Program Computing Project 4 builds upon CP3 to develop a program to perform truss analysis. A truss consists of straight, slender bars pinned together at their end points. Truss members are considered to be two force, axial members. Thus, the force caused by each truss member - and the internal force in each member - acts only along it’s axis. In other words, the direction of each member force is known and only the magnitudes must be determined. To analyze a truss we study the forces acting at each individual pin joint. This is known as the Method of Joints. We will call each pin joint a node and the slender bars connecting the nodes will be called members. The previous project computed a unit vector to describe the vector direction of every member of a truss structure. To analyze the structure a few other key inputs must be included like the support reactions and external loads applied to the structure. With all of this information, you will need to make the correct changes to the provided planar (2-D) truss template program to be able to analyze a space (3-D) truss. What you need to do For a planar truss, every node has 2 degrees of freedom, the e1 and e2 directions. Therefore, for every planar truss problem, the total number of degrees of freedom (DOF) in the structure is equal to 2 times the number of nodes. We will consider the first degree of freedom for each node as the component acting in the e1 direction. So for any given node, i, the corresponding degree of freedom is (2·i)-1. For the same node, i, the corresponding value for the second degree of freedom, the component in the e2 direction, is 2-i. This numbering notation can be modified for a space truss. The difference with the space truss is that every node has 3 degrees of freedom, one degree for each of the e1, e2 and e3 directions. The degree of freedom indices are extremely crucial in understanding how to set up the matrices for the truss analysis. For this computing project, you will first need to understand the planar truss program and the inputs that are needed for that program. The first input is the spatial coordinates (x, y, z) of the nodal locations for a truss. It is convenient to label each node with a unique number (also known as the “node number”). Each row of the nodal coordinate array should contain the x and y coordinates of the node. We will use the matrix name of “x” for all nodal coordinates. Please note that “nNode” is an integer value that corresponds to the number of nodes in the truss and must be adjusted for every new truss problem. For Node 1 this matrix array input looks like: x(1,:) = [0,0]; Once the coordinates of the nodes are in the program, you will need to input how those nodes are connected by the members of the truss. In order to describe how the members connect the nodes you will also need to label each member with a “member number”. This connectivity array should contain only the nodes that are joined by a member, with each row containing firs.

1. Program Computing Project 4 builds upon CP3 to develop a
program to perform truss analysis. A truss consists of straight,
slender bars pinned together at their end points. Truss members
are considered to be two force, axial members. Thus, the force
caused by each truss member - and the internal force in each
member - acts only along it’s axis. In other words, the direction
of each member force is known and only the magnitudes must
be determined. To analyze a truss we study the forces acting at
each individual pin joint. This is known as the Method of Joints.
We will call each pin joint a node and the slender bars
connecting the nodes will be called members. The previous
project computed a unit vector to describe the vector direction
of every member of a truss structure. To analyze the structure a
few other key inputs must be included like the support reactions
and external loads applied to the structure. With all of this
information, you will need to make the correct changes to the
provided planar (2-D) truss template program to be able to
analyze a space (3-D) truss. What you need to do For a planar
truss, every node has 2 degrees of freedom, the e1 and e2
directions. Therefore, for every planar truss problem, the total
number of degrees of freedom (DOF) in the structure is equal to
2 times the number of nodes. We will consider the first degree
of freedom for each node as the component acting in the e1
direction. So for any given node, i, the corresponding degree of
freedom is (2·i)-1. For the same node, i, the corresponding
value for the second degree of freedom, the component in the e2
direction, is 2-i. This numbering notation can be modified for a
space truss. The difference with the space truss is that every
node has 3 degrees of freedom, one degree for each of the e1, e2
and e3 directions. The degree of freedom indices are extremely
crucial in understanding how to set up the matrices for the truss
analysis. For this computing project, you will first need to
understand the planar truss program and the inputs that are
needed for that program. The first input is the spatial
coordinates (x, y, z) of the nodal locations for a truss. It is

2. convenient to label each node with a unique number (also
known as the “node number”). Each row of the nodal coordinate
array should contain the x and y coordinates of the node. We
will use the matrix name of “x” for all nodal coordinates. Please
note that “nNode” is an integer value that corresponds to the
number of nodes in the truss and must be adjusted for every new
truss problem. For Node 1 this matrix array input looks like:
x(1,:) = [0,0]; Once the coordinates of the nodes are in the
program, you will need to input how those nodes are connected
by the members of the truss. In order to describe how the
members connect the nodes you will also need to label each
member with a “member number”. This connectivity array
should contain only the nodes that are joined by a member, with
each row containing first the node at the start of the member
and then the node at the other end of the member. The first node
that is input into the Member array will be called the start node
(SN) and the second node that is input is known as the end node
(EN). For any member it doesn’t matter which end you call the
start node and which is the end node. We will use the matrix
name of “Member” for the connectivity array. Also note that
“nMembers” is a single integer value that must equal the total
number of members for each truss. The nodes and members can
be numbered in any way you CEE/CNE 210—Statics SSEBE
Mechanics Group Arizona State University 2 want, but it can
sometimes be advantageous to use some sort of logical
systematic order if you can discern one. For Member 1 this
matrix array input should look like: Member(1,:) = [1,2]; The
support reactions for the truss must then be input. The variable
“nReactions” is an integer that corresponds to the total number
of supports. Note: a pin support counts as one reaction for the
nReaction count even though it has two unknowns. The support
reactions will be input into the “Reaction” matrix. The first
input value is the node number of where the support reaction is.
The second and third inputs are for the fixity conditions at that
node. If the support reaction provides resistance in a direction
then a 1 should be used otherwise a 0 is used to denote that the

