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Abstract –– A toothpick bridge requires an excessive timespan to build. Thus, a well engineered truss design must becreated to withstand a vertical load. In order to determinethe optimum truss design, a 3-D CAD model of anexperimentally designed toothpick bridge truss will becreated using the software package Pro-Engineer1. Thisdesign will then be analyzed utilizing ANYSYS2, finiteelement analysis software, to determine the locations ofmaximum stress and displacement. It is desired to reducethe maximum Von Mises stress applied to the truss designby 15%.

INTRODUCTIONIn 2003, Michigan Tech hosted their annual Engineering

Olympics. Schools from across the state would compete againsteach other in various events. One of the competitions was thetoothpick bridge challenge. The goal was to design and developa bridge made out of only Diamond flat toothpicks and Elmer’sglue. The bridge had to weigh less than or equal to 50 gramsand span across a 20 inch distance. In addition, there was amaximum truss thickness of three toothpicks. A 6”x6” block ofwood was placed on top of each bridge. Connected to the blockwas a bucket that hung below the bridge. Each contestant addedsand to the bucket until the bridge broke (see Fig. 1). Thewinner of the competition had the greatest ratio of failure load

Fig. 1: Test Procedure

1 Pro-Engineer Wildfire Version 5.02 ANSYS Workbench Version 11.0

versus bridge mass. The bridge design being examined weighed47.44 grams and held 91 pounds. This ratio qualified for secondplace. The bridge fractured roughly 3 inches from its center (seeFig.2).

Fig. 2: Fractured Bridge

The purpose of this project was to take this bridge designand utilize ANSYS to optimize its design. In order toaccomplish this, a 3-D CAD model of one of the side trusseswas created. This model was then be uploaded into ANSYSwhere the boundary conditions and loads were applied toreplicate the experimental model. In addition, with the materialof toothpicks (birch) known, the ANSYS result was determinedand compared to the experimental result. In theory, themaximum Von Mises stress of the ANSYS result should bewhere the experimental bridge broke. The results from ANSYSaided in the detection of specific trusses that had little to noaffect on the structural integrity of the design. The insignificanttrusses were then removed and repositioned to give the bridgemore support where it was needed. In conclusion, the bridgedesign will be optimized and, if built again, the actual bridgetheoretically would hold more weight if designed properly,giving the bridge an even better ratio.

PROCEDUREThe 3-D CAD model of the original bridge design was

created using Pro-Engineer. To simplify the analysis of thebridge, only one side truss was modeled (see Fig. 3).

Eric Dimmer, Ryan Fargen, and Lee Wisinski

TOOTHPICK BRIDGE OPTIMIZATION PROJECT

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Fig. 3: Original Side Truss Design

In order to utilize ANSYS, it was required to determine thetype of wood the toothpicks were made out of. According to theJarden Home Brands Corporation, Diamond flat toothpicks aremanufactured out of birch wood. Upon further research, thespecific type of birch wood used most commonly to producetoothpicks is yellow birch wood [2]. Fig. 4 portrays the regionsof the United States that yellow birch wood can be found.

Fig. 4: Range of the Yellow Birch [2]

Yellow birch wood has an oven dry density of 56.7 lbs. /ft3 [1]and an average modulus of elasticity of 3,385,000 psi [3].

With these properties known, the project then proceeded toanalyzing the 3-D CAD model with ANSYS. Before analyzingthe truss design, a few assumptions were made for the project.The first assumption is that the truss design is a single part. Thisreduced the complexity of the 3-D CAD model. The second wasthat the bridge was made out of only birch wood. There was nodata which specified the modulus of elasticity of Elmer’s Glue.This assumption allowed for a specific value rather than anassumed value, based upon the amounts of glue, to be used ineach region of the truss.

Once the truss was uploaded to ANSYS, the boundaryconditions could be applied. The initial boundary condition wasto constrain the bridge from displacement in the horizontal andvertical directions. This constrain would replicate masonryblocks utilized in the competition. In addition, a 6 inchdistributed load was placed at the center of the bridge to imitatethe experimental load. The magnitude of this load was half ofwhich caused the bridge to fail experimentally since only one ofthe two trusses was analyzed (see Fig. 5).

45.5 lbs.

6”

45.5 lbs.

6”

45.5 lbs.

6”

Fig. 5: Boundary Conditions

Prior to any optimization, a mesh size analysis wasperformed on the original design. The truss was meshed using asolid 10 node brick (element 187). An element size of 5 waschosen as the starting point. With the constraints in place andthe mesh complete, the solution was run and the maximumdisplacement was recorded. To determine if further meshrefinement was needed, smaller mesh sizes were chosen and thepercent change in the maximum displacement was calculated.From this analysis it was determined that after the mesh size of0.1 further iterations yielded less than a 1% change in maximumdisplacement. A graphical representation of the mesh analysiscan be seen in Fig. 6. Using the computed percent differencedata and the graphical data, a mesh size of 0.1 was chosen.This mesh size provided accurate results without putting excessstrain on the PC and software.

