STRESSES IN GUN FORGINGS. 
91 
In these equations P u is the interior pressure per square 
inch which, if applied, would produce an uniform stress, 
# u , in the whole thickness of the wall of the cylinder, de¬ 
pending only upon the dimensions of the cylinder and the 
initial compression p. 
2 P n 2 , 4 Rf P 0 2 
6 
-D 
+ 
;] 
( 4 ) 
.3 (R;‘ - AV) W — B*). 
In this & is the increase of stress caused at radius r by the 
application of any interior pressure, P, within the limit of 
elasticity of the cylinder. 
__r~ ^ P 0 2 . 4 r x P 0 2 ~~i p i 
“ La (P x 2 - P 0 2 ) ^ 3r 2 (P, 2 - P 0 2 ) J ^ ^ 
( 5 ) 
In this p is the relief of stress at radius r, with given values 
of P u and 0 u , under the assumption that the pressure P u 
has been applied and is withdrawn. 
Replacing 0 n in (5) by its value as expressed in (2) and 
designating by p x a stress at radius r x , the ratio of the stresses 
at two different points in the wall may be expressed by 
P = 
r i 
Bo 2 
2 R x P 0 2 -] 
D2 D 2 
■til P) 
(AY 
i 
R 2 
2 R x P 0 2 
jd *- 1 
1 
ft* 1 
1 
of 
1 
Pi 
(6) 
From this the stress p at a given radius, r, may be deter¬ 
mined when p x for the radius r x is given. The symbols p 
and p x in this equation may express either compression or 
tension. 
The radius of the circle on which should be found the 
neutral point of every curve of stress incident to the system 
at rest is found from the equation 
r = Pj 
«)•- 
v (i)-(t) 
m 
