stiffening rings over that in an unstiffened cylinder, are given by 



(86) 



B = 1 -a F2-1/F 



[' 



0.91 



Ni-i/^ J 



B = 1 -aF2 (87) 



where a has already been defined in connection with Equation (31). We 

 see that Equation (86) is a consequence of the outer-fiber location, and 

 Equation (87) is a consequence of the mid-fiber location. Another possi- 

 bility results from Equation (29), i.e., 



_ 1 



B= (88) 



1 + Af/ Lf h 



The choice is left to the discretion of the designer. 



With Equation (85), the nondimensional stress ratio S^^ appearing 



E 



in Equation (84) becomes: 



'^cr^ Pit 



- - ^ "^ B (89) 



"E V Oyh/R 



Substituting Equation (89) into Equation (84) leads to 



2PE 



Equation (90) constitutes a more general relation than that developed by 

 Trilling and Windenburg, who, in essence, assumed B = 1. They assumed 

 that the stress for elastic buckling to be that given by the simple hoop 



formula d = — — ; this neglects the stiffening action of the ring frames. 



h 



62 



