Numerical calculations using Equations (173) are facilitated with the 

 aid of a digital computer. Their solution represents an "exact" solution 

 of the problem within the framework of thin- shell assumptions and the 

 assumed out-of- roundness and buckling functions. However, both 

 Kendrick and Hom developed so-called approximate solutions from these 

 more exact equations; these latter are proving useful in design. Hom 

 gives the following convenient formula for determining the maLximum 

 bending stress in the flange of an imperfectly circular ring frame: 



4 



a = ± 

 bf T 



Ee C 



E^ VPcn'P 



(17 6) 



where e^ is the distance of the frame flange from the median surface of 

 the shell and is positive for internal frames and negative for external 



frames . 



p 



Note should be taken of the magnification term (:r —) in Equation 



t^cn"*' 



(176), which is analogous to that of Equation (127) for the shell out-of- 

 roundness problem. These factors suggest that initial imperfections 

 "grow" in a nonlinear fashion with the applied static pressure p. This 

 phenomenon is similar to the resonance condition in vibration problems 

 when the frequency of an applied force approaches the natural frequency 

 of the structure. In the static pressure problem of interest to us here, 

 "resonance" occurs when the applied pressure p approaches the elastic 

 general-instability pressure p of the perfectly circular ring- stiffened 

 cylinder. The pressures p can be conveniently determined from the 

 curves given by Ball in Reference 48 and reproduced in this report as 

 Figures 15 and 16. 112 



