r/theydidthemath • u/ExistingMulberry • 10h 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/FireCire7 8h ago edited 7h ago
Well, force has units kg*m2 /s2 , so scaling length approximately scales force quadratically.
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/Ecstatic-Seesaw-1007 26m 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/Total-Explanation208 10h 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 10h ago
…instead of imaginary materials? WTF does “real materials” mean?
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u/ijuinkun 9h 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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