Structural Analysis of Stresses Transferred to a Basketball
Backboard from the Rim by Human Loads
by
Ryan Ansaldo
An Engineering Report Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
August, 2012
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© Copyright 2012
by
Ryan Ansaldo
All Rights Reserved
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CONTENTS
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
ACKNOWLEDGMENT .................................................................................................. vi
ABSTRACT .................................................................................................................... vii
1. Introduction.................................................................................................................. 1
1.1
Background ........................................................................................................ 1
1.2
Problem Description........................................................................................... 2
2. Methodology ................................................................................................................ 3
2.1
Abaqus Finite Element Analysis ........................................................................ 3
2.2
Finite Element Development Model .................................................................. 4
2.2.1
Two Part Backboard and Constraints..................................................... 4
2.2.2
Backboard and Rim Constraints ............................................................ 5
3. Results and Discussion ................................................................................................ 5
4. Conclusion ................................................................................................................... 8
5. References.................................................................................................................... 9
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LIST OF TABLES
Table 1: Material Properties .............................................................................................. 2
iv
LIST OF FIGURES
Figure 1: Geometry of backboard and rim modeled in Abaqus/CAE ............................... 3
Figure 2: Backboard sections and highlighted shell-to-solid coupling ............................. 4
Figure 3: Bolt pattern of rim and backboard with constraints highlighted (orange) ......... 5
Figure 4: Boundary Conditions and Load ......................................................................... 6
Figure 5: Von Mises Stresses on Tempered Glass Backboard .......................................... 7
Figure 6: Displacement in the z-direction of the Tempered Glass Backboard .................. 7
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ACKNOWLEDGMENT
Type the text of your acknowledgment here.
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ABSTRACT
The purpose of this project is to perform a structural analysis of a basketball rim
assembly and investigate the type of stresses imparted on the backboard from the rim.
The structural analysis on the rim and backboard mount was performed using
Abaqus/CAE to compare the stresses applied to a backboard of common backboard
materials. The three backboard materials of interests are tempered glass, acrylic, and
steel.
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1. Introduction
1.1 Background
Basketball is a popular sport played all over the world. Since its invention, the sport has
gone through many evolutions. The original “basket” was in fact an actual peach basket
and was nailed to the wall. In modern times, the basket has been replaced by a rim and
net and has a more sophisticated means of being fastened to the backboard. The athletic
ability of basketball players has also changed over the years and since the invention of
the dunk shot, the basketball rim and backboard have been subjected to many changes
and redesigns.
Previously the only loads applied to the basketball rim were imparted by the ball which
has a weight of approximately 22 ounces (Reference 1). When a dunk is performed,
depending on whether or not a player decides to hang, the rim can experience loads in
the magnitude of the weight of an above average human weight (since many collegiate
and professional basketball players are above average height and weight). The force is
then transferred to the bracket which mounts the rim to the backboard.
The stress experienced by the backboard is something that still affects the design of
modern day rims as the consequences are not only catastrophic for its function but
potentially harmful. Professional basketball rims are made of glass and have shattered
when being overstressed. For this reason, the basketball rim and mount are constantly
redesigned to improve the function of the rim. Since basketball has also become a
recreational outdoor sport, the materials of backboards have also changed.
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1.2 Problem Description
For this project, a structural analysis of a basketball rim and backboard were performed.
The load is assumed to be applied at the point on the rim furthest from the backboard to
simulate the greatest possible moment. The geometry of the assembly was modeled and
analyzed in Abaqus/CAE. The load is assumed to be 325 lbs, which is the weight of
retired NBA player Shaquille O’Neal (Reference 2). The three backboard materials of
interests are tempered glass, acrylic, and steel.
Table 1: Material Properties
Material
Modulus of Elasticity (psi)
Poisson’s ratio (ʋ)
Tempered Glass
10,000,000
0.22
Acrylic
290,075
0.37
Steel
27,557,170
0.27
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2. Methodology
2.1 Abaqus Finite Element Analysis
The geometry of the basketball rim and backboard were modeled in Abaqus/CAE using
the dimensions of standard regulation sized rim and backboard. The design chosen is of
a rim with no breakaway feature and assumes the load is directly transferred from the
rim to the backboard. The mounting bracket will be modeled to be bolted to the
backboard using the appropriate constraints. Rigid body tie constraints will be used to
simulate the connection between the bolted connection and the backboard.
