Because it would not be useful. Simply put, you have to think beyond the structure. How about water, sewage, heating and cooling, ventilation. How do you provide emergency services in case of fire? How about if the power goes out – can people easily leave. Will people get stuck in the middle of a huge building with no way out?
How will people get in and out in emergencies and in normal times? How do you make enough parking for vehicles. Can someone get from one side of the building to another without walking miles? How do you deliver heavy goods to the very inside of the building?
Buildings must serve a purpose and must do so with some efficiency and benefits. Simply building “bigger and bigger” does not make sense.
The entire point of skyscrapers is to wring out the maximum amount of available square footage in a given plot of land. Since the cost of the land is generally based on the two dimensional footprint, the more floors you add the more you offset an otherwise prohibitive land cost. Taxes might also play a factor here as well.
An arena sized skyscraper would kind of be the worst of both worlds; expensive in both land cost and prohibitive in terms of engineering since it would be immensely heavy. Usually a big wide building such as a warehouse or factory are built in places where land is cheap in which case it’s more cost effective to make the building longer/wider than taller. Tall thin buildings are constructed in high density areas where commercial/office real estate is very expensive and so will be tower shaped to get as much usable space available.
I haven’t seen anyone mention it yet, but Wind. When you get the real tall skyscrapers, they are designed to sway and flex in the wind. When you get broad structures like an arena, not only does it catch a lot more wind, it can’t flex nearly as well. A large rigid structure that can’t respond to winds is a recipe for disaster.
Most skyscrapers are used for either residential, office or hotel space. Something that people highly value when using buildings is having windows and natural light. You can’t charge as much for windowless rooms, even if they are in areas with high real estate prices.
The other element is land acquisition. Acquiring enough land for a stadium footprint is very difficult. It’s insanely difficult in expensive city centres where skyscrapers make economic sense.
Structurally it would be a lot easier to build a wide building. Many of the issues with tall buildings relate to how slender they are; being wider would make things like wind and earthquake loads a lot less critical.
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