Structural Analysis of Stresses Transferred to a Basketball Backboard from the Rim By

Structural Analysis of Stresses Transferred to a Basketball Backboard from the Rim by Human Loads

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

Ryan Ansaldo

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 6

4. Conclusion 7

5. References 8

LIST OF TABLES

Table 1: Material Properties 2

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 5

Figure 5: Von Mises Stresses on Tempered Glass Backboard 6

Figure 6: Displacement in the z-direction of the Tempered Glass Backboard 6

ACKNOWLEDGMENT

Type the text of your acknowledgment here.

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.

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 In modern times, the basket has been replaced by a rim and net and has a more sophisticated means of being fastened to the backboard.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.

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

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”)

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

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.

Figure 4: Boundary Conditions and Load

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

4. Conclusion

5. References

"Basketball (ball)" Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. 2 July 2012. Web. 4 Jul. 2012. <http://en.wikipedia.org/wiki/Basketball_(ball)

"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>

Abaqus/CAE 6.10EF-1. “Abaqus User Manual.” Dassault Systèmes, Providence, RI, 2010.

http://www.precisionglass.com/tech/gp.pdf

http://www.kaysons.in/acrylic/physicalproperties.pdf

http://www.efunda.com/materials/alloys/alloy_home/steels_properties.cfm