tate a premature overall instability of long cylindrical hulls. Here, as in 

 the case of the first two modes, instability of the elastic type is of interest 

 only as a datum. It is inelastic overall instability which is of prime con- 

 cern in designing an adequate hull; a typical case is shown in Figure 10. 



1 ^ 

 Earlier authors ' have offered the "one-hoss shay" concept, in which 



the best ratio of strength-to-weight is obtained when the hull structure is 

 so designed that the three modes of collapse are expected to occur simul- 

 taneously, as the one for optimum design. However, this is a rather 

 nebulous statement, and the approach even considered oversimplified if it 

 is based on purely elastic considerations of instability because the 

 "ignorance factors" or margins between the various modes would then 

 merely be guesses, and may not necessarily be constant for the wide 

 range of interest. Optimum design must be based on rational consider- 

 ations of inelastic behavior, so that the "ignorance factors" can then be 

 representative of the variability introduced by certain intangibles which 

 are not easily considered in a theory. 



To make structural problems of the type encountered in the analysis 

 and design of pressure hulls for submersibles amenable to mathematical 

 solution, the theoretician must invariably resort to idealizations and 

 approximations of the actual physical conditions. In this way, the designer 

 can only hope to realize upper and/or lower bounds on ultimate load-carry- 

 ing capacity. Some of the intangibles which influence static strength and 

 complicate the problem so that appropriate design formulas cannot be 



14 



