There are several formulas for calculating hoop stresses. Without getting too deep over my head an illustrative example can I think be given by using one known as "Lamé's formula for cylinders subjected to high pressure. Using stress (S), presure (P), outside diameter (D), & inside diameter(d) we have the following formula; S = P times D²+d²/D²-d². Utilizing typical end of chamber dia for 12ga of .800" with .100" walls & a 7000K psi gives a figure of 31889psi as to what the bbl would be stressed to. (I realize the end of chamber is not actual high pressure point, but will still serve as a comparsion).
Switching formula around to work for P (P = S x D²-d²/D²+d²) using 31,889 for S and .685 for d for 20ga & maintaing .100" walls gives a figure of 7995psi for the 20ga pressure necessary to stress the steel to the same level as the 7K load in 12ga.
16ga would work out to 7,556psi (d=.732).
