TOOTHPICK BRIDGE OPTIMIZATION PROJECT

ME-463 Final Report
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-Engineer1. This
design will then be analyzed utilizing ANYSYS2, 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
47.44 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
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2
Pro-Engineer Wildfire Version 5.0
ANSYS Workbench Version 11.0
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ME-463 Final Report
45.5 lbs.
6”
Fig. 3: Original Side Truss Design
Fig. 5: Boundary Conditions
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.
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. /ft3 [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.
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ME-463 Final Report
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. 7: Bridge Design Alternative 1
Maximum
Stress
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 Stresses Acting on Original Design
Maximum
Stress
Maximum
Stress
Fig. 9: Maximum Von Mises Stress 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 Stresses Acting on Redesign 1
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ME-463 Final Report
Maximum
Stress
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 0.006283 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 0.005
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 21.40 percent as compared to the original design.
The maximum deflection experienced was found to be 0.0057
inches; which was greater than that of the first redesign (see
Table 1 & Fig. 14)
ANSYS Analysis Results
Maximum Stress
Truss
Value (psi) % Impromvement
Original
3426
--Redesign 1
3104
9.40
21.4
Redesign 2
2693
Max Displacement
Value (in.) % Impromvement
0.006283
--0.005010
20.3
0.005687
9.49
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 47.44 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 21.40 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 2010.
<http://dnr.wi.gov/forestry/um/pdf/report/YellowBirchReport.pd
f>.
[2] Cassins, Daniel. “Hardwood Lumber and Veneer Series:
Birch.” Purdue University. Purdue University, 09
2007. Web. 21 Nov 2010.
<http://www.extension.purdue.edu/extmedia/FNR/FNR-279W.pdf>.
[3] Vobolis, Jonas, and Lina Zavackaite. “Studies on Birch
Wood
Viscoelastic Properties. “Materials Science”.
12. Kaunas, Lithuania: 2005. Print.
Fig. 14: Maximum Von Mises Stress & Displacement
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ME-463 Final Report
APPPENDIX
Appendix I: Mass Properties of Bridge Designs
Appendix II: Displacement Diagrams of Truss Designs
Fig. 15: Original Truss Mass (0.0249 lbs.)
Fig. 18: Maximum Displacement of Original Design
Fig. 16: Re-design 1 Truss Mass (0.0244 lbs.)
Fig. 19: Maximum Displacement of Redesign 1
Fig. 17: Re-design 2 Truss Mass (0.243 lbs)
Fig. 20: Maximum Displacement of Redesign 2
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