I did the math for Hoop Stress generated by the chamber pressure and based upon a barrel made of AISI4140 you could theoretically go a lot smaller. I also asked the same question on Rim Fire Central and got several answers that bordered on ignorant. The consenses was about 5/16\" was the minimum and the .22 barrel liners are 5/16\". Of course the liners are usually backed up by a drilled out barrel, but I have never heard any reports of a liner bulging which would indicate that the material been stressed above it\'s yeild point.
With that being said the .22LR, contrary to common belief is not a low pressure cartridge. The .22LR is a medimum pressure cartridge at 22,000 to 25,000Psi. According to the official C.I.P. guidelines, the .22 LR case can handle up to 205 MPa (30,000 psi) copper crusher (measuring method crusher conformal) pressure. In C.I.P. regulated countries, every rifle cartridge combo has to be proofed at 125% of this maximum C.I.P. pressure to certify for sale to consumers. In comparison a .38Special\'s chamber pressure is 17,000psi and a .45ACP is 21,000PSI.
http://www.lasc.us/SAAMIMaxPressure.htmSo being the conservative corward that I am, I backed off of the .312\" minimum and considered that the RGG Gatling Gun Barrels are typically threaded 7/16\"-20 which has a root diameter, which by the way forms a vee notch stress riser inviting a failure, of .375\" and they don\'t fail at this size and went with a .400\" minimum for my barrels which a clamped in place using a draw wedge.
nitewatchman