[7] 



p^ - 0.84 /E^(_± \ [8] 



P (R-L f 



o' = 5 [9] 



^^S 2 h 



\ 



where h is the average thickness over a critical arc length, 



R is the local radius to the midsurface of the shell over a 

 critical arc length, and 



R-j is the local radius to the outside surface of the shell over a 







critical arc length. 



These equations may be used to predict the collapse strength of both near- 

 perfect shells and shells with initial ing^erf ections . In Reference 6 it 

 is assumed that the critical arc length L may be determined by: 



L =~^yK^ [10] 



c 0.91 la 



The primes in Equations [6] through [9] simply indicate that the local 

 geometry is used to calculate the pressures and stresses. 



Thus, for the case of the spherical shell with imperfections, it is 

 necessary to determine the local radius over a critical arc length. The 

 simplest way to do this is to express the local radius in terms of devia- 

 tions from a nominal radius or in terms of out-of-roiindness. Figure 4 

 shows the assumed relationship between deviations from a nominal radius * , 

 out-of-roundness A, and local radius R over a critical arc length. With a 

 given out-of-roundness the ratio of R-,/R may be calculated in terms of 



A/h and h /R from geometry. The results of these calculations are 

 a a 



presented graphically in Figure 5. 



To verify the validity of the analysis given above, models with 



In this analysis it is assumed that the critical arc length is 

 associated with a e value of 2.2. 



