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Old Posted Jul 5, 2011, 3:06 AM
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How high could you build a stack of Legos?

I was fiddling around with some idle calculations when I started to wonder how high you could stack Legos before they would deform (ignoring, of course, stability and all other forces but compression). I can't find any quoted spec of the compressive strength of Lego blocks, but they're apparently made from Acrylonitrile butadiene styrene (ABS), which is listed as having a compression strength of 9000 psi. If we ignore subtleties and just use this number, I figure the total weight (above the base) has to be about 850 lbs, translating into roughly 308,000 blocks, giving a height of about 9,600 feet.

Since I'm relying on info I had to track down through some pretty obscure sites, and in particular a material compression force rather than a structural one, I take zero responsibility for the accuracy of any of these figures.
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Old Posted Jul 5, 2011, 3:52 PM
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I'm assuming compression strength is based upon a solid block of the material. As we know, Lego is essentially hollow.
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Old Posted Jul 5, 2011, 4:08 PM
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Quote:
Originally Posted by Tony View Post
I'm assuming compression strength is based upon a solid block of the material. As we know, Lego is essentially hollow.
As noted, I couldn't find the compression strength spec for Legos. The spec for the material is all that was available. Ironically, I ran into tons of bulletin board postings where people complained about their inability to find Lego specs anywhere.
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Old Posted Jul 5, 2011, 9:51 PM
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Quote:
Originally Posted by Troubadour View Post
As noted, I couldn't find the compression strength spec for Legos. The spec for the material is all that was available. Ironically, I ran into tons of bulletin board postings where people complained about their inability to find Lego specs anywhere.
This suprises you?

There a several physical problems here, but the three primary issues I can see are overturning (you are creating a giant vertical cantilever), lateral wind pressure and base shear.
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Old Posted Jul 6, 2011, 1:52 AM
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are you using tower cranes to assemble these fraction-of-inch blocks thousands of feet in the air?

as plinko said... base sheer and lateral g's would be my two primary issues with that.
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Old Posted Jul 6, 2011, 9:11 AM
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Originally Posted by plinko View Post
This suprises you?
Yes, kind of. I had thought Legos had a big DIY cult around them that would have posted all sorts of obscure physical specs, but nope - it was a chore to even find reliable length measurements.

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Originally Posted by plinko View Post
There a several physical problems here, but the three primary issues I can see are overturning (you are creating a giant vertical cantilever), lateral wind pressure and base shear.
Yeah, but that wasn't the subject of inquiry - it was how high you could build before compression forces would deform the base: A question I haven't even really answered because I couldn't find the right spec. What I was able to figure is a maximum. But as for these non-vertical forces, if you were to actually build it, it could be as thick as you want to deal with torques and whatnot, as well as using extraneous stabilization measures (I believe the current record holder for a Lego tower uses guy wires).

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Originally Posted by brian.odonnell20 View Post
are you using tower cranes to assemble these fraction-of-inch blocks thousands of feet in the air?

as plinko said... base sheer and lateral g's would be my two primary issues with that.
Who cares? No one's doing this - I was just curious what Legos are capable of in themselves.
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Old Posted Jul 6, 2011, 7:39 PM
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Quote:
Originally Posted by Troubadour View Post
Yeah, but that wasn't the subject of inquiry - it was how high you could build before compression forces would deform the base: A question I haven't even really answered because I couldn't find the right spec. What I was able to figure is a maximum. But as for these non-vertical forces, if you were to actually build it, it could be as thick as you want to deal with torques and whatnot, as well as using extraneous stabilization measures (I believe the current record holder for a Lego tower uses guy wires).
Yes, but such an endeavor isn't possible in a vacuum and thus those forces have every bit as much an effect as pure dead load.
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Old Posted Jul 7, 2011, 3:25 AM
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What about self weight? Among a million other things, something to be taken into account is that a 9,600 foot Lego pyramid is going to weigh a fuck ton.
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Old Posted Jul 7, 2011, 5:45 AM
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^^Self weight is the gist of Troubadour's question.

Lets take a 1x1 brick for a simple example.


http://www.clear.rice.edu/elec201/Book/legos.html

Measuring a brick myself, it looks like the walls of each brick are 1.5 mm thick.
That gives a cross section for a 1x1 brick of 8mm x 8mm - 5mm x5mm, or 39mm^2.

9000 psi converts to 6.33kg/mm^2.

39mm^2 x 6.33kg/mm^2=267kg that a 1x1 brick can support.

267kg/.00000108kg/mm^3 =228,600,000mm^3

Approximating the stack of bricks as a hollow column,
228,600,000mm^3/39mm^2=5,860,000mm=5.86km high stack.

As others have noted, this figure will be further limited by other considerations such as buckling and overturning. Unfortunately, I'm too tired to consider them right now.
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Old Posted Apr 2, 2015, 4:10 PM
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Dr. Ian Johnston from Open University has calculated that the 2x2 bricks would be able to support a tower

Quote:
So, 375,000 bricks towering 3.5km (2.17 miles) high is what it would take to break a Lego brick.
http://www.bbc.com/news/magazine-20578627

Hat tip to Randall Monroe's What if column book.
http://store.xkcd.com/pages/if-you-r...e-what-if-book
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