Truss Analysis and Optimization

This project was for my Statics class. The assignment was to design, analyze, build, and test a simple planar truss from straws and foam gusset plates. The analysis was done in MATLAB using a program I wrote. I made sure to make the program very easy to use, so that new designs could be entered and analyzed very rapidly. I also wrote a optimization code that used iteration and a brute-force solver to optimize the truss for strength. I was the team leader for this project.

Test Day

Here is our completed truss in the testing rig. Our truss came in 4th place for highest load sustained. Our truss also failed exactly when we predicted. This was more important to our grade than how much we actually ended up holding.

Assembling the Truss

I made a scale drawing of the truss to aid in the assembly. A pinning jig was used to create holes in the straws in the right location. The gusset plates were cut to the right size and shape with an X-Acto knife.

Fully Assembled

Truss Plot

The program plotted the truss and displayed the critical members(s) in red. I also added the ground supports and the arrow for the load, just for fun!

Optimization

These dots constitute a Virtual Joint Region (VJR) - a collection of possible locations in which to place a joint. In the optimization, the user can select which joints to optimize, and the size and density of the VJRs.

Optimization

This shows how the optimization works. For each location in the VJR, the program re-analyzes the results. Each location in each VJR must be analyzed with each location in every other VJR, so it can take a while to solve!

5 VJRs, Low Density

5 VJRs, High Density

5 VJRs, High Density and Smaller Area

10 VJRs, Low Density

Introduction

The goal for the straw truss project was to design a simple, planar truss using MATLAB to perform a computational analysis, build the truss using the materials provided, and test the truss to determine the accuracy of our analysis. Every group in the class was given plastic drinking straws to use as members, foam core to use as gusset plates, and 'T' shaped hobby pins to secure the joints.

Design and Analysis

There are three basic aspects of truss design:

Topology
Geometry
Member Size & Material

The topology of the truss is the number of nodes, the connections between them, and the supports of the truss. In our computational analysis, a connection matrix was defined that contained the information for the topology of the truss, and a support matrix contained information about where the truss was supported. The geometry of the truss concerns the location of the joints. The coordinates for each joint were stored in x and y position vectors for the computational analysis. Combined with the connection matrix, this allowed for the determination of the lengths and unit vectors for each member. Once the topology and geometry of the truss has been determined, an external load on the truss could be defined, and the forces in each member could be computed. Because the size and material of the members was already constrained (drinking straws were the required material), the buckling strength of each member, the maximum load the truss could sustain and the critical member(s) could be calculated using the member forces. The buckling strengths of the straws were based on data obtained from a lab testing the buckling strengths of different lengths of straws. In addition to this basic computational analysis, our group added an optimization feature to our program, which allowed a design to be refined. The optimization used a discrete combinatorial method and an exhaustive search to determine the best truss from a set of thousands of other trusses.