Speaking as an ex-aerospace-stress analyst, I found the article lacking. 2x2 Lego bricks individually fail by plastic deformation. The weight of an unreasonably tall tower could cause it, but we know that such an unreasonably tall tower can't exist because of stability concerns. So: what actually limits the height of a Lego tower? Elastic buckling, or some other kind of buckling, or is it something weird because of the friction fit of Lego bumps in the bottom of the block above? That's where the really interesting stuff comes into play. The Prague tower in the picture appears to have a square cross section, but is it hollow, or solid? What special construction techniques did they use, or is it just a matter of craftsmanship and selecting exactly nominal bricks for construction?
As an ex-civil engineer, this would be an awesome, but expensive competition for freshman engineering students. I actually remember a problem set containing questions like "how tall a tower" ignoring things like stability for various materials.
Backing out some numbers from the piece, the 2x2 held 950 lbs, which is roughly 1000 lbs in 1/2"x1/2", or 4000psi. That's roughly the strength of ordinary unreinforced concrete, at a far lighter density. Legos are also similar to unreinforced concrete in their tensile strength, which is low, variable, and brittle. The usual calculation is that tensile strength is ~ 10% of the compressive strength for concrete, but it depends greatly on the cracks and other discontinuities.
From the problem set though, there's an interesting effect. If you taper the tower with an exponential curve, 1/e^x, the pressure on the bottom of the tower can be constant as you increase the both the footprint and the height. Not coincidentally, that's the same curve you find in towers in the real world like the Eiffel Tower and the CN Tower.
The ultimate height that you could make with a tower would certainly depend on what constraints you're applying. Is there a limited number of bricks? A limited base area? Any supports at all? How do the people actually assemble the thing? What safety regs are there?
With no constraints, I don't see a reason that legos couldn't be built to the height of the great pyramids. Apart from the obvious one that it would be hellaciously expensive.
Once you start talking about constraints and something more tower shaped than mountain shaped, stability is the biggest concern. Elastic stability will affect the tower, at least as an upper limit to the height/cross section ratio.
> If you taper the tower with an exponential curve, 1/e^x, the pressure on the bottom of the tower can be constant as you increase the both the footprint and the height.
As a tower? Mainly because the base gets exponentially larger as you get taller. You'd start talking about a mountain that's significantly taller than the diameter of the earth.
Earth's radius is 4k miles. Geostationary orbit is ~25k. Space elevators IIRC, are proposed for ca 60k miles out. Assuming a 10-20x height/width ratio, the base would be 3-6k miles on a side. Even just getting to geostationary orbit would require a mountain with a base the size of a continent.
SO the rules of Lego-tower-building have to have the slope of the sides of the tower steeper than the angle of repose of a mass of bricks, eh? Otherwise, it's just a pile, not a tower.
Yep. But that's with no constraints. I'd think that a good combination would be a limited floor space and a set quantity of bricks. No other supports, no guy wires.
And for extra credit, the tower should survive a run on the shake table.
A friend and myself managed a slightly less epic 9.45m in 1989. We did it in the gap in the stairwell of our old flats. The base was only 8x8 and tapered every couple of meters and it was essentially hollow (to reduce weight and because we didn't want to run out of bits). We provided horizontal stabilisation with some string between the banisters to stop it falling during construction.
It was stopped by one of the whingy old fart neighbours wondering what we were doing and threatening to complain to the management company. We had a good 5m left and probably enough bits left to cover it!
Smashing it was awesome and made one hell of a mess which took hours to clear up.
Most of the Lego came from a car boot sale in two large bins and was purchased for a mere 5 GBP. Went on ebay in 2001 for nearly 200 GBP (good investment!)
I'm a little confused. That's the weight that a single Lego brick can withstand, correct? So assuming you made a "tower" that was essentially a vertical line of 2x2 Lego bricks, it'd collapse after 3,591m.
But that's not how we build towers. If you create a proper foundation with Lego bricks and distribute the weight evenly across them, and taper the tower as it goes up, am I wrong in assuming it could go a lot more than that? The entire weight of a structure never rests on a single brick...
