Late to the party.
P. Webley & Son began using Siemens steel barrels about 1880 and reported excellent results.
John Henry Walsh,
The Modern Sportsman's Gun and Rifle: Including Game and Wildfowl Guns, Sporting and Match Rifles, and Revolvers, Volume 1, 1882
“Siemen’s Steel for Gun Barrels”
http://books.google.com/books?id=OLwUAAAAYAAJ&pg=PA445&vq A 13 bore Siemens barrel did not bulge until 19 1/4 Dram Black Powder with a 1 1/4 oz. ball. Siemens then reported a tensile strength of 55,000 - 60,000; other sources list 62,700 psi.
The average tensile strength for Crolle Damascus is 54,700 psi.
New fangled steel barrels were developed rapidly thereafter. Lot of infro here, including the 1891 Birmingham Proof House Trial report
https://docs.google.com/document/d/1dnRLZgcuHfx7uFOHvHCUGnGFiLiset-DTTEK8OtPYVA/editThe British 12 bore service loads of that era for 2 1/2" and 2 5/8" chambers were:
Nitro - 1 1/8 oz. with 42 grain Bulk Smokeless = 3 Dr. Eq. (1200 fps) at 5330 - 6110 psi
Nitro - 1 1/4 oz. with 45 grain = 3 1/4 Dr. Eq. (1220 fps): 6360 - 8620 psi
BTW: minimal wall thickness measurements mean little unless we know where that number was obtained, and wall thickness from the end of the chamber to about 18" is of much greater importance, as are our eyes and fingers. OD-ID doesn't work because of barrel eccentricity.