Whenever we discuss barrel bursts, wall thickness, and tensile strength it is important to clarify that tensile strength is only a part of the equation for estimating bursting pressure. If the barrel is made of Winchester Nickel Steel with a 100,000 psi tensile strength, that does NOT mean that it will withstand a 10,000 psi load by a factor of 10.

Barlow's formula P=2 S t / D
P=Bursting pressure in psi.
S=Tensile strength of material in tube wall.
t=Wall thickness in inches.
D=Outside diameter in inches.

Barlow’s refers to a pipe capped at both ends with a static pressure (a pressure cylinder). Shotgun barrels are not designed to be pressure vessels as one end is open and the pressure rises and falls quickly.

Burrard used the Alger Burst Formula, and there are others
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID

A mechanical engineer friend with interest in barrel failures explained that the Hoop Stress Formula doesn't reliably predict shotgun barrel failure either
https://www.engineersedge.com/material_science/hoop-stress.htm
Shotgun barrels are “thin wall cylinders”
hoop stress = pr/t
p= pressure; r is the inside radius; t is the wall thickness
He was working on setting up a hydraulic pressure testing apparatus for barrels, but work and marriage got in the way.

Wallace H. Coxe, in "Smokeless Shotgun Powders: Their Development, Composition and Ballistic Characteristics" published by E.I. du Pont de Nemours & Co. in 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 only 5,600 psi.

A study by the Royal Military College of Science, sponsored by the Birmingham Proof House and the British Association for Shooting and Conservation, showed that an obstruction by 2 fibre wads (total weight of 4 grams) was sufficient to bulge or burst a 12 gauge barrel shooting a 28 gram (slightly less than 1 ounce) load. Peak pressure occurred 22mm (.866”) past the leading edge of the obstruction.

OTOH there are many studies documenting how difficult is can be to burst a barrel, including Greener's attempts in 1886
http://books.google.com/books?id=inQCAAAAYAAJ&pg=PA92

and of course The Double Gun & Single Shot Journal “Finding Out For Myself” series by Sherman Bell with technical assistance from Tom Armbrust esp.
Vol 18, Issue 1, Spring 2007 -
Destructive testing on a Damascus barrel with thinned walls; calculated by O.D. - I.D. and not measured.
Destructive testing using various obstructions, including a 20g shell.
Destructive testing using a shell loaded with 3 1/4 Drams by volume or 56 grains of Unique (similar to “Infallible”) with 1 1/4 oz. shot. The chamber burst with the first shot. The 3 1/4 Dram Equivalent load is 24 grains of “Infallible”, and 56 grains estimated pressure was 50,000 psi.

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