Probably the proper translation out of geek-speak and into reality is that there is almost certainly no real structure that can be made purely out of Lego bricks that will cause the lower level to mechanically fail. (I'm hedging for safety. I really want to say there isn't one at all, but I've learned not to underestimate people's ingenuity. But let me point out by "real structure" I mean one that can be reasonably built in the real world, not, for example, a structure a mile high with millimeter tolerances made out of mass-manufactured plastic bricks.)
For another example, one could try to create an inverted pyramid on one brick to crush it, but it will topple long before it crushes the brick.
The structural strength under that circumstance (pure Lego, nothing else) is so enormously high, as determined by this experiment, that there's no reason to ever worry about this eventuality.
A counterexample is if you build a huge non-inverted pyramid and then put an extra brick in the middle on the bottom. It wouldn't balance but you could easily imagine putting many tons of weight on that single brick sticking out on the bottom like this, thus technically causing the lowest level to mechanically fail. This is pedantic, but I think you asked for it:)
Assuming the rest of the pyramid base doesn't end up flexing around that one brick (which would not be very tall) and distributing more of its weight on the ground...
Well, sure. You can do all sorts of things. But you're still looking at stacking rather a lot of bricks on top of one brick.
I mean, were it just a matter of "a brick can support 100 meters of brick on top of it", I'd say, sure, obviously we can do that in real life. It'll be hard, but we can probably do it. But you have to put another ~1.5 orders of magnitude of pressure on... this is going to be "decidedly nontrivial", to borrow the mathematician's phrase. I'm not ready to say it's absolutely impossible, but it's in the "I'll believe it when I see it" class. That is a lot of bricks you are trying to stack on with no other failures getting in you way, and when you're dealing with that sort of accumulation of brick, micrometer variations you'd normally never even consider worrying about start stacking up....
You are right but I'd prefer to have this answer as you can predict the maximum height of the tower that you designed using this. Also, a question that accounts for complex towers, would not be a question about legos much, I think.
Its been a while since I watched that episode, but that was built with a steel superstructure surrounded by lego right? The lego was only partially load-bearing?
Around 23:30 you can see that they added a wooden safety structure, which did not (normally) hold any weight. It was just there in case the Lego failed. The Lego alone actually held itself, and the occupants, just fine. The first test is at 40:30.
Is anyone else excited by the fact that your average Lego brick can easily hold a human's weight? So if you built things out of LEGO you could, at least in theory, stand on them.
Unfortunately something else tends to go wrong first - so you can stand on a solid Lego structure fairly easily, but if you try to build a bridge it's very hard to keep it from failing when weighted in the middle because the weight tends to push the bricks apart from one another.
There's an episode of James May's Toy Stories on Lego, where he builds a house from it; it turns out to be pretty tricky to build the floor of the upper storey to support him.
This seems to simulate the pressure due to the weight of the bricks, but I wonder how much the height comes down by if you factor in the extra pressure you have to put on the top brick to get it to clip on.
Does this add non-negligibly to the pressure on the bottom brick, or is it almost nothing once dispersed through the whole tower?
(You may be able to tell that I have very little knowledge of the physical sciences, so apologies if this is a stupid question!)
> The average maximum force the bricks can stand is 4,240N.
Ah, but that's not quite the issue, if the question is how high of a tower you can build.
If a tower is 3.5 km tall, then the lower 100m (to pull a number out of the air) are all supporting pretty much the same weight. And that 100m is about ... 10,000 bricks thick? If one of those bricks goes, then the tower goes. So what you want to know is not the average strength of a brick, but the expected strength of the weakest brick out of 10,000. I imagine that's significantly less.
Exercise for the reader: Given the probability distribution of brick strength, how do we compute the height at which we expect a one-brick-wide tower to fail? (Assume that vertical compression of bricks is the only issue; there are no lateral forces, the tower is perfectly balanced, etc.)
More or Less is a great program that introduces statistics to current affairs topics and listener questions. This was in response to a listener question. It being on the news is the usual BBC thing of using BBC news as an advertising medium for BBC shows.
There seem to be two Lego-related articles on the front page right now. One a piece nominally for "geeks", demonstrating how adults can continue to do novel and interesting creative things with Lego bricks; the other an emotionally-resonant piece (probably aimed at parents) showing that Lego-the-company/brand "cares about kids."
Both of these showing up just at the inflection point of the Christmas shopping season.
