CEE/CNE 210 Statics & Mechanics Group Arizona State Univ

CEE/CNE 210 Statics SSEBE Mechanics Group Arizona State University 1comp

CEECNE 210 Statics Ssebe Mechanics Grouparizona State University1comp

CEE/CNE 210 Statics SSEBE Mechanics Group Arizona State University 1 Computing Project 3: Connectivity and Unit Vectors Program Computing Project 3 is preparatory for CP4 which will be the analysis of truss structures. In other words, a good performance on CP3 will make CP4 much easier for you. A truss consists of straight, slender bars pinned together at their end points. Truss members are considered to be axial force members, which means that all the external and internal forces act only along the axis of the bar. 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 position vector between the end points of each truss member, from one pin joint to the next, will allow us to determine the length of each member and the direction of each member’s axis, which is described by a unit vector along the axis. So, the focus of CP3 is to determine the geometric arrangement of the members of any given truss. To do this you must input the coordinates of the pin joints and the relationships of the truss members in order to determine the direction vectors along the axis of each member. What you need to do Part 1 For this computing project, you first need to input all the coordinates of the joint locations 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 numberâ€). Create a Joint Coordinate Array that is 3 columns wide and has the number of rows equal to the number of joints in the truss. Each row of the joint coordinate array 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. For 2-D trusses just leave the z coordinate as zero for each joint. Once the coordinates of the joints are stored in the program, you will need to input how those points are connected to each other by the members of the truss. Not every member is connected to every joint or to each other so you need to identify which members are connected together and at which joints. In order to describe how the members connect to the nodes you will want to label each member with a “member number†(see Figures 1 and 2). This connectivity array should be 2 columns wide and have the number of rows equal to the number of members in the truss. Each row of the Member Connectivity Array should contain the start node and end node 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, sequential order if you can discern one. For example, member BK in Fig. 1 starts at joint 2, which has coordinates of x = 2 m and y = 0, and ends at joint 11, which has coordinates of x = 4 m and y = 3 m. The coordinate array and connectivity array will allow you to calculate the position vector along each member, the length of each member, and a unit vector to describe the direction of each member. The direction of the unit vector will depend on which end of the member is arbitrarily designated as the start node and which end is designated the end node. Verify your code by using external references (textbook examples, online, etc.) and computing the unit direction vectors for other truss structures. Plot all your trusses including all nodes and members. If your plot looks like the original truss then you were successful. 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 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. This simulates a truss of any shape and with any number of members. Figure 3: Arc The semi-circular arc shown in Figure 3 has been described by 5 members with 6 joints. 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 consisting of a large arc and a small arc with 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. Use the provided MATLAB code template, “CP_3_Template.m†to get you started. Change the file name to include your name (eg. “CP_3-John Doe.mâ€). Report Write a report documenting your work and the results (in accord with the specifications given in the docu- ment CEE210 Guidelines for Computing Project Reports). Include figures, plots, and results. Discuss your discoveries and explorations. Include your name in the report file name and convert the file to PDF (eg. “CP3 Report-John Doe.pdfâ€). Upload your report .pdf file to Blackboard prior to the deadline. Upload your .m program file to Blackboard as well. Remember if your code doesn’t run then you get zero for the project. However, most of your grade on the project is earned from the report.

Paper For Above instruction

This project involves developing a computational tool for analyzing the geometric configuration of truss structures, focusing on the calculation of direction vectors, lengths, and unit vectors for each member based on joint coordinates and connectivity data. The task is divided into two main parts: initial modeling of typical trusses and generating complex polygonal trusses that include arcs and multiple connection points. The project emphasizes understanding spatial relationships, programming logical loops in MATLAB, and visualizing the truss structures accurately.

In the first part, the goal is to input the coordinates of joints in 2D or 3D space and establish the connectivity between these joints to form the truss structure. This involves creating arrays to store joint coordinates and member connectivity—each represented by start and end node numbers—and using equations to compute the position vector for each member. The length and direction (unit vector) of each member are then calculated using these vectors. Visual plots of the trusses are essential for verification, and the code must handle 3D rotations for space trusses to ensure an accurate depiction.

The second part extends the analysis to polygonal trusses formed by points lying on a semi-circular arc, with the ability to specify the number of sides (n) and the radius (R). The coordinates of these points are generated programmatically using trigonometric functions within loops. Connectivity is then established between adjacent points, also via programmed loops that assign connections and compute direction vectors. The challenge lies in generalizing the process to handle arbitrary numbers of points on both upper and lower arcs, creating complex geometries that include connecting members between the arcs. Visualization of these polygonal structures, including combined large and small arcs, enhances understanding and validation of the algorithm.

Throughout the project, MATLAB code is utilized to automate these calculations, requiring careful programming of loops, matrices, and plotting functions. The documentation of the process, including code snippets, figures, and interpretations of findings, must be detailed in a comprehensive report, adhering to the university’s guidelines. The ultimate goal is to produce an accurate, flexible, and visualizable model of various truss configurations that facilitates further structural analysis. Proper code functioning and insightful reporting are critical for earning full credit in this assignment.

References

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