bility of ring- stiffened cylindrical shells. It can be shown that this 

 formula may be expressed as follows: 



E h 

 s 



\ 



(n^-l + ^){n^+\Y 



1_3.(1__1)_X 



4 B ' Z ,2.2 

 t (n +\ ) 



EI 

 ^+(n -1) -^-^(177) 

 RE. 



where X - 



ttR 



It is instructive for us to compare Equations (177) and (136). The 

 form of the first term, the so-called shell contribution, in each of these 

 two formulas is identical except for two differences which reflect the 

 difference between inelastic and elastic behavior, respectively; first, the 

 elastic modulus E of Equation (136) is replaced by the secant modulus Eg 

 in Equation (177); and second, the denominator term of Equation (177) has 

 a multiplying factor in brackets which is exactly the same as the second 

 multiplying factor in brackets in the denominator of Equation (104). The 

 form of the second term, the so-called frame contribution, in each of 

 Equations (177) and (136) is identical with one exception: the elastic 

 modulus E of Equation (136) is replaced by the tangent modulus E^ in 

 Equation (177). This latter stems from the replacement of the elastic 

 modulus in the column-buckling equations with the tangent modulus to 



generalize the Euler formula so that it applies in both the elastic and 



6 3 

 inelastic ranges; this is due to Shanley. 



Since Equation (177) can be easily deduced from what has already 



been developed in the preceding sections, and from what has been said 



above, details of its development will not be given here. Investigations 



114 