3. truss is free to move in that direction. For example, if a roller
support was used at node 4 and had resistance in the e2
direction but was free to move in the e1 direction it would be
input as follows: Reaction(2,:) = [4,0,1]; Finally, the external
loads must be input. The variable “nLoads” is a single integer
value that corresponds to the number of loads placed on the
truss. The matrix name of “Load” will be used to store all
external loads. The first input is the node number where the
load acts. The second and third inputs are the magnitude of the
force in the e1 and e2 direction at that node. For a load placed
at node 3, that has a magnitude of 1200 N in the –e2 direction
should be input like: Load(1,:) = [3,0,-1200]; Next, the unit
vectors (direction vectors) must be computed for every member.
The direction of the unit vector will depend on the node of the
connection you chose to be the start node and the node that was
selected as the end node. Implement your CP3 code (the part
that computes the unit vectors) into the code. Use the matrix
name “UnVec” for the matrix that will store all the positive unit
vector values (the vectors pointing from SN to EN). Use the
matrix name “OppUnVec” to store all the negative unit vector
values (the vectors pointing from EN to SN). Once all the unit
vectors are created for every member, the coefficient matrix is
formed. We will call this matrix “C” and it will have the size of
(DOF, Members). For each member the SN and EN must be
determined. These nodal values have components in the member
unit vector array that correspond to a degree of freedom value
in the truss. This component from the unit vector array is stored
in the matching degree of freedom row and corresponding
member column in the “C” matrix. Note: the negative value of
the unit vector should be stored for every end node. The load
vector is then created. The load vector has the same number of
rows as DOF. The external loads have the same corresponding
degree of freedom value as the nodal coordinates, so a loop is
used to create this vector to store the load values in the correct
row. The array name of “F” will be used to store all external
forces. Once the coefficient matrix has been created, this matrix

4. must be partitioned into two separate matrices. The first matrix
contains the rows that correspond to a degree of freedom value
that has a support reaction, and the second matrix will contain
the rows that are not restrained. For every support reaction
using the corresponding degree of freedom, that row from the
coefficient matrix should be placed in the “Crest” matrix. The
“Crest” matrix should have the same number of rows as the
number of degrees of freedom that are restricted in the system
(i.e. support reactions – 2 for a pin and 1 for a roller).
CEE/CNE 210—Statics SSEBE Mechanics Group 3 When the
reaction force matrix has been created then the member force
matrix is created using all the rows not in the “Crest” matrix.
This matrix can be labeled “Cfree”. This member force matrix
should be a square matrix of the size (Members, Members) for
any statically determinate truss. The load vector must also be
partitioned to contain only the degree of freedom values that are
not restricted by a support. The new load vector (called “Ffree”)
should have the same number of rows as the number of
members. Once the free coefficient matrix has been created then
an array named “T” solves for the individual member forces
using { } [ ] { } −1 T Cfree Ffree = − Then an array named
“Reactions” solves for the support reactions using {Reactions
Crest T } = −[ ]{ } Once the reactions are calculated a
“SupportReaction” matrix is created that contains all the values
of the support reactions in the corresponding degree of freedom
spot for each node. The first input for the support reaction
matrix is the node number of the support and the second and
third input are the corresponding reaction value for the two
degrees of freedom for that node. Note: if there is no resistance
for a degree of freedom then the value should be 0. The
template file provided to you will work for any planar truss
once you implement the unit vector calculation code. You need
to get the planar truss code working and understand it. Then
make all the necessary changes to create a space truss program.
The changes do not need to be very extensive. Note: when your
code is graded there will be at least two different truss problems

5. run in your code to ensure your code is robust. Also provided is
a truss data input file. Use this file to create several input
sections that can be easily copied and pasted into the input
section of your truss analysis code. This allows you to create
and store several trusses (2-D and 3-D) that can be analyzed
quickly and easily. Be sure to test your code with a few
different 2-D trusses and several 3-D trusses. Report Once you
have a working 3-D truss analysis code, write a report
documenting all your work and the results. Follow the document
CEE210 Guidelines for Computing Projects (posted on
Blackboard). Include all your screen clips, plots and results.
Discuss your discoveries and explorations. All test cases need
to be included in your report with detailed documentation of the
problem (i.e. a figure and tables) and the results (i.e. a table of
the member forces and reactions). For every truss you test, there
needs to be back-up calculations to verify that the code is
working correctly (either hand calcs or copies of existing
problem solutions with proper source citations). The back-up
calculations should be placed in the Appendix of the report.
Also include a copy of your MATLAB .m program code and you
truss input data .m cod in the appendix. Also include any
struggles you are still having with MATLAB. Include a copy of
your entire MATLAB code in an appendix of your report.
CEE/CNE 210—Statics SSEBE Mechanics Group Arizona State
University 4 Submittal You must submit two files: a report file
and an executable program code. We will read your report file
and we will run your code file through MATLAB to analyze the
results. Most of the CP grade is based on the content and quality
of your report. However, if your code does not run, then your
report will not be graded and you will receive no credit for the
project. Convert your report file into a .pdf file format and give
it a descriptive filename, such as CEE210_CP4_Your_Name.pdf
that includes your name. Give your code file a descriptive
filename like CEE210_CP4_Your_Name.m that includes your
name. Be sure to run your code with the new filename to ensure
that it is a legal filename accepted by MATLAB. Submit your

6. report .pdf and your executable MATLAB script file (.m)
through the submittal link under the Computing Projects menu
on Blackboard prior to the deadline.