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The most obvious question must be WHY!
WHY would anyone want to build a skyscraper ONE KILOMETRE high? (It was originally intended to be ONE MILE high!)
The problems in building such a tall tower are almost countless. Imagine the pressure needed for water distribution, how long it would take to get to the top, or even the complications of the sewerage system.
I hear that to reach the pinnacle several different lifts will be needed as the chains begin to stretch after a certain distance. This means taking one lift to a first level, then taking another one, and then (if one was mad enough to live at the top) taking a third. Anyone buying the penthouse apartment would need to spend quite a while in three separate lifts to get home; you wouldn't want to forget to buy the cat food!
Saudi Arabia is not short of empty space (unlike London or New York), so going 'sideways' is not an issue.
This silly billion dollar Kingdom Tower is just a big ego-trip for Prince Al-Waleed bin Talal. He wants THE TALLEST; perhaps he has shortcomings in another area.
Maybe, when it's finished, the whole caboodle will be blown over by a sudden gust of desert wind; you wouldn't get Cro up there, that's for sure!