There still remains to formulate an expression for the nbndimension- 

 al quantity S^^ which, as defined by Equation (74), is the ratio of the 

 average stress at buckling to the yield stress. If we assume that the 

 same general expression (Equation (85)) is valid in the inelastic range as 

 well as in the elastic range, then the "average stress" for buckling in the 

 inelastic range is 



V/- — ^ (91) 



so that then 



"^cr, Pt 



cr 



~ ~~ a } 

 I y y 



s.. =-^— =d-h7^^ (92) 



Substituting Equation (92) into the left-hand side of Equation (90) and solv- 

 ing for pj leads to 



1+ 



2Pe 



Equation (93) represents a more general semi-empirical formula for in- 

 elastic buckling of ring -stiffened cylindrical shells than that developed by 

 Trilling and Windenburg. The general form of Equation (93) is similar to 

 analogous formulas given by Timoshenko in Reference 9 for the inelastic 

 buckling of straight columns and circular rings. 



An important point to be made is that the same value of B must be 

 used in both the numerator and denominator terms of Equation (93), 



63 



