TOOTHPICK BRIDGE OPTIMIZATION PROJECT

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1 TOOTHPICK BRIDGE OPTIMIZATION PROJECT Eric Dimmer, Ryan Fargen, and Lee Wisinski Abstract A toothpick bridge requires an excessive time span to build. Thus, a well engineered truss design must be created to withstand a vertical load. In order to determine the optimum truss design, a 3-D CAD model of an experimentally designed toothpick bridge truss will be created using the software package Pro-Engineer 1. This design will then be analyzed utilizing ANYSYS 2, finite element analysis software, to determine the locations of maximum stress and displacement. It is desired to reduce the maximum Von Mises stress applied to the truss design by 15%. INTRODUCTION In 2003, Michigan Tech hosted their annual Engineering Olympics. Schools from across the state would compete against each other in various events. One of the competitions was the toothpick bridge challenge. The goal was to design and develop a bridge made out of only Diamond flat toothpicks and Elmer s glue. The bridge had to weigh less than or equal to 50 grams and span across a 20 inch distance. In addition, there was a maximum truss thickness of three toothpicks. A 6 x6 block of wood was placed on top of each bridge. Connected to the block was a bucket that hung below the bridge. Each contestant added sand to the bucket until the bridge broke (see Fig. 1). The winner of the competition had the greatest ratio of failure load versus bridge mass. The bridge design being examined weighed grams and held 91 pounds. This ratio qualified for second place. The bridge fractured roughly 3 inches from its center (see Fig.2). Fig. 2: Fractured Bridge The purpose of this project was to take this bridge design and utilize ANSYS to optimize its design. In order to accomplish this, a 3-D CAD model of one of the side trusses was created. This model was then be uploaded into ANSYS where the boundary conditions and loads were applied to replicate the experimental model. In addition, with the material of toothpicks (birch) known, the ANSYS result was determined and compared to the experimental result. In theory, the maximum Von Mises stress of the ANSYS result should be where the experimental bridge broke. The results from ANSYS aided in the detection of specific trusses that had little to no affect on the structural integrity of the design. The insignificant trusses were then removed and repositioned to give the bridge more support where it was needed. In conclusion, the bridge design will be optimized and, if built again, the actual bridge theoretically would hold more weight if designed properly, giving the bridge an even better ratio. PROCEDURE The 3-D CAD model of the original bridge design was created using Pro-Engineer. To simplify the analysis of the bridge, only one side truss was modeled (see Fig. 3). Fig. 1: Test Procedure 1 Pro-Engineer Wildfire Version ANSYS Workbench Version

2 45.5 lbs. 6 Fig. 3: Original Side Truss Design In order to utilize ANSYS, it was required to determine the type of wood the toothpicks were made out of. According to the Jarden Home Brands Corporation, Diamond flat toothpicks are manufactured out of birch wood. Upon further research, the specific type of birch wood used most commonly to produce toothpicks is yellow birch wood [2]. Fig. 4 portrays the regions of the United States that yellow birch wood can be found. Fig. 5: Boundary Conditions Prior to any optimization, a mesh size analysis was performed on the original design. The truss was meshed using a solid 10 node brick (element 187). An element size of 5 was chosen as the starting point. With the constraints in place and the mesh complete, the solution was run and the maximum displacement was recorded. To determine if further mesh refinement was needed, smaller mesh sizes were chosen and the percent change in the maximum displacement was calculated. From this analysis it was determined that after the mesh size of 0.1 further iterations yielded less than a 1% change in maximum displacement. A graphical representation of the mesh analysis can be seen in Fig. 6. Using the computed percent difference data and the graphical data, a mesh size of 0.1 was chosen. This mesh size provided accurate results without putting excess strain on the PC and software. Fig. 4: Range of the Yellow Birch [2] Yellow birch wood has an oven dry density of 56.7 lbs. /ft 3 [1] and an average modulus of elasticity of 3,385,000 psi [3]. With these properties known, the project then proceeded to analyzing the 3-D CAD model with ANSYS. Before analyzing the truss design, a few assumptions were made for the project. The first assumption is that the truss design is a single part. This reduced the complexity of the 3-D CAD model. The second was that the bridge was made out of only birch wood. There was no data which specified the modulus of elasticity of Elmer s Glue. This assumption allowed for a specific value rather than an assumed value, based upon the amounts of glue, to be used in each region of the truss. Once the truss was uploaded to ANSYS, the boundary conditions could be applied. The initial boundary condition was to constrain the bridge from displacement in the horizontal and vertical directions. This constrain would replicate masonry blocks utilized in the competition. In addition, a 6 inch distributed load was placed at the center of the bridge to imitate the experimental load. The magnitude of this load was half of which caused the bridge to fail experimentally since only one of the two trusses was analyzed (see Fig. 5). Fig. 6: Mesh Analysis of Original Design Once the mesh analysis was complete, the original bridge could then be redesigned in Pro-Engineer and analyzed using ANSYS. Upon review of the maximum stress contour plots, the beams of least significance to the design were removed and/or replaced to improve the integrity of truss design. This process was performed a second time to further improve the design (see Fig. 7&8). With the constraint of the bridge mass being less and or equal to 50 grams, the redesigned trusses had to consist of a mass less than or equal to the original truss design. To simulate this condition, the density of yellow birch was updated into the 3-D CAD models. A mass analysis was then performed. The mass of each of the truss redesigns were in fact less than the mass of the original truss. The mass values of each of the bridge designs can be seen in Appendix I. 2

