so that 



<I> h 



E ■^^"^1 



B cosh X X + 





zd-i' )_ 



FcoshXx (13) 



where the subscripts o and i in Equations (11) and (13) refer to the outer 



and inner fibers of the shell plating in conjunction with the plus and minus 



signs, respectively. 



The total radial ring -load Q* is found from Equations (7), (8) and (2) 



to be 



Eh3 



Q^ 



6(1-1/2) 



3 , L .3 . ii 



BXiSinhXi ~2 ^ F>«^sinhA.o £ 



-pb(l-i//2) (14) 



When boundary conditions (b) and (c) are invoked, the integration con- 

 stants B and F are determined and the following expressions for the more 

 important shell stresses are derived in terms of the convenient notation 

 of Reference 10: at midbay between adjacent ring frames (i.e., at x = o) 



"^"^^ 1 + ^xbm 



(15) 



$°m 

 _J_= 1 



.(.W) 



F, ± 



z-i'-s- 



xbm 



(16) 



23 



