N^ is the number of heavy ring frames, and the 



subscripts f and F refer to light and heavy ring 



frames, respectively. 



The original ring-energy integrals. Equations (140) and (141), as used for 



the present problem were modified by Kendrick to include some additional 



terms as follows: 



2 TT 2v 



e 2R 



("^'99 + "') I -("'0-"^) 



^2 



N 



d9 + 



2R 



j(^.q + -.9-'"'9^)(' + r) 



e 



+ 2v, 



'0 



O"(^'90 + "^)i 



m 



d9 



:i53) 



ZlT 



EI ( , .2,„ 



154) 



Reynolds pointed out certain shortcomings in regard to the hoop thrusts 

 in the ring frames just prior to buckling as assumed by Kendrick, and the 

 following expressions have been used in the revised theory: 



N 



^ F f 

 OF " ~ A + L h 



155) 



N . = - 



pRA L^ 



of ^f + Lf^ 



156) 



for the heavy and light frames, respectively, and where Ap and Ar are the 

 cross-sectional areas of the heavy and light frames, respectively. 



99 



