^ ,6 ,2 2, 2 ^ ,2 , , (150) 



C^ = X + SX n (n +2X +1) ^^ > 



Note the similarity between Equations (149) and (55) and between the' 

 coefficients, Equations (150) and (56). 



Bodner working at the Polytechnic Institute of Brooklyn derived an- 

 other set of equilibrium equations for an orthotropic cylindrical shell 

 which are considerably simpler than those of Flugge. He used these 

 equations to solve the case of a simply supported shell under hydrostatic 

 pressure; and by relating the stiffness properties of the orthotropic shell 

 to those of the ring- stiffened shell, he was able to derive a simple 

 formula for the elastic general-instability pressure. For our purposes 

 here, it suffices to give this final equation, which in the present notation 



takes on the following form: 

 Eh/ 



\n."+ X"/2/ 



^cr R I 2 ,2 



\n + X /2/ (n + >, ) 6R (1-1/ )^ 'J / 2 , X \ I^ L, 



n+^l f 



where X - . The similarity between Bodner' s formula (151) and the 



Lb 



Tokugawa-Bryant formula should be noted. The second term, that^N^h , 

 of the so-called shell contribution to p of Equation (151), is usuaJly of 

 minor importance so that the circumferential bending rigidity is pre- 

 dominately reflected by the frame term, i.e. , the third term in Equation 

 (151). In such a case, the Tokugawa-Bryant and Bodner formulas are 

 almost identical in overall form except for two very important differences, 

 These will now be discussed. 



95 



