As part of a discussion on tire inflation and cold weather I spotted one special post. With the permission of the author Cushing Hamlen, who has a PHD in engineering who said his education translates into many, many classes in thermodynamics, including statistical thermo. Which is a real mind bender (conceptually and mathematically).
Here is what he said about tire inflation supporting the load:
"A plane wing flies because of two things: the curved top of the wing
which produces lower pressure on the top of the wing than on the bottom
(the Bernoulli effect - which is is a pressure thing and has nothing to
do with density), and the angle of attack of the wing (where, when the
front of the wing is tilted upward and the wing pushed forward, air
hitting the bottom of the wing is deflected downward, which exerts an
upward force on the wing (newtons third law - when an object exerts a
force on another object, the second object exerts an equal and opposite
force on the first - strictly a density/mass thing, and has nothing to
do with pressure).
Your density altitude thing is mostly a result of the angle of attack of a wing allowing it to "push" downward on the air - the denser (colder) the air, the stronger the upward force (because the air molecules are closer together, and the wing pushes more molecules downward for a given amount of forward motion .... kind of like throwing downward two baseballs versus one ... it takes more force to throw down two of them.
Inside a tire, there is no such "pushing" of air, and so its density becomes a non-issue. The ONLY thing acting inside a tire is the pressure the air exerts on the tread, walls, and rim of the tire. This works because a given pressure pushing on the tire "stiffens" the tire, and limits how much the sidewalls of the tire will deflect for a given load. If the pressure is lower, the tire sidewalls are not held stiffly in place, and can deflect more (very much like a very underinflated balloon is easy to squeeze and deform, but a highly inflated balloon is very stiff, and difficult to deform - it can support more weight without deforming.
To understand pressure - you really need to understand statistical thermodynamics .... but the simple explanation is that pressure is the result of lots and lots of gas molecules hitting the inside of the tire .... it is nothing more than that. It is the summation over time of many, many small "balls" (molecules) each with very very small mass and momentum hitting a wall. So .... the fewer the number of molecules inside the tire (like letting air out of the tire), the fewer will be hitting the wall in a given time, and the pressure is lower (the opposite is true when you add air to the tire.
As for temperature - it turns out that the speed a gas molecule flies through space is directly dependent on the temperature (the maxwell-boltzmann distribution). So for a tire with a certain amount of air in it, if the temperature goes down, the speed that the gas molecules are moving at goes down, and they each hit the inside of the tire with less momentum - and the pressure (and thus stiffness of the tire) goes down - for a given amount of weight on the tire, the tire deforms more. The tire may technically be supporting the weight, but upon each revolution it deforms more than if it were supported by a higher pressure - and it is this ongoing increased amount of deformation that causes increased stress and damage to the tire."
So I hope this clarifies why I have been saying for years that it is not tie tire construction that supports the load but the air pressure.
If you doubt this, then please explain where the "Construction/Load Capacity" tables are as all I can find are "Inflation/Load Capacity" tables.