There are several bursting formula:

Barlow's Formula P = 2 x S x 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.

Burrard preferred the Alger Burst Formula
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID

Lame Formula
Burst pressure psi = Ultimate Tensile strength x (OD squared – ID squared) / OD squared + ID squared

Mechanical engineers (plural) with whom I have discussed barrel bursts explained that all 3 apply to a pressure vessel; a pipe capped at both ends.
An UNOBSTRUCTED shotgun barrel is very very briefly "obstructed" by the ejecta, which very quickly begins to move in response to the gas pressure, which then rapidly falls.

[Linked Image from photos.smugmug.com]

SO the bursting formula do not work well for non-obstructional shotgun barrel bursts

Anywhere along the length of the tube where the gas pressure exceeds the bursting pressure, the burst becomes the "path of least resistance."