This is what I am telling you and any engineer knows this as well. The only time an I-beam is stronger than a solid beam is when it has greater dimensions. No. The only time a solid beam has the strength, of even a much smaller cross-sectioned I-beam is in direct tensile or compressive force. The weight of the solid beam makes it weaker because it has to support it's own weight over distance. Granted this doesn't apply to the average length of our barrels. But, yeah, The shape of the beam makes tons (pun intended) of difference. Same with the shape of a barrel.
However, I-beams are far more cost effective, I beams are cost effective because they use less material than a solid beam. however, they cost more to make. and sufficiently strong for their purposes. I-beams are used because they make a more efficient use of the material. Ding Ding!
This is not a same principle as fluting a barrel though, as I mentioned above. A more accurate representation would be taking an 8in by 8in solid piece of steel of whatever length, and then whittling out two sides until you have an I-beam shape. The original solid square beam would be considerably stronger. Or, grinding out all the material you wouldn't use in diagonal or diamond patterns. The piece is lighter, yet just as strong in the directions you need it.
As mijp5 said earlier, if you could take a barrel and somehow introduce the flutes into it without removing any material, it would definitely be stronger. Naturally, this would remove the weight-saving effect of flutes, which is arguably it's most desired property. That's easy...run it through a roller preformed for flutes, material moved. Not added or removed. It's a materials process thing. Engineers use it a lot. M-16 mags are good example. Not only do the ribs act as guides for the cartridges, they strengthien the magazine.
Don't get me wrong, I'm not just bashing flutes. I like them. I think they are aesthetically pleasing and most of my rifles are for hunting where any weight savings I get are much appreciated. But stronger, they are not. I'm not bashing flutes either. Just saying that for equal outer diamters, they are as strong. For larger diameters with the same amount/kind of steel, they are stronger.
To Milo, as an extreme example, take a piece of 1in pipe vs a piece of 1in round stock, and it's easier to see why one with a hole through it is easier to bend. But I agree, when just picturing it in my head, a drilled blank seems like it would be harder to bend. I would have to say that analogy is not the same. It's the opposite of what we are talking about