frames are "light," in the sense that they are not of sufficient cross 

 section and/or of sufficient inertia, and if the overall length of the 

 cylinder is large, say exceeding something on the order of two diameters 

 or more, then another mode of collapse may intervene. 



If this situation exists, then local frame failure could precipitate 



"bodily collapse" or general instability of the shell and ring frames. This 



31 

 possibility was first recognized by Tokugawa. Just as in the case of 



shell lobar instability, this overall mode could possibly lead to premature 



collapse of a pressure hull unless the design is based on considerations 



governed by those geometric parameters which do not influence the 



axisymmetric and panel-instability collapse behaviors. 



31 

 Tokugawa' s was the first rational attempt at developing some 



theory to predict the general-instability behavior. His approach was 



essentially based on a method which has come to be known in modern 



47 

 terminology as the "method of split rigidities." Much later, Bryant 



working at the Naval Construction Research Establishment, Dunfermline, 



Scotland, arrived at practically the same end result but from a different 



point of view. This latter formulation was based on considerations of the 



elastic potential-energy of the shell and ring-frame system; however, the 



"true" interaction between shell and ring frames was approximated by 



Bryant. 



For our purposes here, it suffices to give the final Tokugawa- Bjrya-nt 



formula. In the notation of this report, it takes the following form: 



82 



