If I knock down this building, how many other buildings do I knock down as well?

Question

Buildings are 32,000 feet tall and a quarter of a mile wide and long. They are made of concrete, glass, other standard building equipment, and some hand-wavy metal that makes up the main support structure. You can assume really strong steel if that helps. Now take this building, and copy+paste it right next to each other with a 300 foot gap between it and the next. Now make a grid of these spread out around the entire earth. Once that is done, you've pretty much built the world I'm writing about.

For some reason, somebody decided to blow up one of these buildings, pretty much just blowing out the bottom supports and the whole thing came crashing down. Now, being only 300 feet from other buildings and almost 6 miles high, this is sure to knock over other nearby buildings. So what I want to know is,

How big of a domino effect is there before it stops and the dust settles?

Answer 1

In your case, I think close packing of such buildings is actually a good thing and will prevent a disaster from happening.

Consider cutting down a tree in a meadow. What happens when you slice through the trunk? Right: it topples and falls to the ground.

What happens when you cut down a tree in a dense forest? Right! It falls onto another tree or two and is more or less suspended above the forest floor. It never actually falls to the ground.

Your city will be the same. You've posited a super strong material that holds the build upright and rigid even though it's several miles tall. All the other buildings are the same. Miles tall and incollapsible without application of considerable external force.

What's going to happen is, having "blown out the bottom supports", the otherwise rigidly intact building is going to gracefully tip over, crash onto a neighbouring building or two and then come to rest, never actually falling over. This is because the other buildings are also super strong. The additional stress, distributed over their own footings, is easily managed. There will be relatively minor external & cosmetic damage, but no domino effect.

Note: the buildings it crashes into won't even notice much, structurally speaking, because they're all built to withstand earthquakes.

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So I got bold and wandered into the minefield that is mathematics. I found this Right Triangle Maker and input the numbers. 32000 feet high by 300 feet for the base (the distance between buildings). The damaged building will only just barely shift: there will be a 1 degree tilt. Leaning tower of Pisa has a 5.5 degree tilt.

I'd say, people inside won't even notice!

Answer 2

Total Domino!

Your buildings are just too close together!

Even if your building collapse perfectly straight down, and your building once collapsed only occupies 10% of its original volume, and there is no violent ejecta to the sides(there would be!) the resultant pile of debris is wider than the available footprint under and between buildings.

Thus the collapse of one building would inevitably undercut the foundation layers of all the adjacent buildings, causing them to collapse too. Chain reaction!

Also bear in mind that once you have a couple cubic miles of building falling at the same time, the resultant earthquake will drop everything around it, too! The Twin Towers' fall generated earthquakes of 2.1 and 2.3 each. And they were 24 times shorter than yours! Earthquake intensity is proportional to energy. Energy of falling objects is proportional to mass * height. Your towers are 950 times the volume, and 24 times the height, of those towers.

Answer 3

Completely Arbitrarily Up To You

You have come up with an arbitrarily strong material to support these skyscrapers which is also, incidentally, arbitrarily rigid, since they are vertical columns of sufficient height to need to resist quite a bit of wind. Therefore, the rresults of an explosion are entirely up to you. I quickly mocked up the dimensions of a small 10x10 block of these buildings from your question in a 3D model:

It's certainly close enough for a catastrophic domino effect, if the colossal weight of one of these buildings is enough to overcome the stability of its nearby structures.

It's also close enough for them to support it without it deflecting more than a couple of degrees, if they are able to support it.

The ludicrous weight of these things cannot be overstated. At 1000 times the total volume of the original WTC towers, you can expect this thing to have a total mass of 500,000,000 tons – greater than the combined mass of all humans alive today, equal to 75 Hoover Dams, or 4 times the weight of all the buildings in Manhattan combined.

Answer 4

It depends on the way you blow them up some demolitions produce more sideways force than others. It depends on the handwavyness of the supports and the strength of the structures in general and how difficult they are to demolish. But I imagine the destruction would be huge, with an aspect ratio of 24:1 and the potential energy from 6 miles up I imagine that most of the buildings would be destroyed

Answer 5

It depends (up to you)

The key factor is the relationship between tensile and compressive strength reserves.
If a slab bends to the right (because the neighbouring slab is pushing it or because of structural damage), there will be tension on the left side and pressure from the right. Metal tends to have better tensile than compressive strength, so it's the right side where the building may collapse; concrete has much better compressive than tensile strength, so a concrete building will rip at the left (making it susceptible to sideways forces that might start rotating the building, putting more concrete under tension).
This is the reason why reinforced concrete is popular: Under tension, the thing will expand slightly, then the steel strands will be pulled and hold it together; under compression, the concrete will take up the pressure. (Prestressed concrete is where the steel strands are made to have some tension even without load, by pulling them apart before the concrete sets.)

If the planners were worth half their money, the will have considered the situation and made sure the necessary reserves are in.
A catastrophe is still possible, even likely, for a number of reasons:

• Buildings at the edge of the city need to withstand wind force (inner areas do not, the neighbouring buildings will have forced the wind up). This leaves room for mixups where a rim building accidentally gets built with the weaker inner-city plans.
• The building company might not have been honest and used substandard materials with less strength than advertised.
• The company was honest but its employees were not.
• Buildings need maintenance. Water and frost can get in if you don't do this, meaning the concrete will weaken or even crumble. This doesn't mean the building will fall, just that the planned reserves won't be there when hit by the neighbouring building.

There is a number of plot points you can pull out of this:

• If different areas of the city have different economical strength, maintenance will be on different levels. You can have a plot where the poor districts fall like domino but the domino stops at the border to the next wealthy district. People will notice, making them susceptible to conspiracy theories of all kinds (notice how the unusual disintegration pattern of the WTC has caused a CT proliferation).
• If the city was built in a piecemeal fashion, you will have rows of stronger-than-usual buildings inside the city. This will break the poor-wealthy pattern, making people even more confused.
• Natural hazards can make buildings topple, too.
• Buildings of that height have a ginormous weight; you need bedrock under them to prevent them falling over (or you have to dig down to bedrock for the foundations). If the geologists made a mistake and the ground is softer than expected, the buildings may have started to lean even before disaster strikes. Needless to say that this will make falling over much easier. (Fun fact: New York City is built on a slab of granite. Speculation: NYC's proliferation of skyscrapers was only possible with that stable ground.)

BTW here's the frame challenge: If you want to be science-based, the whole thing might not work because no rock is strong enough to withstand such weight.
Hmmm... maybe they're forced to extend the city forever, because rock will fracture more easily at the stress border (remember the thing about pressure and tension? rock is like concrete in this regard, and having high pressure right next to no pressure creates tension because the pressured rock will be compressed, you'll have shear at the border).
The other option would be to have lower and lower buildings towards the border, to distribute the pressure differential.
I still don't know if granite is strong enough to withstand that kind of pressure, a geologist would be able to answer that.