Also, the effective frame cross-sectional area A^ff. appearing in boundary- 

 condition (c) is defined by the following for internal and external framing, 

 respectively: 



^eff 





^eff 



(9) 



where R is the radius to the median surface of the shell and R^g is the 

 radius to the centroid of the frame cross section. 



The total longitudinal stress dy in the shell is given as the sum of the 

 longitudinal bending comiponent o^b pl^s the longitudinal membrane com- 

 ponent "^xM* i'^M 



. =±— ^^_P^ (10) 



X 2(1-1/'^) dx'^ 2h 



so that enforcing boundary condition (a) in Equation (2) results, in 

 Eh 



2 2 



BXi coshXiX+FX3COshX.3X 



pR 



fc- (11) 



Xi 2(1-1/'^) 



The total circumferential stress 0^ in the shell is given as the sum 

 of the circumferential bending component i/d plus the circumferential 

 membrane component c ,i.e., 



2(1-1/2) dx 



I/Eh d w E pR nz^ 



22 



