(h ) to outside local radius (R, ) was obtained for each pressure hull, 

 a ±Q 



The local geometries for these critical areas are presented in Table 2. 



Using these values of h and R-, in Equations [8] and [9], the collapse 

 a 1q 



depths pg were calculated. The results of these calculations indicate 



that Hulls No. 1, 2, and 3 will collapse at depths of 15,800, 16,100, and 



15,100 ft, respectively. The lower collapse depths for Hull No. 3 may be 



attributed to its relatively low yield strength (see Figure 8). 



A high degree of confidence can be placed on these collapse depths 



for a number of reasons. First and primarily, the shape of the hull has 



been measured accurately. Previous tests have indicated that the collapse 



strength of a spherical shell can be predicted accurately if the critical 



local geometry is known. Second, the analysis presented in this report is 



conservative for stable shells; i.e., for those shells whose empirical 



inelastic buckling pressure is considerably lower than the classical 



elastic buckling pressure. The average ratio of p' to p' for the three 



E 1 



ALVIN hulls is approximately 0.20 (see Table 2). Figure 5 indicates that 

 the analysis is conservative in this range. The reason for this is that a 

 Poissons ratio of 0.3 was used in the plastic range and the three-dimensional 

 Hencky-Von Mises effect of the pressure was neglected. In addition, 

 buckling coefficients higher than 0.84 are possible. Third, the effect of 

 secondary moments, which are not considered in the analysis, is negligible. 

 This is shown by the experimental results plotted in Figure 3 which indicate 

 that even for clamped edges, the effect of secondary moments is very slight 

 for stable shells with 9 values of 2.2 or greater. 



The viewing port and access hatch inserts should not adversely 

 affect the collapse strength of the pressure hulls. Reference 8 reports 

 tests of two 0.286-scale hemispherical models of ALVIN, each penetrated by 

 a single viewing port. Strains were measured on the penetration insert as 

 well as on the adjacent portion of the spherical shell. These strains and 

 the calculated experimental stresses in and around the penetration inserts 

 indicated that the design of the penetration inserts was adequate. 



Obviously this confidence would be destroyed if significant changes 

 occur in the shape of the hulls due to any additional penetrations or welding. 



32 



