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Not a bad idea -- but the ground is too weak for this design.
A rigid, steel core with diagonal bars would make this skyscraper super stiff in the wind. The diagonal bars transform the rectangular core into a series of triangles -- and triangles are one of the strongest shapes used in construction today. Unfortunately, this super-stiff design requires a lot of steel -- and steel can be quite heavy. The ground is too weak to support a really heavy building. There's a different, lighter design that you can use to brace this skyscraper against wind forces.
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