I've got a mechanical engineer on this, but here are some formula for a thick wall (wall thickness greater than 1/10 - 1/20 ID) pressure vessel (again a closed system under static pressure)
Our subject Remington 1894 barrel:
Wall thickness at the end of the chamber was .119"
ID at the end of the chamber = .815”
OD = ID + wall thickness X 2 = 1.053”. This does not include the brazed flats which obviously provide significant additional metal/strength to the breech, but the barrel blew out laterally.
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.
Burst pressure = 2 x 54000 x .119" divided by 1.053" = 12,205 psi
Burrard quotes Alger Burst Formula
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID
54000 x 3(1.053 - .815) / 1.053 + 2 x .815 = 14,370 psi
Lame Formula
Burst pressure psi = Ultimate Tensile strength x (OD squared – ID squared) / OD squared + ID squared
54000 x .446 / 1.774 = 13,576 psi
Short version of wave pressure per Burrard is that it can be more than 200% of shell pressure depending on the load, location, and degree of obstruction
