The point is that stiffness is provided by reducing the degrees of freedom that would cause flopping to those that would require you to "stretch, shrink or tear" the piece of pizza. As a result, in cases where your stresses are negligible compared to the yield strength of your material this approximation accurately predicts the behavior without resorting to FEM or in depth analysis.
While I agree that there are more complicated theories that are correct for more diverse circumstances, I think it's tremendously valuable to find the simplest models that describe the easiest situations if only for the purposes of developing intuition. I must admit that this is very much a physicist's perspective, though.
This has nothing to do with yield strength, which is relevant only where the materials "yields" or plastifies. This is just linear elastic beam bending theory - you have two different beam cross sections in either case with two different moments of inertia. See also my other comment:
https://news.ycombinator.com/item?id=8276173
You could fold a piece of fabric like you do the pizza, and it will not keep its shape.
Sorry, I meant it depends on the elastic modulus. Mechanics was a while ago.
If the model matches the prediction, the model works. The argument is only over what regime. In this regime it matches.
If you read the article it specifically mentions it applies to paper. I expect it would apply to many fabrics as well. When it doesn't it's because it's outside the regime of the model because stress enables significant "stretching".
You could use beam theory as well, and I would be surprised if the author hasn't heard of it, but that doesn't mean it's the only technique available.
While I agree that there are more complicated theories that are correct for more diverse circumstances, I think it's tremendously valuable to find the simplest models that describe the easiest situations if only for the purposes of developing intuition. I must admit that this is very much a physicist's perspective, though.