for some special cases of stiffening. The basic idea is that the ring 

 frames can be replaced by equivalent increases in the circumferential 

 direction of the bending and extensional rigidities of the shell. If Elg is 

 the flexural rigidity of one ring frame together with an effective width of 

 shell plating and Lf is the center-to-center distance between adjacent 

 ring frames, we use Elg/Lf instead of Kh-^ / lZ(l-l/^) in considering bend- 

 ing in the circumferential direction. An equivalent thickness 

 hg = h(l + Af/Lfh), instead of h, is used in considering the hoop com- 

 pression. Using the notations 



Ie(^-^') = o(i ; ^ed-'^') , s (148) 



LfhR^ 



the equation for determining the critical values of general-instability 

 pressure becomes 



C. +C,^ + C,<:^ = C A. +C_<t>. (149) 



1 2 31 41 52 



in which c<, <j),, and cj)2 have the same meaning as given by Equation (53), 



and the coefficients Cj^, C2» ••• etc. are as follows: 



4 

 C^ = sx 



C = \^{Zn^+\^} +S^X^n^ [2(\^-l)^ + 2(n^-l)^ +5X^n^-2] 



2 2 

 C^ = (n -1)^ 



X* +S(n^ + 2X^)n^J (150) 



C, = n^X^ + S(n^ + 2X^)n^ - S(n^+3X^)n^ 

 4 



94 