3 Fig. 7: Bridge Design Alternative 1 Fig. 10: Truss Design w/o "Ears" The sides were then constrained in the X and Y directions to replicate the function of the ears without using them in the analysis. Figures 11, 12, & 13 portray the Von Mises stresses acting on the three truss designs. The displacement figures obtained from ANSYS were included in Appendix II. Fig. 8: Bridge Design Alternative 2 RESULTS It can be seen in Fig. 9 that the maximum Von Mises stress for the original truss design was located at the outermost edge where the truss was in contact with the cylinder block. Fig. 11: Von Mises es Acting on Original Design Fig. 9: Von Mises at the "Ear" However, it was known from the experimental bridge that failure did not happen in this region. Thus, the ears at the ends of the truss were removed from the CAD model (see Fig. 10). Fig. 12: Von Mises es Acting on Redesign 1 3

4 Fig. 13: Von Mises stresses Acting on Redesign 2 Upon further investigation, the original truss redesign experienced a maximum Von Mises stress of 3426 psi at a distance of 3 inches from its center. This design also had a maximum displacement of inches. The first redesign improved considerably in comparison to the original design. When the same load of 45.5 lbs. was applied, and the maximum Von Mises stress the truss experienced was found to be 3104 psi. This was a reduction of 9.40 percent. It also had a maximum displacement of inches. A second redesign was created to further improve the truss. Under the 45.5 lb. load, this truss was found to undergo a maximum Von Mises stress of 2693 psi. This resulted in a final reduction of percent as compared to the original design. The maximum deflection experienced was found to be inches; which was greater than that of the first redesign (see Table 1 & Fig. 14) ANSYS Analysis Results Truss Max Displacement Value (psi) % Impromvement Value (in.) % Impromvement Original Redesign Redesign Table 1: ANSYS Analysis Results CONCLUSION The goal of this project was to optimize the toothpick bridge design. The new design was required to have a mass less than or equal to the original truss design. The original mass of the bridge was grams and it failed under a load of 91 pounds. The experimental bridge was comprised of two identical trusses, and therefore it was decided to analyze one truss under a distributed load of 45.5 pounds on the principle of symmetry. After collecting the stress data from ANSYS for the original design, it was noticed that the maximum Von Mises stress acted on the exact section that the experimental bridge failed. This confirmed that the information collected from ANSYS was accurate. In conclusion, the original truss was redesigned to more efficiently distribute the load applied to the bridge. The second redesign was chosen and experienced a percent reduction in the maximum Von Mises stress, which was within the established goal. ACKNOWLEDGMENTS The team would like to acknowledge and extend gratitude to the following persons who have made the completion of this Project possible: Gordon Kendall, Preble Engineering Team Head Coach, for his contribution of critical historical data from the Engineering Olympics. Jarden Home Brands Corporation, for the distribution of information on their Diamond brand toothpicks. REFERENCES [1] United States. Wisconsin Department of Natural Resources.. Yellow Birch., Web. 21 Nov < f>. [2] Cassins, Daniel. Hardwood Lumber and Veneer Series: Birch. Purdue University. Purdue University, Web. 21 Nov < W.pdf>. [3] Vobolis, Jonas, and Lina Zavackaite. Studies on Birch Wood Viscoelastic Properties. Materials Science. 12. Kaunas, Lithuania: Print. Fig. 14: Von Mises & Displacement 4

5 ME-463 Final Report APPPENDIX Appendix I: Mass Properties of Bridge Designs Appendix II: Displacement Diagrams of Truss Designs Fig. 15: Original Truss Mass ( lbs.) Fig. 18: Displacement of Original Design Fig. 16: Re-design 1 Truss Mass ( lbs.) Fig. 19: Displacement of Redesign 1 Fig. 17: Re-design 2 Truss Mass (0.243 lbs) Fig. 20: Displacement of Redesign 2 5