Stress Analysis Within Sports
To continue the current overview series about stress analysis in sports we will examine one piece of equipment that rarely fails, but when it does, it causes quite a commotion; the basketball hoop. Interestingly a basketball rim only weighs about 22ounces, but when those highlight dunks occur it can experiences forces and stresses much higher than that of an average human, sometimes as much as 1000lbs. These forces are then transferred directly to the bracket and backboard.
Strength and stress in the glass
What does this mean in terms of the pros and cons of the engineering and design work that is put into the creation of this state of the art equipment? The main problem with professional and college backboards is that they are made from glass. If you have ever dropped or hit glass then you are aware that it is relatively low fracture toughness, or that it is brittle. It can experience only a small maximum strain before it fractures. Originally wooden and steel backboards were used because they were cheap and easy to come across, however, so as not to block the view for fans, the NBA™ sticks with the glass back board. The difference between steel and glass is that steel is considered a ductile material and thus under high stress it yields, or deforms, whereas glass will shatter. For the Plexiglas that the NBA uses, it only requires about 10,500 psi to make the glass fail in tension.
[i] Plastics tend to fail in the fracture mode by tension. One might think of it as the material tearing.
Due to the weakness exhibited by the backboard, the bracket and the rim must be constantly redesigned to handle the repeated forces that are applied to it. For a few years in the late 1970’s, the NBA used a breakaway rim that simply detached if pulled with enough force. However this also led to injury for players expecting to hang on to the rim and not bracing for the fall. With hoops that remain attached, the largest stress concentrations are seen at the bolt holes where the bracket and rim are attached to the backboard. At these points the stress from a Shaquille O’Neal sized dunk (SOSD) could reach as much as 22,743 psi, causing immediate failure in the backboard. If the NBA were to still use a steel backboard this would only cause a slight deformation near the areas of highest concentration because the yield strength of steel is about 55,100 psi.[ii] By using a steel backboard, it is thought that the rim would break before the backboard, however this has never been tested.
Currently, mechanical engineers are creating designs with springs, or similar shock absorbers in the bracket to absorb the force. Similar to the shocks of a car these work to help dissipate the force so that the bolt holes don’t have to experience such a stress. Also, this new design, so far only used in the NBA and NCAA, is constructed differently than previous hoops. Instead of being connected to a plate that sandwiches the glass, it is connected to the main frame of the hoop. To test the new design, the show Sport Science™ chained a piano to the front of the rim and dropped it from above the backboard and although it pulled the entire frame of the hoop to the ground it was unable to shatter the backboard. The force generated from this piano was estimated to be about 6000 lbf which bent the rim and caused the arm of the hoop to fail, but did not affect the glass.[iii] Thanks to this technology, it seems that a shattered backboard after an SOSD is a thing of the past.
[i] http://web.archive.org/web/20130515073946/http://www.rplastics.com/plexdesign.html Arkema, Inc. September 2011
[ii] Ansaldo, Ryan “Finite Element Analysis of Basketball Backboards” Rensselaer Polytechnic Institute, Hartford CT, August 2012
[iii] Sport Science “Shattered Backboards” John Brenkus July 10, 2009