2^1- E f 



L^(^\'(jm' 



34,(1-^^) \^/ \ ^ J 



1--^(1-E .E) 



3-2 <j)(l-f) 



(111) 



In determining the stress ratio f = — — , the stress "^-v is still equal to 



P since it comes about from simple equilibrium considerations, and the 

 2h 



stress '^_ is again taken to be that midway between ring frames as given 

 by the theory of Von Sanden and Gunther, but with v a variable defined by 

 Equation (110). It is found, however, that '^o is practically insensitive to 

 variations in V and that it is sufficient to treat f as a constant which 

 depends only on the geometry of the cylinder; thus Vq can be used for 

 determining the stress ratio f. 



The final equations given by Reynolds in Reference 42 for determin- 

 ing the inelastic buckling pressure p^ are as follows: - 



where 



P_ - P, 



l-v 



1-1/ /L 



H-H 



E 



+ — cb -— 

 4^ E 





(112) 



113) 



4>= 1.23 



v^ 



(114) 



^e-2 



\- rf)h^.^)[i-h) 



1 + 



A + bh 

 f 



be[ 'u. ) 



-1 



(115) 



73 



