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Pneumatic structures obtain their stability through internal pressurization.  It is basically a bubble.  The same way that water and soap bubbles stabalize, so do pneumatic structures.  An English engineer by the name of William Lanchester was the first to attempt to apply this bubble, or balloon principle to a building in 1917.  Only now pneumatic structures are beginning to become well known forms of construction.
An air-supported structure consists of a single membrane enclosing a space, which is supported by a small internal pressure difference.  The air inside is at a pressure higher than the atmospheric.
An air-inflated structure is supported by pressurized air contained within inflated building elements.  The air inside and the atmospheric pressure stays the same.
These are some of the formulas used to find the effect of the wind on pneumatic structures.
The manner in which an air-supported structure meets the ground is a critical part of the design.  The connection must be airtight.  The biggest structural problem is that the structure exerts a large uplift force and also, depending on the exact shape of the structure, horizontal forces on its supports.
One of, if not the most interesting problems dealing with a pneumatic air-supported structure is deciding on the profile of the structure.  Most long-span structures are low-profile and use cable-net membranes.  Small-span structures are high-profile structures, the majority of the time.
A common concern with pneumatic structures is what happens if the membrane is punctured.