Giant Lego towers
Jearl Walker www.flyingcircusofphysics.com
February 2015 Lego bricks (under copyright by Wham-O, Inc.) are small, plastic, toy blocks that come in various shapes.
Let’s consider a simple brick: There are four holes on one side and four short projections on the opposite side. One brick can be stacked directly over another so that four connections are made (projections into holes), or the top brick can be shifted by half a brick’s length so that two connections are made. In recent years, a popular social project has been to build Lego towers, trying to capture the record for the tallest tower. Here are two examples. This one is over 34 meters high:
But this is even taller at 36 meters:
These constructions beg the question: What is the limit to the height of a Lego tower? Assume it consists of a column of single bricks that are somehow stabilized so that it does not buckle or fall over due to some disturbance such as wind. As each additional brick is added to the top, the lowest brick is compressed more. Eventually it will fail. Rather than dramatically collapsing, it will begin to deform (melt) because it is plastic.
The idea was tested in a compressor by placing a Lego brick between the two horizontal plates. As the top plate was forced downward, the pressure on the brick gradually increased, until the brick effectively melted. The researchers tested several bricks. The average of the limiting downward forces was 4240 newtons, which is equivalent to a mass of 432 kilograms resting on the brick. The researchers then calculated that because each brick has a mass of 1.152 grams, that limiting force was equivalent to a having a tower height of 3.5 kilometers. Of course, building and stabilizing such a tower to check this limit would be just about impossible.
In contrast, here is a pressure test in which a concrete cylinder is squeezed. The failure point comes at much larger force value (over 6.7 million newtons), but the failure mechanism is much different.
https://www.youtube.com/watch?v=cfVvzjVzeE0&x-yt-cl=84838260&x-yt-ts=1422327029 same video
The concrete is obviously not plastic, will not gradually deform, and fails in a much more dramatic (even frightening) fashion. That type of failure draws an audience but watching plastic brick deform and melt would not.