Wallace H. Coxe, in "Smokeless Shotgun Powders: Their Development, Composition and Ballistic Characteristics" published by E.I. du Pont de Nemours & Co. in 1927 and 1931 cites a study in which a fluid steel barrel was cut to 9 and capped, then a series of progressively increasing pressure loads fired. The barrel cap was blown off and barrel burst at 5,600 psi.

Keith: the barrel was from a "12-gauge pressure gun which was equipped with piston for recording pressures". No mention of wall thickness.

This is interesting.

"Measurement of Pressures"
The common method of taking pressures in small arms in this country is known as the Radial Pressure system. A housing is built around the barrel, and a hole drilled through the housing and barrel into the chamber at a distance of 1 inch from the breech and at right angles to the axis of the bore. The hole is then bushed and drilled to a uniform diameter of 0.2250 inch. Then a piston is made the length of the piston hole and 0.2250 inch in diameter. Next the piston hole is lapped to permit the piston to fit snugly without either sticking or getting out of alignment.
In firing the gauge, the piston is inserted and seated, then a lead crusher cylinder is placed on the head of the piston and held firmly in place by a screw and anvil attachment built into the housing. When the cartridge is fired, a portion of the same gas pressure that pushes the bullet through the barrel drives the piston against the lead cylinder and compresses it.
The length of the lead crusher cylinder after compression is naturally less than before the shot was fired and the difference between the original length and the length after compression therefore represents the amount of pressure which has acted upon the lead. Thee exact pressure is read from a table giving a pressure reading for every remaining length reading and commonly called a Tarage Table.
Pressures that are determined at ballistic laboratories are merely relative values and are not absolute values.