Fig. 6: Mesh Analysis of Original Design

Once the mesh analysis was complete, the original bridgecould then be redesigned in Pro-Engineer and analyzed usingANSYS. Upon review of the maximum stress contour plots, thebeams of least significance to the design were removed and/orreplaced to improve the integrity of truss design. This processwas performed a second time to further improve the design (seeFig. 7&8). With the constraint of the bridge mass being less andor equal to 50 grams, the redesigned trusses had to consist of amass less than or equal to the original truss design. To simulatethis condition, the density of yellow birch was updated into the3-D CAD models. A mass analysis was then performed. Themass of each of the truss redesigns were in fact less than themass of the original truss. The mass values of each of the bridgedesigns can be seen in Appendix I.

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Fig. 7: Bridge Design Alternative 1

Fig. 8: Bridge Design Alternative 2

RESULTSIt can be seen in Fig. 9 that the maximum Von Mises stress

for the original truss design was located at the outermost edgewhere the truss was in contact with the cylinder block.

Fig. 9: Maximum Von Mises Stress at the "Ear"

However, it was known from the experimental bridge thatfailure did not happen in this region. Thus, the “ears” at theends of the truss were removed from the CAD model (see Fig.10).

Fig. 10: Truss Design w/o "Ears"

The sides were then constrained in the X and Y directions toreplicate the function of the “ears” without using them in theanalysis. Figures 11, 12, & 13 portray the Von Mises stressesacting on the three truss designs. The displacement figuresobtained from ANSYS were included in Appendix II.

Fig. 11: Von Mises Stresses Acting on Original Design

Fig. 12: Von Mises Stresses Acting on Redesign 1

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Fig. 13: Von Mises stresses Acting on Redesign 2

Upon further investigation, the original truss redesignexperienced a maximum Von Mises stress of 3426 psi at adistance of 3 inches from its center. This design also had amaximum displacement of 0.006283 inches.

The first redesign improved considerably in comparison tothe original design. When the same load of 45.5 lbs. wasapplied, and the maximum Von Mises stress the trussexperienced was found to be 3104 psi. This was a reduction of9.40 percent. It also had a maximum displacement of 0.005inches.

A second redesign was created to further improve the truss.Under the 45.5 lb. load, this truss was found to undergo amaximum Von Mises stress of 2693 psi. This resulted in a finalreduction of 21.40 percent as compared to the original design.The maximum deflection experienced was found to be 0.0057inches; which was greater than that of the first redesign (seeTable 1 & Fig. 14)

Value (psi) % Impromvement Value (in.) % Impromvement

Original 3426 --- 0.006283 ---Redesign 1 3104 9.40 0.005010 20.3

Redesign 2 2693 21.4 0.005687 9.49

TrussMaximum Stress Max Displacement

ANSYS Analysis Results

Table 1: ANSYS Analysis Results

Fig. 14: Maximum Von Mises Stress & Displacement

CONCLUSIONThe goal of this project was to optimize the toothpick

bridge design. The new design was required to have a mass lessthan or equal to the original truss design. The original mass ofthe bridge was 47.44 grams and it failed under a load of 91pounds. The experimental bridge was comprised of twoidentical trusses, and therefore it was decided to analyze onetruss under a distributed load of 45.5 pounds on the principle ofsymmetry.

After collecting the stress data from ANSYS for theoriginal design, it was noticed that the maximum Von Misesstress acted on the exact section that the experimental bridgefailed. This confirmed that the information collected fromANSYS was accurate.

In conclusion, the original truss was redesigned to moreefficiently distribute the load applied to the bridge. The secondredesign was chosen and experienced a 21.40 percent reductionin the maximum Von Mises stress, which was within theestablished goal.

ACKNOWLEDGMENTSThe team would like to acknowledge and extend

gratitude to the following persons who have made thecompletion of this Project possible:

Gordon Kendall, Preble Engineering Team Head Coach, for hiscontribution of critical historical data from the EngineeringOlympics.

Jarden Home Brands Corporation, for the distribution ofinformation on their Diamond brand toothpicks.

REFERENCES

[1] United States. Wisconsin Department of Natural Resources..Yellow Birch. , Web. 21 Nov 2010.<http://dnr.wi.gov/forestry/um/pdf/report/YellowBirchReport.pdf>.[2] Cassins, Daniel. “Hardwood Lumber and Veneer Series:Birch.” Purdue University. Purdue University, 092007. Web. 21 Nov 2010.<http://www.extension.purdue.edu/extmedia/FNR/FNR-279-W.pdf>.[3] Vobolis, Jonas, and Lina Zavackaite. “Studies on BirchWoodViscoelastic Properties. “Materials Science”.12. Kaunas, Lithuania: 2005. Print.

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APPPENDIX

Appendix I: Mass Properties of Bridge Designs

Fig. 15: Original Truss Mass (0.0249 lbs.)

Fig. 16: Re-design 1 Truss Mass (0.0244 lbs.)

Fig. 17: Re-design 2 Truss Mass (0.243 lbs)

Appendix II: Displacement Diagrams of Truss Designs

Fig. 18: Maximum Displacement of Original Design

Fig. 19: Maximum Displacement of Redesign 1

Fig. 20: Maximum Displacement of Redesign 2