rpenmanparker 

Rob, concerning the above assertion: I want to test a contrary idea on you to get your response. Of course the spokes are in tension and the spokes nearest the point of stress (say contact with the road) can't keep the rim from compressing i.e. moving upward in response to the stress. But don't spokes further away from the place where the stress is applied provide a dimensional limitation? If you think of a half-circle arc of the rim, when the bottom on the ground tries to move inward/up, it pushes the ends of the half-circle outward. but that outward movement IS constrained by the spokes in tension.

Such geometric constraint is a commonly used feature of many constructions. In fact it is just what makes the strength to mass ratio of the I-beam you reference possible. Another example is the complex shaping of 16 oz plastic juice bottles. All the curves and creases strengthen the bottle to crushing forces much better than a perfectly smooth surface would without the need for the bottle to be heavier. An even more significant example is all those decorative creases on the sheet metal of modern automobiles. Sure they achieve a certain look, but they also strengthen the body to deflection under impact without adding weight.

Similarly the OTHER spokes in the wheel, not the ones right near the point of stress are what help to keep the rim from flexing inward by limiting the motion outward of the rim sections they affect. And one would expect that more spokes, shorter spokes, and/or heavier gauge spokes would be more effective in accomplishing that.

I don't think it is just the characteristics of the rim itself that keep it from deflecting.