Anothe formula sometimes quoted is known as Lamé's formula. Burrard quotes this as the "Gunmaker's Formula". Using t (tension) as the allowable internal pressure the formula is;
P = t x (R²-r²)/R²+r²). He states this gives the pressure necesary to stress the "Internal Layer" of the wall.
He quotes a different version of Alger's formula as stressing the entire wall as follows;
P = t x 3(R-r)/R+2r
Note that with either of these it is not actually necessary to obtain the radius, but diameter can be used by simply substituting D & d for R & r as long as you do so for the entire formula.
It is also, I think, worthy of note that actual experiments have been performed which by these figures "Should" have resulted in a burst bbl, but didn't. Greener reported on a 12ga chamber wall turned extremely thin & Hatcher reported on an '03 springfield bbl turned to .060" over the chamber as I recall. I can only in my limited ability account for this as similar to the LUP pressure difference from tranducer pressure, ie the time lag for the very short period of applied pressure, simply did not allow full deformation to take place. These formulas were, I think worked out for a continous load.
