A "pencil" style building in New York City appears, in my view, to be a great picture of the limitations of technology in architecture. How so?
Well, the residents are noticing cracks in the concrete already, indicating that the engineers' work to support the nearly 1400' tall building is insufficient. What strikes me is that the building is only 100 feet wide, whereas the similar-height Sears Tower (*) in Chicago is over twice that width. The key issue here, structure-wise, is that the lateral strength/rigidity is proportional to the square of the outer dimensions. This means that, all else the same, the Sears Tower is four times as robust as 432 Park Avenue, and the stresses on the lateral support beams that much greater on 432 Park Avenue. It makes a difference.
A side note here is that since this is not an office building, but a residential building, what we have is a building where the inner hallway/atrium around the elevators is going to be up to 35 feet from the windows. In contrast, at a truly big mansion, Buckingham Palace in London, the windows are only about--except for the great hall--about twenty feet from the inner hallways, I'd guess.
In other words, when you try to go too tall--I'd guess a ratio of height vs. width of 10:1 or greater--you get to a point where a wonderful apartment becomes, due to a lack of proximity to windows, an unlivable closet. So if we're talking the "Buckingham Palace Rule", we are talking an approximate upper limit of about 500 feet tall or about 40 stories. You could get some additional room for height by using the old World Trade Center's center zone for elevators and utilities--probably up to about 700 feet or fifty stories--but all in all, you're limited if your goal is to provide liveable space.
It is worth noting as well that there are additional economic/engineering and practical reasons not to build too high. Building 100 stories high costs about five times as much per square foot as building five stories or less, and how many people really want to be looking out from their 50th story window at....someone else's 50th story window?
* Yes, I know it's called the Willis Tower now, but like any Chicagoland native who values the past, my view is that it keeps its original name, no matter what the corporate types say.
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