = 37;
 
   node_connect(1, 75) = 32;   % element 75
   node_connect(2, 75) = 37;
 
   node_connect(1, 76) = 32;   % element 76
   node_connect(2, 76) = 35;
 
   node_connect(1, 77) = 33;   % element 77
   node_connect(2, 77) = 35;
 
   node_connect(1, 78) = 34;   % element 78
   node_connect(2, 78) = 36;
 
   node_connect(1, 79) = 35;   % element 79
   node_connect(2, 79) = 37;
 
   node_connect(1, 80) = 36;   % element 80
   node_connect(2, 80) = 38;
 
   node_connect(1, 81) = 37;   % element 81
   node_connect(2, 81) = 44;
 
   node_connect(1, 82) = 38;   % element 82
   node_connect(2, 82) = 39;
 
   node_connect(1, 83) = 39;   % element 83
   node_connect(2, 83) = 40;
 
   node_connect(1, 84) = 40;   % element 84
   node_connect(2, 84) = 41;
 
   node_connect(1, 85) = 41;   % element 85
   node_connect(2, 85) = 42;
 
   node_connect(1, 86) = 42;   % element 86
   node_connect(2, 86) = 43;
 
   node_connect(1, 87) = 43;   % element 87
   node_connect(2, 87) = 44;
 
   node_connect(1, 88) = 38;   % element 88
   node_connect(2, 88) = 45;
 
   node_connect(1, 89) = 39;   % element 89
   node_connect(2, 89) = 45;
 
   node_connect(1, 90) = 43;   % element 90
   node_connect(2, 90) = 46;
 
   node_connect(1, 91) = 44;   % element 91
   node_connect(2, 91) = 46;
 
% connect all beam elements by connectivity array
   for i =  1 : n_elem;
      node_1 = node_connect(1,i);
      node_2 = node_connect(2,i);
      xx = [x(node_1),x(node_2)];
      yy = [y(node_1),y(node_2)];
      zz = [z(node_1),z(node_2)];
      xx2 = [x2(node_1),x2(node_2)];
      yy2 = [y2(node_1),y2(node_2)];
      zz2 = [z2(node_1),z2(node_2)];
      xx3 = [x3(node_1),x3(node_2)];
      yy3 = [y3(node_1),y3(node_2)];
      zz3 = [z3(node_1),z3(node_2)];
      plot3(xx,yy,zz,'--',xx2,yy2,zz2,xx3,yy3,zz3,'-r')
      hold on
   end
 
   title('Electric Pylon')
   xlabel('x (mm)')
   ylabel('y (mm)')
   zlabel('z (mm)')
   legend('Undeformed','Deformed Truss','Deformed Frame',4)
 
     view([0 0 1])      % xy plane view
    %view([0 1 0])     % xz plane view
    %view([1 0 0])     % yz plane view

Contributing Members[edit]

The following Team Wiki members contributed to this report.

Thomas Kehoe --Eml4500.f08.wiki.Kehoe 17:15, 9 December 2008 (UTC)

Gonzalo Barcia -- Eml4500.f08.wiki.Barcia 14:32, 9 December 2008

Ricardo Lopez -- Eml4500.f08.wiki.Lopez 15:06, 9 December 2008

Rodney Dagulo --Eml4500.f08.wiki.dagulo.r 20:18, 9 December 2008 (UTC)

Renee Hood --Eml4500.f08.wiki.hood 17:01, 9 December 2008 (UTC)

Cortland Glowacki --Eml4500.f08.wiki.cort 15:08, 10 December 2008 (UTC)