Later tests with the ring-stiffened oval cylinder incorporated tubes parallel to the minor 

 axis of the oval cross section to determine the effects of this type of structural discontinuity 

 on the overall strength of the structure. 



THEORETICAL DEVELOPMENT 



The experimental studies conducted at the Model Basin are closely related to the ana- 

 lytical efforts at Polytechnic Institute of Brooklyn. These latter studies presently constitute 

 a major part of the overall program on transverse strength of submarine structures which is 

 being sponsored jointly by the Office of Naval Research (Code 439) and the Bureau of Ships 

 (Code 442) at that Institute. A number of publications have already appeared which present 

 the findings of the Polytechnic studies; Kempner^ summarizes the results through 1961^- It is 

 of interest here to note the more significant results so that structural designers can better 

 understand and appreciate the difference in behavior between circular and noncircular cylin- 

 drical pressure hulls. 



The first problem amenable to mathematical solution, and one which could provide an 

 insight into the mechanism of deformation of noncircular cylindrical pressure hulls, was that 

 of the simply supported oval cylinder. The analysis developed by Romano and Kempner^ 

 indicated that for this case, the use of the local radius of curvature of the oval cross section 

 in the well-known and proven formulas for circular cylinders'* gives very good agreement in the 

 stresses and deformations with the "exact" Fourier series solution developed in Reference 3. 

 The results of the analysis of the simply supported oval shell also showed that even with a 

 small eccentricity (ovality), the stresses in an oval shell differ significantly from those in a 

 circular shell of equal length and weight. 



The next logical step in the development of adequate theory for the realistic interaction 

 problem in the case of an oval cylinder stiffened with ring frames possessing finite elastic 

 stiffness properties was to investigate the problem of the clamped oval shell. Vafakos, 

 Romano, and Kempner have developed such an analysis,^ and their results indicate that the 

 stresses in an oval shell differ significantly from those in an axisymmetric circular shell of 

 equal length and weight. Just as in the case of the simply supported shell, these investigators 

 found that a simple equivalent circular cylinder solution based on the local radius of curvature 

 concept yields good results for the deformations and stresses in a clamped oval shell. The 

 maximum stress was shown to be an axial stress due principally to bending; it occurred at 

 those points of the clamped edges which had the least curvature. 



The analysis for the ring- stiffened oval cylinder was obtained by the Polytechnic 

 group by coupling the equation^ for the noncircular shell of arbitrary edge conditions with 

 expressions for the displacements and stresses in the oval ring which is subjected to the 

 interaction load between the ring and shell. 



In contrast to the simple analogy of the equivalent circular cylinder using the local 

 radius of curvature concept for the simply supported and clamped oval shells of short length, 



