shells) lend considerable support to Zoelly's equation. Tests of small, 

 near-perfect machined hemispherical shells which had ideal boundaries and 

 which failed at stress levels below the proportional limit have given 

 experimental pressures ranging from 70 to 90 percent of the classical 

 buckling pressure. The tests indicated that the classical buckling co- 

 efficient of 1.21 may be attainable for the ideal spherical shell. How- 

 ever, the tests also demonstrate that for small, almost unmeasurable im- 

 perfections, the buckling coefficient falls off very rapidly to about 70 

 percent of the classical value. Based on these results, the Model Basin 

 recommended that the following formula be used to predict the collapse 

 strength of near-perfect spherical shells whose initial departures from 

 sphericity are less than 2 1/2 percent of the shell thickness : 



p, = 0.84 E (h/R )^ for u = 0.3 [21 



3 o 



where R is the radius to the outside surface of the shell. Initially 

 perfect shells may buckle at pressures approaching 43 percent greater than 

 the pressure given by this empirical equation. However, it appears 

 unrealistic at this time to rely on this additional strength due to the 

 difficulty in measuring the initial contours of most practical shells to 

 the degree of accuracy required. 



Based on the results of the elastic buckle specimens, an empirical 

 formula was also developed which adequately predicted the collapse of near- 

 perfect machined hemispherical shells vdiich had ideal boundaries and which 

 failed at sti 

 expressed as 



3 

 failed at stress levels above the proportional limit. This formula may be 



Pt^ = 0.84 /E E^ (h/R ) for u = 0.3 

 E s t ^ o-^ 



[3] 



where E is the secant modulus and E is the tangent modulus. 

 For stress levels below the proportional limit. Equation [3l reduces to 

 Equation [2]. From simple equilibrium, the average stress may be expressed 

 as 2 



^ ^ [4] 



avg 



2h R 



Equation [3] can then be solved by a trial and error process using the 

 stress-strain curve for the material used in the test specimen. The 



