The Mile High Illinois, Illinois Sky-City, or simply The Illinois was a proposed mile-high (1,609 metres/5,280 feet) skyscraper, envisioned by Frank Lloyd Wright in 1956. The design, intended to be built in Chicago, would have included 528 stories, with a gross area of 18.46 million square feet (1.71 million square meters; 171 ha). Had it been built, it would have been the tallest building in the world.
This is arguably the most famous of the semi-serious visionary buildings meant to be an alternative to the increasing urban sprawl occurring in most cities. None of these have, before now, been viewed as financially feasible.
Wright believed that it would have been technically possible to construct such a building even at the time it was proposed. At the time, the tallest skyscraper in the world was New York's Empire State Building, at less than a quarter the height suggested for the Illinois. It probably would have been possible to erect a self-supporting steel structure of the required height, but there are a number of problems which occur when a building is that tall.
The material used for towers at the time, steel, is quite flexible. This causes the tower to sway substantially in the wind, causing discomfort for occupants of the higher floors. Though Wright acknowledged this problem in his original proposal, he claimed the tripod design of this tower (similar to that of the CN Tower) combined with its tensilized steel frame and the integral character of its structural components would counteract any oscillation. It is also possible this could have been solved by placing a counterweight somewhere within the tower such as in the Taipei 101.
Also, the late 1990s and early 2000s has seen substantial increases in the load-bearing strength of concrete, making it a possibility to build entirely in this less flexible material.
The space needed to service the elevators (needed to reach the higher levels) would occupy all of the space available on the lower floors, thus defeating the purpose of the building's height. This was complicated by Wright's slender design. This problem has also been addressed in smaller buildings, such as in the Taipei 101, by using double-deck elevators. In the World Trade Center, the building was divided into three sectors, each with its own sky-lobby, where occupants changed between large express elevators and smaller local elevators. However, even with both of these measures implemented, the problem would still exist. Wright's solution was five-story elevators, running on ratchet interfaces located on the outside of the building (presumably on the unseen side in his painting) to conserve building space.
Another concern is fire safety. The need for emergency stairwells would bind much of the available space in the lower floors in a similar fashion. This could be overcome by designing elevators to remain operational during a fire.
Albeit at a smaller scale, the same problem as with the elevators is encountered with water and sewage. A possible solution would be to recycle the water used in the upper floors, although this is easier today than it was in the 1950s.
(Information comes courtesy of the Wikipedia amongst other sources.)