Step 1:
After the design was chosen, it was modeled in Abaqus/CAE using the regulation
dimensions of a basketball rim and backboard. A common bolt pattern was used for an
accurate simulation of the interaction between the rim and backboard. The figure below
shows the geometry in Abaqus.
Figure 1: Geometry of backboard and rim modeled in Abaqus/CAE
Dimensions:
Backboard:
72 in length x 42 in width x ½ in thick
Basketball rim:
18 in diameter, 5/8 in diameter rod (inside diameter is 6 inches away from backboard)
Mounting plate:
4 bolt pattern (5” x 5”)
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Step 2:
Once the basketball rim and backboard assembly were finalized, the appropriate material
properties, boundary conditions, mesh and loads are applied to the model. A rough
model was used as a proof of concept using a coarse mesh while exploring the most
accurate and appropriate boundary conditions and constraints.
Step 3:
After the proof of concept study was completed, a suitable mesh was chosen for the
assembly. The material properties for the first model were of tempered glass (see Table
1 of Section 1.2). After appropriate boundary conditions and constraints were applied,
the load specified in Section 1.2 was applied on the rim. Once the load case is run, stress
and deflection data in the post processing menus are used to interpret how the backboard
reacts to the given load. After using the tempered glass material properties, the analysis
will be repeated two more times for the materials of interest shown in Section 1.2.
2.2 Finite Element Development Model
2.2.1
Two Part Backboard and Constraints
The finite element model of the basketball backboard and rim assembly was developed
consisting of 3 parts with 2 of the parts consisting of sections of the backboard. The
section that consists of a majority of the backboard was created as a 3D deformable
shell. The smaller section of the backboard was created as a 3D deformable solid. Each
section of the backboard had a thickness of 1/2 an inch thick with total dimensions as
specified in Section 2.1. A shell-to-solid coupling was used at the edges where the two
backboard sections meet (see Figure 2).
Figure 2: Backboard sections and highlighted shell-to-solid coupling
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2.2.2
Backboard and Rim Constraints
The rim was created as a 3D deformable solid based on the geometry shown in Figure 1.
The part consists of a circular ring with a mounting bracket with a shape similar to an L
bracket. The mounting bracket has a 4 bolt pattern as described in Section 2.1. The bolt
pattern holes were created on both the mounting bracket of the rim and section 2 of the
backboard (see Figure 3).
Figure 3: Bolt pattern of rim and backboard with constraints highlighted (orange)
Reference points were created at the center of each hole diameter and depth. Rigid body
tie constraints were used to tie the surfaces (highlighted in Figure 3) to the reference
points to simulate where a nut and washer would fix the mounting bracket to the
backboard with a threaded pin.
A contact relationship was also created between the backboard and rim. This is to
ensure a more accurate simulation of the stresses transferred from the rim to the
backboard. The mounting bracket and section 2 of the backboard both consist of similar
meshes.
2.2.3
Boundary Conditions and Load
The boundary conditions for the backboard and rim assembly were created to simulate
previous backboard designs in which the backboard is fixed at its edges by an aluminum
frame that mounted to the structural frame and arms of the backboard stand. The
backboard was encastred at all four edges. The load was applied to a reference point
created at the point of the rim furthest from the backboard and a load of 325 lbf was
applied in the negative y-direction as shown in Figure 4.
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Figure 4: Boundary Conditions and Load
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3. Results and Discussion
Results of the finite element analysis of the tempered glass backboard are as follows.
The backboard experiences a maximum Von Mises stress of approximately 9000 psi
under the given load. The maximum deflection of the backboard in the z-direction was
approximately 0.0456 in.
Figure 5: Von Mises Stresses on Tempered Glass Backboard
Figure 6: Displacement in the z-direction of the Tempered Glass Backboard
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4. Conclusion
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5. References
1. "Basketball (ball)" Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. 2
July 2012. Web. 4 Jul. 2012. <http://en.wikipedia.org/wiki/Basketball_(ball)>
2. "Shaquille O’Neal." Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc.
22 June 2012. Web. 4 Jul. 2012. < http://en.wikipedia.org/wiki/
Shaquille_O%27Neal>
3. Abaqus/CAE 6.10EF-1. “Abaqus User Manual.” Dassault Systèmes, Providence,
RI, 2010.
4. http://www.precisionglass.com/tech/gp.pdf
5. http://www.kaysons.in/acrylic/physicalproperties.pdf
6. http://www.efunda.com/materials/alloys/alloy_home/steels_properties.c
fm
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