This is a bit off-topic, but they are called "wide flange beams" not "I" beams. If you think there isn't a difference, try calling it a "gun" and not a "rifle" when talking to a drill instructor! [abused]
Saying that a fluted barrel is stiffer is a bit misleading, and I'll use the wide flange beam as an example. If you had a solid shaft of steel and a wide flange with the same veritcal and horizontal dimensions, the solid shaft will deflect (bend) more due to the force of gravity. In effect, the weight of the shaft itself is pulling it down because there is more material for gravity to pull on.
Essentially (and this is simplified considerably) what makes the cross section of the steel stiff (i.e. minimize deflection) is the veritcal and horizontal dimensions and the [bold]profile[/bold] of it, not the mere amount of material.
I would take issue with the comment that the I beam is stiffer due to the increased surface area. However, I think we all are on the same page as to why fluting makes the barrel stiffer- more efficient profile.