Simulate Early, Simulate Often... In Rhino
The date is November 26th, 2015. The family is just finishing up their second helpings of turkey on what appeared to be another successful thanksgiving dinner at Aunt Ellen’s until… Crack! It seems Uncle Dave had one to many servings of stuffing this year, and the chair he was sitting on broke from under him. While the initial reaction was to make sure there were no serious injuries (which there weren’t), Aunt Ellen was later quite upset about her piece of furniture. It was a part of a 6 chair set hand made by her grandfather, that had been passed down 2 generations of her family, and someday she hoped to make it 3. Knowing my engineering background, she proceeded to ask me for my help in repairing the chair. Since I was in between things at the time, I had the time to take the on the project. Her only condition was that I could ensure nothing like this would happen again; “many elders sit in my chairs. I would hate to be responsible for their serious injury”.
After analyzing the break and preparing a possible fix, I decided to use Scan-and-Solve Pro to run a few simulations that would ensure ease of mind regarding future safety. The chair failed on both legs at roughly the same location; on the back leg, at the seat interface. My plan to repair the chair was to make a vertical bandsaw cut at the location depicted below, and insert a sheet of steel to support the chair in tension and compression (Image #1). Additionally epoxy was to be used to keep the chair leg and steel sheet together. Epoxy wood bonds are designed to be mechanically stronger than the wood itself, so the epoxy does not need to be thoroughly examined for failure (http://www.azom.com/article.aspx?ArticleID=1093 ).
Image #1: The original chair (left), original non fractured chair leg (middle), and chair leg displaying the break and location of longitudinal saw cut (right).
My bandsaw allows the use of both a .025” and .035” saw blade, however the .035” blade had been severely damaged and no longer functioned. So, if I could get away with using the .025” blade it would save me the money of buying a new blade. Nonetheless, I set up my first simulation with the .035” cut and steel thickness to ensure that my design would be mechanically sufficient. The simulation was set up with an extensive load of -225 lbs. downward, and 50 lbs. backward for precautionary measures (Image #2). The results were then gathered and analyzed (Image #3).
Image #2: The cuts were made and the steel sheets with thickness .035” were inserted at the highlighted location of the chair, with epoxy and screws to keep the steel and chair together (left). The simulation was set up with -225 lbs. in the –Z direction and 50 lbs. in the Y (right).
Image #3: The simulation indicates that the chair head will have a maximum deflection of over an inch under these conditions (left). More importantly, this bending will induce a stress exceeding the yield stress of the steel support by almost 90% (right).
These results sent me back to the drawing board. The problem was that the tensile stress from the backward 50 lbs. force was too much for the steel plates to handle. After brainstorming, I decided to add an additional side support to the chair (Image #4).
Image #4: The additional supports to help stabilize the bending moment are highlighted by the red box.
With this support intact, the simulation would be set up with identical conditions as the original, only this time both the .025” and .035” steel reinforcements would be simulated for comparison. Not only would I be looking for an option to provide the necessary mechanical stability, I would be determining if the mechanical advantages of the .035” steel sheet would be exceedingly superior to the .025” steel sheet, making it worth purchasing a new blade. The simulations were run and the data was collected for analysis (Image #5, #6).
Image #5: The maximum displacement experienced by the chair head in the .025” steel support (left) and the .035” steel support (right)
Image #6: The maximum danger level resulting from the .025” steel support (left) and the .035” steel support (right). Both images indicate that the maximum area of concern is in the steel support plate.
Looking at Image #5, the difference in displacement between the two steel thicknesses appears to be a nonfactor. The .035” support displays merely .002” less of displacement than the .025” support. While this is promising, the danger level must also be analyzed. Since the .025” support has a smaller cross sectional area, we see a more significant difference in this category. The .025” support displays a maximum danger level of .751 while the .035” support displays a maximum danger level of .615. While this is a considerable difference, the determined factor of safety necessary for this chair under these over strenuous conditions is 1.25, which equates to a maximum acceptable danger level of 0.8 (http://www.maelabs.ucsd.edu/mae3/Assignments/Energy_Analysis/factor_of_safety/FactorOfSafetyGuidelines-Ullman.pdf). Both the .025” and .035” supports satisfy this criteria, so I decided I could save myself the money and extra trip to the store by using my .025” blade.
As a final simulation, I was curious to see just how beneficial the added side supports were to the chair, and if it was worth adding them to all 6 chairs to prevent further failures. With the same external conditions, I analyzed the compressive and tensile stresses in the two models. Currently there isn’t a good mathematical model for computing the danger level in wood materials. For this reason, danger level cannot be used to analyze the wood, so the axial compressive and tensile stresses (which we know is what caused the chair leg failure) were analyzed and manually interpreted (Image #7)
Image #7: Tensile stress is represented by orange while compressive is represented by yellow. The bending induced by the backward force causes the wood on one side of the neutral axis to be in compression and the other to be in tension. The addition of the braces (left) significantly decreases the compressive and tensile stress.
From this image it is clear that the side support braces play a substantial role in the chair’s ability to withstand larger forces applied against the backrest. The maximum tensile stress induced in the chair without braces is larger than when the chair has the braces by about a factor of 10. This implies that the chair with braces is far less likely to fracture since it is more capable of handling bending induced tensile forces. So, as a final project I added supportive side braces to the remaining 5 chairs (Image #8)
Image #8: The final chair product.
Since Scan-and-Solve was not around in the time the chair was built, I cannot blame my ancestors for their poor design. However, with this tool I was able to run a few simple simulations providing insight into what went wrong leading to failure, and an approach for preventing this from recurring. Now the chairs are fully functional, and are expected to remain so for some time to come.