Comments on: Tallest possible Lego tower height calculated

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 14:12:00 +0000

Thanks. Academic life has its entertaining moments.

By: jpgsawyer

jpgsawyer — Wed, 05 Dec 2012 12:52:00 +0000

My comment wasn’t a complaint that the presenter said that the brick looked like it melted I think that is a very good description.

It was more that Cory then described the process as “brick basically melted” which was not what the presenter had said or what happened.

Nice work by the way.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 12:03:00 +0000

Thank you. It was fun and interesting.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 12:02:00 +0000

Overall the walls buckled outwards about 75% of the time and inwards 25% of the time. I would only expect significant stiffening when two adjacent walls tried to buckle outwards into each other, which would occur about 9/16 of the time.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 12:00:00 +0000

Thank you for your comments. Having researched and taught in materials and structural engineering for twenty five years, I have picked up a few basic ideas about the processes involved.

My brief in this case was to answer a simple question about the crush strength of a Lego brick. If you listen to the BBC podcast, or read the original BBC article, you will see that I clearly made the point that structural failure through buckling would occur first, and this was backed up by a professional Lego builder who was also interviewed.

Incidentally, buckling of a Lego column is significantly more complicated than simple elastic / Euler buckling, because of the possibility of bricks pulling apart under tension. It’s more like buckling of concrete columns, which crack under relatively low tensile stress but can take very high compressive ones.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 11:54:00 +0000

The failed bricks did indeed look as if they had melted, although of course it wasn’t a melting process. Remember that we did this for a radio programme, so the reporter needed a good verbal description of the results.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 11:52:00 +0000

We didn’t see much creep in this case. We ran tests at different strain rates and the loads were very similar.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 11:50:00 +0000

See my previous reply. There is another vertical load-bearing region – the tube down the middle. However, it’s very thin compared to the walls and I don’t think contributes much.

By: Ian Johnston

Ian Johnston — Wed, 05 Dec 2012 11:41:00 +0000

We used buffer plates top and bottom to simulate real life loading as closely as possible.

By: Chris Blackmore

Chris Blackmore — Wed, 05 Dec 2012 10:25:00 +0000

Rats! I was going to build a black hole. Out of black bricks, obviously.

By: bob

bob — Wed, 05 Dec 2012 07:51:00 +0000

What about the force required to press on the top block?

Clearly this was left out of the calculations.

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:23:00 +0000

Actually, the question has not been answered. When surrounded by other bricks, the bottom bricks become stronger, because they’re forced to buckle inwards rather than outwards, and they can take more force that way (presumably from the fact that the test brick failed by buckling outwards). So a Lego pyramid could be EVEN TALLER than the 10777m.

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:20:00 +0000

Not only that, but each brick becomes stronger (can take more compression before it buckles locally) when it’s surrounded by other bricks (since the brick in the photo failed by having its walls buckle outwards, where other bricks could have been placed). By how much? I don’t know. Time to squash a Lego brick constrained inside a rectangular tube with thick steel walls…

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:18:00 +0000

There is also the lesser-known Mount Olympus in Washington state… The only one of those that I have actually seen. (Although it’s possible that some photons from the one on Mars have hit my eye in the few times when I looked at Mars in the sky). A quick visit to Wikipedia surprises me in revealing that the “real” Mount Olympus is only a little taller than the one over here.

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:15:00 +0000

How many bricks to build a space elevator? ;]

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:14:00 +0000

But the failure mode of the brick will change when there are bricks on each side preventing the sides from buckling outwards. If each side of each brick can only buckle inwards, then each brick gets a lot stronger. In other words, a whole bunch of 375000-brick-tall towers all stacked against each other would be able to take quite a bit more stuff on top, even though a single 375000-brick-tall tower is on the verge of collapse. (And that’s not even pointing out the obvious simplification that global buckling is being ignored as the most likely failure mode. In reality, a 375000-brick-tall tower would collapse for the same reason that a human hair could not be balanced on its end, for reasons other than compressive forces destroying the material at the base).

