But an 8x8 I-Beam would not be any stiffer than an 8x8 piece of bar stock. it would weigh much less, thus the appeal.
Something that I was told many years ago by a very trusted machinist. He told me that the less machining one could do to a barrel after the bore was cut, the better the chance of the bore remaining more true. I was told, and it makes sense, since steel is grain oriented, it will have inconsistencies, and that machining relieves any stresses present in the material if there are any present in the area being removed. The more one cuts out of a piece of material, the more they risk relieving these stress points. Now that doesn't sound too bad until you figure that the bore is already cut, and could be effected. Even if not when it's cold, after it's heated things could move even more than they originally would have.
For this reason, he would never have had a barrel fluted. I also so the point of a fluted barrel being no more rigid than a round barrel of an equal diameter. I do see how a fluted barrel of a larger OD could be more rigid, or just as rigid, as a smaller barrel while weighing close to the same. That makes sense.
as for the surface area thing. I have seen fluted barrels that no doubt gain some surface area. I see what the poster above is trying to relate, that if you merely dent a round object intermittently, then you really haven't changed the surface area any. But most flutes are cut a tad deeper, so some gain would be present. Enough to make a difference? I make no claims there.