Buckling Pop Can [Video]
Ever see the trick were someone stands on an empty pop can? The pop can is able to support the weight of the person until the side of the can is slightly dimpled and then the can is subject to a sudden collapse. So what’s happening? As long as the can holds its “perfect” cylindrical shape, it’s able to support the load, but as soon as a small imperfection is introduced to the cylinder, the can catastrophically fails due to buckling.
I decided to recreate this in our lab and take a brief look at how it’s relevant to engineering. I started by determining how much load an undimpled, empty pop can could support. To do this, I loaded an empty can into our universal testing machine and compressed it slowly until it buckled. After testing three cans this way, I found the load range at buckling to be between 135 and 190 pounds. Not wanting to push too close to this limit, I decided that for my experiment I would load the can with 100 pounds of dead weight.
Then, I ever-so-carefully set two 50-pound weights on an empty can. Next, I attached a cotton-tipped applicator to the end of a rod (to keep my hands out of the danger zone!), and I gently pushed on the side of the can to create a small dimple. The can instantly collapsed and was crushed by the dead weight. Check out the video I took of the can collapsing.
To get a better idea of the stresses in the can when it collapsed, I measured the wall thickness of a can with a micrometer and found it was 0.003 inch. With a measured OD of 2.65 inches, the cross-sectional area of the can was 0.025 square-inches, so with a 100-pound load, that works out to nominally 4,000 psi of compressive stress in the can wall. A little internet research leads me to believe that pop cans are made from 3000 series aluminum, with yield strengths in the upper 30’s to lower 40’s ksi. This means that we were only at about 10% of the theoretical yield load when the can buckled.
This shows just how sensitive some systems can be to buckling and how small, unaccounted-for geometric imperfections and/or unexpected loads can cause real problems. One real-world example of this was the failure of a radial-arm, tainter gate on the spillway at Folsom Dam in California in July 1995.
As you may have noticed when driving past a dam, a spillway gage is typically comprised of a large, curved section of fabricated steel (next to the water in the forebay), connected to a radial arm, the other end of which is connected to a bearing, which is anchored into the concrete structure of the spillway. The gates are operated by lifting on the gate, causing the entire structure to pivot around the bearing at the fixed end of the radial arm.
The radial arms are primarily designed to withstand axial, compressive stresses due to holding back the water in the forebay. In the case of the failure at Folsom Dam, the original design had failed to account for friction in the bearing, which, over time, had increased. The increased friction in the bearing resulted in higher bending stresses than the arms were designed for when the gate was operated, causing the arm to buckle under the weight of the forebay water load.
This phenomenon also shows up in Finite Element Analysis (FEA) when performing buckling analyses of structures. When we generate a model it is geometrically “perfect”, and when we add loads and boundary conditions in an FEA code, they are applied “perfectly”. Unfortunately, nothing in the real world is perfect, but since the FEA code doesn’t realize that it’s not in the real world, the analysis will return artificially high critical buckling loads (i.e., it will overestimate the strength of the component). To account for this, we apply buckling “seed loads” into the analysis. These are small, insignificant loads applied perpendicular to the primary load. These loads by themselves add only a minuscule amount of stress to the structure being analyzed; however, by creating a slight imperfection in the loading conditions they more accurately re-create the real world, allowing for a much more realistic critical buckling load to be determined.
As always, feel free to contact us if you have any questions about the contents of this blog.
…..and you didn’t really think we’d load a can in the universal tester and stop after a few pounds, did you? Here’s a video of what 100,000 pounds of force does to a pop can.