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:09:00 +0000

The top and bottom, including the nubs, just hold the bricks together. It’s the walls on the side that carry the weight. There are no other vertical regions connecting the top of the brick to the bottom of the brick, so all vertical loads must go through the walls. So that’s where failure would happen. The question is: Did they apply the force mostly along the perimeter (as if another 2×2 brick is on top, which is accurate) or down the nubs in the middle (which would bend the top and be less accurate)? I think the answer is the latter, but even then, the failure was on the side, so the top is stronger in bending than the sides are in compression.

By: airshowfan

airshowfan — Wed, 05 Dec 2012 07:06:00 +0000

Indeed. As someone who does fracture mechanics research and who tests structures to understand failure modes, I’m not even going to begin criticizing this description of how the brick failed. (But yes, it was “due to buckling of the walls and then a tear”, which I would think is both obvious and very different from melting. Does an empty soda can “melt” when you flatten it?)

By: Jeremy Quinn

Jeremy Quinn — Wed, 05 Dec 2012 03:19:00 +0000

Since they are material testing Legos, they should go ahead and test the shear and tensile strength too – of individual Legos, and then for connected Legos. I imaging they would only do slightly better than dry stacked masonry in shear though, and have no practical strength in tension. Then we could get to work on testing some Lego building assemblies, and incorporate them into the building code.

By: Jeremy Quinn

Jeremy Quinn — Wed, 05 Dec 2012 01:34:00 +0000

true. tower was only implied, or even imposed on the question by my reading of it (as well as many others). also, its rather well covered anyway on some comments further up the chain here. I would like to see a giant Lego ziggurat tho. that might be limited by lego brick supplies though

By: Halloween_Jack

Halloween_Jack — Tue, 04 Dec 2012 23:48:00 +0000

Find a place on earth with absolutely zero wind at every height along the way, so that it doesn’t get blown over. Good luck with that.

By: sburns54

sburns54 — Tue, 04 Dec 2012 22:58:00 +0000

Yeah, well who’s gonna put the top ones on? Not Felix Baumgartner, he’s over a thousand meters too low.

By: Donald Petersen

Donald Petersen — Tue, 04 Dec 2012 22:30:00 +0000

And they’re referring to Mount Olympus in Greece, not the big-ass volcano on Mars. They are, in fact, two different mountains, not easily confused with each other except for the name.

By: Marko Raos

Marko Raos — Tue, 04 Dec 2012 21:35:00 +0000

Oh, sorry I see the question’s been answered already (scanned the comments for “pyramid” and so missed “ziggurat”…)
Three times as much? 10,777 m… Now we’re talking!

By: yushi

yushi — Tue, 04 Dec 2012 21:29:00 +0000

Well it can be much higher if you start with a wide radius column and end it with a one block column, like they build the real buildings!

By: Marko Raos

Marko Raos — Tue, 04 Dec 2012 21:27:00 +0000

A more interesting question (at least to me and probably the olympian gods keen on dancing) would be “how high a lego pyramid can be built?”
I suppose that it might be quite a bit taller, considering how the weight spreads and all… I’m sure any architect with a geeky bent (or a mathematician) can easily provide us with an answer to this burning question.
(all the necessary data is in the article; 2×2 bricks stacked in the obvious pyramid pattern..)

By: jpgsawyer

jpgsawyer — Tue, 04 Dec 2012 21:07:00 +0000

Well that only really works if lego are considered a fluid. They aren’t and have shear stiffness and so the shape makes a difference.

By: AnthonyC

AnthonyC — Tue, 04 Dec 2012 20:54:00 +0000

Well, of course I’m wrong. But I’m working on becoming less wrong :)

By: Cowicide

Cowicide — Tue, 04 Dec 2012 20:42:00 +0000

You’re all wrong until you also calculate condensation, atmospheric pressure, etc. ^_^

By: Michael Smith

Michael Smith — Tue, 04 Dec 2012 20:37:00 +0000

For a moment there I thought Mount Olympus was Olympus Mons on Mars.