The old Hubert H. Humphrey Metrodome, Minneapolis, Minnesota, United States (Roof deflated January 18, 2014, demolished in February 2014)in Minneapolis dome was supported by air I know.
some more.
Carrier Dome, Syracuse, New York, United States
Tokyo Dome, Tokyo, Japan
the old Pontiac Silverdome
many more in link
https://en.wikipedia.org/wiki/Air-supported_structure
Advantages:
Can be engineered to attach to a pre-existing structure
Considerably lower initial cost than conventional buildings
Lower operating costs due to simplicity of design (wholly air-supported structures only)
Easy and quick to set up, dismantle, and relocate (wholly air-supported structures only)
Unobstructed open interior space, since there is no need for columns
Able to cover almost any project
Custom fabric colors and sizes, including translucent fabric, allowing natural sunlight in
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Among its many uses are: sports and recreation facilities, warehousing, temporary shelters, and radomes. The structure can be either wholly, partial, or roof-only air supported. A fully air-supported structure can be intended to be a temporary or semi-temporary facility or permanent, whereas a structure with only an air-supported roof can be built as a permanent building.
What will be the largest air-supported dome in the world is currently being constructed on the IBM campus in East Fishkill, New York. Scheduled to open in summer of 2018, the Sports KingDome will feature a
160 feet (49 m) high ceiling and 350,000 square feet (33,000 m2) of training space for athletics. Currently the largest air-supported dome in the world is "The Dome" in Anchorage, Alaska at 180,000 square feet (17,000 m2).
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