and I is the moment of inertia of the heavy-frame- shell section deter- 



n 



mined for p from Equation (165). Any further increase in the strength 

 of the heavy frame will not increase the critical pressure because the 

 failure will occur between the heavy stiffeners. 



In Reference 58, the authors compare calculations using Equations 

 (165) and (167) with observations from model tests. On the basis of the 

 good agreement obtained between prediction and measurenaent, they suggest 

 that the pressures p and p-p be computed using the Tokugawa- Bryant 

 formula, Equation (136), and that p be computed using the following 

 formula: 



n(n+2)EI^ 



"" = -^ '''" 



In this way, the need for drawing curves similar to those of Figure 19 is 



eliminated. Figure 19 shows the results of calculations for a specific 



geometry considered by Blumenberg and Reynolds as part of their model 



test program. The pressures p , p , and p entering into Equations (166) 



B F n 



and (167) are shown for this case, 



ELASTIC DEFORMATIONS AND STRESSES IN 

 IMPERFECTLY CIRCULAR RING FRAMES 



The theories and formulas presented so far for predicting the elastic 

 general-instability strength of ring- stiffened cylindrical pressure hulls 

 have all been based on the assumption that the structure is initially per- 

 fectly circular. In the fabrication of submarine hulls, it invariably turns 

 out that due to the cold-forming process and welding of steel plating into 



107 



