# CEE/CNE 210—Statics [ Computing Project 3 Connectivity and Unit Vectors ]

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**CEE/CNE 210—Statics **SSEBE Mechanics Group

Arizona State University**Computing Project 3 Connectivity and Unit Vectors****Program**

Computing project 3 is preparatory for CP4 which will be the analysis of truss structures. A truss consists of slender members pinned together at their end points. Truss members are considered to be two force members, which means that the internal force in each member acts only along its axis. To analyze a truss we study the forces acting at each pin joint, one at a time. It is therefore essential to determine the axis direction of each truss member. The direction of each member’s axis can be described by computing a unit vec-tor along the axis. Additionally, the length of each member must also be known when analyzing a truss. Both of these calculations require the use of a position vector between the end points of the truss member.**What you need to do****Part 1**

For this computing project, first you need to input all the coordinates of the joint loca-tions for the two trusses (see Figures 1 and 2). It is convenient to label each joint with a unique number (also known as the “node number”). Each row of the joint coordinate ar-ray should contain the x, y, and z coordinates of the point. The node number is the same as the row number where the coordinates are stored in the joint coordinate array.

Once the coordinates of the joints are in the program, you will need to input how those points 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” (see Figures 1 and 2). This connectivity array should contain only points that are joined by a member, with each row containing the node number at one end followed by the node number at the other end of the member. The joints and members can be numbered in any way you want, but it can sometimes be advantageous to use some sort of logical order if you can discern one.

Then, using a for loop, compute the length of each member and a unit vector to describe the direction of each connection. The direction of the unit vector will depend on the point of the connection you chose to be the start point (SN: start node) and point that was selected as the end point (EN: end node).

Once you get your code working for this part, look in a textbook and online and compute the unit direction vectors for other truss structures. Plot all your trusses including all nodes and members. For a 3-dimensional truss, the plot can be rotated to see all three axes.

Figure 1a: Planar Truss

Figure 1b: Planar Truss with node numbers

(a)(b)

(a) (b)

Figure 2a: Space Truss

Figure 2b: Space Truss with node numbers**Part 2**

The second part of this project is to consider a polygon with points that lie on a half circle. The task in this case is to generate the coordinate array and connectivity arrays for the points with the flexibility to specify any number of sides on the polygon, say n sides.

Figure 3: Arc

The half circle arc shown in Figure 3 has been split into 6 points with 5 members. The coordinates of each point can be described as a function of R and θ (which should be values input in the program at the start). A for loop can be used to generate the coordinates of each point. Once the coordinates have been created, a second for loop can be used to compute the connections between each point along with the unit vector that describes the direction of each connection. The number of points and the radius of the arc should be able to be varied by one small input change in the program. Plot the polygon trusses you create.

Can you expand on this part further? Can you create an actual polygon truss that is made up by a large arc and a small arc and members connecting the two arcs together? Can you generalize this algorithm to be able to use any number of points on the top arc and bottom arc? This is your time to play around with the connectivity between nodes and members and see what you can get MATLAB to do.**Report**

Write a report documenting your work and the results (in accord with the specifications given in the document CEE210 Guidelines for Computing Project Reports). Include figures, plots, and results. Discuss your discoveries and explorations. Upload your report to

Blackboard prior to the deadline. Upload your .m program file to Blackboard as well.

CEE/CNE 210 Statics Amie Baisley, Chris Lawrence

Arizona State University

© SSEBE Mechanics Group, 2014**Guidelines for Computing Project Reports**

Introduction

The Computing Projects are designed to introduce you to MATLAB and promote a more robust computational environment. To demonstrate what you learned in each project, the final results will be submitted in the format of a report.

The main purpose of the computing projects is to experience the use of a modern tool to help you solve and analyze more complex and in depth problems than what is typically solved in a classroom setting. The ability to develop an understanding of computer programming to solve problems will tremendously broaden your engineering skill set.

Unlike the recitation problems, the computing projects are produced solely outside of class time. They will take a large amount of your homework time so good time management is essential. Since your grade for the project will come from your report and you cannot write a report until you have a working code, you will need to be sure your code is working several days prior to the due date. There needs to be enough time after completing the code to still be able to write a meaningful and organized report. So please plan accordingly!

This brief guide is meant to give you an outline of what your report should consist of. The format and organization of your report must be professional and make sense, as a portion of your grade will come from the overall report presentation.

What should be in the reports?

The report should have the following sections:

1. Introduction. In this part of the report you present the problem description. It should not be copied directly from the computing project assignment sheet.

2. Theory. You need to present the equations that you have coded into your computer program. If the equations were not given to you then you need to include a deri-vation of those equations. Make sure that every symbol you use in your equations are defined somewhere in the text. Make sure that your equations meet the stand-ards of report presentation (i.e., typeset). Do not use MATLAB code notation in the presentation of the theory.

3. Study and Results. In this section, discuss anything interesting that you observed about the project. If the results for the project are in tabular or graphical form they should be placed here. If the problem description includes items to discuss or in-clude in your report they should be placed in this section.

CEE/CNE 210 Statics Amie Baisley, Chris Lawrence

Arizona State University

© SSEBE Mechanics Group, 2014

Label every table and figure in your report with a number and caption. Table captions go above a table. Label them Table 1, Table 2, etc. Figure captions go below a figure (picture, graph, etc.). Label them Fig. 1, Fig. 2, etc. Be sure to include descriptive text in your table and figure captions that briefly describe what they are about. If you refer to any table or figure in the text of your report you must refer to them by their corresponding table or figure number.

4. Conclusions. The project must have conclusions and they must relate to the study. This is not the section to discuss how valuable this project was, but to discuss how this project will relate to statics and your future courses. It is important to be able to relate these ideas and talk about these projects in a professional way related to engineering.

5. Appendix—MATLAB code. Always include your complete MATLAB code in an appendix to the report. This will allow the evaluator to easily look over your code. The code should be nicely presented, with comments, indentation, and other features that help to make it readable. You should think about your program as some-thing someone else will read, not just something that you understand because you suffered through every line. Even you will forget what you were thinking a few weeks later if the code is not well documented.

You will also be asked to submit the .m MATLAB file so that the evaluator can run the program if necessary. Include a copy of the .m file in the appendix of the report as well.

If you have these five sections in your report then you are off to a good start. You can have more sections, but you should not have fewer. Write the report so that someone who was not a part of the process can make sense of it.

The quality of the report is about how well you write (spelling grammar, sentence structure, writing style), your attention to important details, and how good the report looks. Professionalism is paramount! If you put a plot in your report make sure it meets professional standards (i.e. title, axis labels, legend). If you include a sketch, make sure it is neat, correct, and easily interpreted. The purpose of graphics is to communicate ideas that are difficult to convey in words. If the reader cannot make sense of your graphics then you have not provided enough communication.

You can always seek feedback from the Instructional Team about how to do the projects and how to write the reports.

Submittals

Reports must be submitted in .pdf format along with your .m file. For each submittal your .m file will be run first to ensure that your code is working. If your code is not working or if you have neglected a part of the project then your report will not be graded and you will receive no credit for your submittal.