Structural Analysis of Basketball Backboards:
Stress and Deflection Analyses based on Material
RPI Master's Preliminary Final Report
Ryan Ansaldo - 8/7/2012
Problem Description:
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The purpose of this project was to perform structural analyses of
basketball backboards using 3 materials.
Stresses were compared to failure and yield criteria to determine
whether or not the backboard material failed.
The load chosen will be applied at the furthest distance on the rim
from the backboard to simulate the highest bending moment.
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The load used was of an NBA player dunking on the rim. This force
was determined to be 1000 lbs [2].
Modeled Geometry
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The design chosen consisted of 3 parts as shown in the figure
below. The assembly consisted of the backboard sandwiched
between the rim and mounting plate.
The geometries were modeled in ABAQUS/CAE using the
appropriate regulation size dimensions.
Constraints:
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Rigid body tie constraints were used to tie the surfaces (highlighted
in the figure below) to the reference points to simulate where a nut
and washer would fix the mounting bracket to the backboard with a
threaded pin.
Surface-to-Surface Contact
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Surface-to-surface contact was used between the backboard and
the mating surfaces of the rim and mounting plate.
The rim, backboard, and mounting plate were assigned the same
global seed sizes in order to obtain as close to a uniform mesh
between the contact surfaces and also provides a faster
convergence rate.
Backboard Mesh at Contact Surface
Assembly Mesh
Rim Mesh at Contact Surface
Boundary Condition and Load:
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The backboard was encastred about its edges to simulate being
mounted by an aluminum frame to the arms and base of a
basketball stand.
The load is applied at the point on the rim furthest from the
backboard.
Failure Criteria:
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The table below shows the Failure criteria of the three materials.
Because Acrylic and Tempered glass are brittle materials, the
stress results of the two are compared to their failure stresses
which indicate cracking and fracture.
Steel stress results are compared to its yield strength to determine
whether or not the material will deform elastically or plastically.
Material
σy (psi)
Failure Stress (psi)
Tempered Glass [8]
N/A
14,000
Acrylic [5]
N/A
10,500
Steel [7]
55,100
N/A
Results:
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The Acrylic and Tempered Glass stresses each exceeded their
respective failure stresses
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Tempered Glass Max Stress = 22743 psi > Failure Stress = 14,500 psi
o
Acrylic Max Stress = 22141 psi > Failure Stress = 10,500 psi
Front Contact Surface
Front Contact Surface
Rear Contact Surface
Rear Contact Surface
Tempered Glass Von Mises
Stress Contour Plot
Acrylic Von Mises Stress
Contour Plot
Results:
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The Steel did not experience stresses above its Yield Strength and
therefore did not yield plastically.
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Steel Max Stress = 22743 psi < Yield Strength = 55,100 psi
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Steel Max z-displacement = 6.456e-02 inches
Front Contact Surface
Rear Contact Surface
Steel Von Mises Stress Contour Plot
Steel z-displacement Contour Plot
Conclusion:
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The results of this study validate that the stresses applied to a
basketball backboard by an NBA player dunking on the rim are
adequate to cause failure on tempered glass and acrylic
backboards. The previous rim designs and mounting have proven
to be outdated in preventing the shattering of professional and
collegiate backboards. More sophisticated rim designs are
equipped with a breakaway feature that allows the rim to pivot
slightly using springs and snap back in order to prevent the entire
load to be transferred to the backboard [14].
References:
1. Hiner, Jason (2005). Indiana University Basketball Encyclopedia. United States: Sports Publishing. pp.
447
2. “Busted Guts,” Sports Science. Fox Sports Network. CSN New England, Massachusetts. 3 May 2009
3. "Basketball (ball)" Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. 2 July 2012, 4 Jul.
2012, http://en.wikipedia.org/wiki/Basketball_(ball)
4. W.A. Dalgliesh, D.A. Taylor, “The Strength and Testing of Window Glass,” Canadian Journal of Civil
Engineering, Vol. 17, No.5 October 1990, pages 752-762
5. Laird Plastics, Plexiglas® G Acrylic Plastic Sheets, Accessed on 7/26/12,
lairdplastics.com/content/view/264/
6. “ARENAPRO 180 GOAL,” Spalding Specifications, dated 15 Oct 2009,
http://www.spaldingequipment.com/SpecLibrary/Basketball/Breakaway-ReflexGoals/413583Arena_180_goal.pdf
7. Matweb.com AISI 1045 Steel, as cold drawn, Accessed on 7/15/2012,
http://www.matweb.com/search/DataSheet.aspx?MatGUID=20fffdaa96f14dd98f5032c4014b9587
8. Read, Thomas L., “Failure Analysis of a Tempered Glass Basketball Backboard,” Read Consulting,
Accessed on 7/30/12,
http://readconsulting.com/publications/whitepapers/tempered_glass_backboard.html
References:
9. “Rule No. 1---Court Dimensions--Equipment,” The Official Site of the National Basketball Association.
17 Oct 2006. National Basketball Association. 22 Jul. 2012,
http://www.nba.com/analysis/rules_1.html?nav=ArticleList
10. Abaqus/CAE 6.10EF-1. “Abaqus User Manual.” Dassault Systèmes, Providence, RI, 2010.
11. Choi, Seung-Woo, “Technical Tips for Surface-To-Surface Contact Analysis in MES,” ALGOR, Inc.,
Accessed on 7/29/2012,
http://www.algor.com/news_pub/tech_white_papers/surface_contact/default.asp
12. Richard G. Budynas, J. Keith Nisbett, “Shigley’s Mechanical Engineering Design,” Eighth Edition,
McGraw-Hill, 2008
13. Read, Thomas L., “Tempered Glass Fractures,” Read Consulting, Accessed on 7/30/12,
http://readconsulting.com/publications/whitepapers/failure_analysis-tempered_glass.html
14. Winn, Luke. “Breaking Away,” Sports Illustrated 23 Dec. 2007. Accessed on 7/31/12,
http://sportsillustrated.cnn.com/si_blogs/basketball/ncaa/2007/12/breaking-away.html