I cannot argue with your model under the simplifying assumptions that you have made. However, if one adds some reality to the assumptions, your model breaks down. These assumptions as I see it are: 1) no flaws exist in the iron and steel strips welded together to make the twist tube, 2) the welds holding the strips together are perfect and cannot be broken and 3) the pressure is always uniform in the tube and does not vary with position. In reality, the welds are not perfect and the pressure indeed varies in the tube in reality. The pressure in front of the shot column is essentially atmospheric and the pressure behind the base wad is whatever pressure is created by the powder burn. At the moment of peak pressure, there is a tremendous pressure gradient in the direction of the bore axis and this gradient exists over a very short distance. This pressure gradient can create a large force in the barrel wall in a short distance and can tend to pull the welds apart. This effect also exists with Damascus barrels but because of the twisting, individual welds in the piled bar are not under stress and there is much less probability of damaging a weld with the twisted construction of Damascus barrels. The most compelling argument is, however, made by John Brindle in Part I of his series in Vol. IV, Issue 2 of the Double Gun Journal. His argument is that the iron and steel strips used to make these barrels inherently have longitudinal and transverse flaws that can result in rupture under pressure. The twisting of the welded bar of iron and steel strips confines any one flaw (no matter how long or wide) to a very small area and in doing so allows the adjacent strips to compensate and take up the slack in holding the barrel tube together under pressure. He also argues that the same cannot be said for twist barrels. I highly recommend reading this article for anyone interested in this subject.

With regard to British Laminated steel, Greener also points out that there were two varieties of British Laminated barrels. The older type did not necessarily have a high percentage of steel and could be either twist or Damascus. The modern “Laminated “ barrels as he called them were the kind that fared best in the 1898 Birmingham tests. These barrels, with up to 75% steel content could look exactly like Damascus (three iron for example) or could have the herringbone pattern because of a variation in construction..