This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
From: Jobst Brandt <firstname.lastname@example.org>
> What forces keep the rim of a wheel with pneumatic tires off the
> ground. It obviously can't be the air pressure because that's acting
> from top as well as from below.
As has been pointed out, the casing walls pull on the rim (or its
equivalent) and thereby support the load. The casing leaves the rim
at about a 45 degree angle, and being essentially a circular cross
section, it is in contact with the rim over its inner quarter circle.
At least this is a good representative model. The visualization may
be simpler if a tubular tire is considered. It makes no difference
whether the tire is held on by glue or is otherwise attaches to the
rim such as a clincher is. Either way the tire is attached to the
rim, a relatively rigid structure.
Under load, in the ground contact zone, the tire bulges so that two
effects reduce the downward pull (increase the net upward force) of
the casing. First, the most obvious one is that the casing pulls more
to the sides than downward (than it did in its unloaded condition);
the second is that the side wall tension is reduced. The reduction
arises from the relationship that unit casing tension is equivalent to
inflation pressure times the radius of curvature divided by pi. As
the curvature reduces when the tire bulges out, the casing tension
decreases correspondingly. The inflated tire supports the rim
primarily by these two effects.
Tire pressure changes imperceptibly when the tire is loaded because
the volume does not change appreciably. Besides, the volume change is
insignificant in small in comparison to the volume change the air has
undergone when being compressed into the tire. In that respect, it
takes several strokes of a frame pump to increase the pressure of a
tire from 100 psi to 101. The air has a low spring constant that acts
like a long soft spring that has been preloaded over a long stroke.
Small deflections do not change its force materially. For convenience
car and truck tires are regularly inflated to their proper pressure
before being mounted on the vehicle.