The small difference in the magnitudes of the stresses on the con- 

 cave and convex surfaces of the head indicate that the head should be con- 

 sidered as a thin shell. Using thin shell theory, the membrane stress per 

 unit of external pressure load was 



0- r 11. 373 , , „ , , . 



p-"^2l = Z(0-T8T) =^^-^P^^/P^^ 



The critical buckling stress'^' is: 



Et 



cr 



r(l-hi2) 



1 - \i.^ \ \i±_ 



2r 



3 



(10. 4 X 106)(0. 381) 

 Ih 373( 1-0, 33^) 



212 ksi 



1 - 0. 33' 



1/2 



0. 33(0. 381) 

 2(11. 373) 



The critical buckling stress given by this equation varies between 3 and 4 



times as much higher than that found by e-^periment. Using a factor of 



three, the resultant shell stresses rather than buckling considerations are 



shown to govern the strength of the hemisphere. 



The following empirical relationship can be used to determine the 



buckling pressure in the given limits: 



2 



Per 



= 0. 3E 



1 - 0. 175 



g - ZO 

 20 



07y 

 400 t 



when 



and 



400 <-r < 2000 



20° < Q < 60° 



