RPI Master's Preliminary Final Report Ryan Ansaldo - 8/7/2012

1. Structural Analysis of Basketball Backboards: Stress and Deflection Analyses based on Material RPI Master's Preliminary Final Report Ryan Ansaldo - 8/7/2012

2. Problem Description: • 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. • The load used was of an NBA player dunking on the rim. This force was determined to be 1000 lbs [2].

3. Modeled Geometry • 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.

4. Constraints: • 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.

5. Surface-to-Surface Contact • 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.

6. Boundary Condition and Load: • 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.

7. Failure Criteria: • 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.

8. Results: • The Acrylic and Tempered Glass stresses each exceeded their respective failure stresses • Tempered Glass Max Stress = 22743 psi > Failure Stress = 14,500 psi • Acrylic Max Stress = 22141 psi > Failure Stress = 10,500 psi Acrylic Von Mises Stress Contour Plot Tempered Glass Von Mises Stress Contour Plot

9. Results: • The Steel did not experience stresses above its Yield Strength and therefore did not yield plastically. • Steel Max Stress = 22743 psi < Yield Strength = 55,100 psi • Steel Max z-displacement = 6.456e-02 inches Steel Von Mises Stress Contour Plot Steel z-displacement Contour Plot

10. Conclusion: • 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].

11. References: • Hiner, Jason (2005). Indiana University Basketball Encyclopedia. United States: Sports Publishing. pp. 447 • “Busted Guts,” Sports Science. Fox Sports Network. CSN New England, Massachusetts. 3 May 2009 • "Basketball (ball)" Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. 2 July 2012, 4 Jul. 2012, http://en.wikipedia.org/wiki/Basketball_(ball) • 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 • Laird Plastics, Plexiglas® G Acrylic Plastic Sheets, Accessed on 7/26/12, lairdplastics.com/content/view/264/ • “ARENAPRO 180 GOAL,” Spalding Specifications, dated 15 Oct 2009, http://www.spaldingequipment.com/SpecLibrary/Basketball/Breakaway-Reflex-Goals/413583Arena_180_goal.pdf • Matweb.com AISI 1045 Steel, as cold drawn, Accessed on 7/15/2012, http://www.matweb.com/search/DataSheet.aspx?MatGUID=20fffdaa96f14dd98f5032c4014b9587 • 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

12. References: • “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 • Abaqus/CAE 6.10EF-1. “Abaqus User Manual.”DassaultSystèmes, Providence, RI, 2010. • 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 • Richard G. Budynas, J. Keith Nisbett, “Shigley’s Mechanical Engineering Design,” Eighth Edition, McGraw-Hill, 2008 • Read, Thomas L., “Tempered Glass Fractures,” Read Consulting, Accessed on 7/30/12, http://readconsulting.com/publications/whitepapers/failure_analysis-tempered_glass.html • 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