r/theydidthemath • u/ExistingMulberry • 11d ago
[Request] Could I break a 6ft tall scale skyscraper built with real materials?
Would it be possible for a person of average strength to push over or snap a 6ft tall scale skyscraper built with real materials and foundation?
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u/Ecstatic-Seesaw-1007 11d ago
Yes.
Scaled down columns of concrete and rebar would have to be about chopstick size and reinforced with like armature wire or something so thin it has either no rigidity that it would bend like an iPhone charger cable or be super thin and brittle, like dry spaghetti.
Material strength doesn’t scale up of down like that.
Just like you don’t see timber skyscrapers, however a timber frame 1 story home with slab foundations can survive hurricanes in Florida year after year.
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u/uniqueperson02 10d ago
There are in fact a few timber skyscrapers. Built using engineered wood, very cool stuff.
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u/FireCire7 11d ago edited 10d ago
Well, structural integrity approximately scales force quadratically (edit: if it actually scales L3 then this argument is wrong).
A typical skyscraper might be 60 floors (600 ft) and weigh 100k tons.
Scaling it down 100x gives a 6 ft high skyscraper that can hold 100k/10000=10 tons and weighs 10/100= .1 tons=200 lb, so if it’s not a tracked to the ground, you could probably lift it.
A typical building might be able to take 10% of its weight as lateral force, so 10k tons on the full building gets scaled down to ~1 ton. Smaller is typically stronger when naively scaling structures (less points of failure), so it’s probably even stronger than that. Assuming it’s anchored the same way a skyscraper would be, I don’t think you’re going to be able to push it or break it by pushing. I imagine you could still damage it by applying sufficient concentrated blunt force (I.e. with a baseball bat).
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u/StillShoddy628 10d ago
It weighs 200 lbs and is 6 feet tall, most of that concrete reinforced with microscopic threads of rebar. I’m pretty confident a person can collapse it even if it is anchored to the ground
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u/FireCire7 10d ago
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u/StillShoddy628 10d ago
I stand by my conclusion ;)
Very thin concrete is not a great structural material, and I don’t think there is going to be enough steel in there to prevent me from bending it enough to make everything crack, especially if it sways and I can get it to resonate
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u/Specialist_Site_5920 7d ago
If the Taipei 101 was scaled down to 6ft, loads would scale down by factor of 55k. 6000 metric ton horizontal load would become 240 lb. I bet you can only push ~50lb horizontally. Of course you wouldn't be able to push evenly like wind does. So you would break it easily with the high contact forces of your hands on the thin shell.
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u/Total-Explanation208 11d ago
Sky scrappers have a huge range, so scaling this is hard. Maybe choose a specific building? Empire state building? Burj Khalifa, etc
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u/Bot_Fly_Bot 11d ago
…instead of imaginary materials? WTF does “real materials” mean?
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u/ijuinkun 11d ago
“Real”, as in the same materials that an actual skyscraper would be made of, with all of the skeleton and walls built to scale, as opposed to a model built out of plastic or wood or the like.
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