Are Fluted Barrels More Rigid Than Standard Ones? This seems to be quite a debated topic in the shooting community and is something I'm not sure about.
A fluted barrel is a barrel that has grooves milled into it to reduce weight, help it cool faster and supposedly to make it less flexible (see picture below)

I don't see how removing material like this would make it more rigid, because surely by removing mass the barrel would have less inertia to help keep it rigid when under the stress of firing, unless it had the same effect as corrugated sheet metal. For example if you had a flat strip of material compared to a corrugated piece the corrugated piece would have a lot less flex. 
So if you had two barrels made of the same material being the same length and width with one being fluted and the other being a smooth cylinder which would be more rigid under the stress of firing?
(Sorry if this is not how you should post on here, I normally only use StackOverFlow.)
 A: If you have the same mass, then the fluted beam will be more rigid because the second moment of area is larger - in the same way that an $\mathrm{I}$ beam is more rigid than a circular rod of the same mass.
In the case of a gun barrel, lighter weight helps in a number of ways - portability, ability to hold the gun still as you aim... but making it lighter will make it less rigid. So people do a few different things.
First - the barrel is thicker near the stock: the internal pressure is higher there (so it needs to be stronger), but so is the bending moment (induced by the recoil). A little bit of bending there will cause a big deviation of the muzzle and you want to avoid that.
Second - they can add a bit of mass at the tip of the barrel (near the muzzle). This increases the moment of inertia; when done right ("tuning"), it will actually make the gun more accurate as well (see for example this earlier answer I wrote on that topic).
A: A 'more rigid' barrel is actually a relative question. If two barrels start with the exact same profile and then one is fluted, and only the resistance to bending is measured, then the difference is extremely small. One barrel will be significantly lighter, but generally not more rigid since the rigidity is largely a function of the exterior cross section.
The reason barrels are fluted isn't to make them more rigid, but reduce the weight of an already-rigid barrel that would otherwise be too heavy for its application. The enhanced cooling of additional surface area and shorter distance from the heat source (the bore) and the outer barrel surface is another reason, 
I recently fluted a barrel that started at 5 lbs 3 ounces. 6 flutes (1/4" ball endmill, 1/8" deep, 13" long) took about 7 ounces off the barrel, weight savings is bigger that it looks.
