formula was used: 



^/^s^t ^t , , 



— Tr-+Pf- [1] 



■where Pg and p£ are the shell and frame terms, respectively, in Bryant's 

 formula,^ and E, Eg, and E^ are the elastic, secant, and tangent moduli, 

 respectively, of the material. Equation [l] has found considerable exper- 

 imental verification, as reported in Reference 6. 



Above the proportional limit, the secant and tangent moduli vary 

 with the stress intensity as seen in Figure 20. Therefore, Equation [l] 

 cannot be used directly to determine the collapse pressure p^, ; a knowl- 

 edge of the membrane stresses in the sandwich structure is required to 

 first determine a stress intensity which is then used in conjunction with 

 the uniaxial stress-strain curve to determine appropriate values of E 

 and Ej.. The following membrane stresses were assumed for the sandwich 

 cross section: 



Circumferential stress: 



2{Ro+ ih„)Lp 



— P = Kjp [2] 



2 A^ 



Longitudinal stress: 



7r(Ro+ |h„)2 



p = K2P 



27r(Roho+ R.h.) 



where h^ , h^ are the thickness of the inner and outer shells, 

 respectively, 



R^ , Rq are the mean radii of the inner and outer shells, 

 respectively, and 



Arp is the area of the sandwich cross section for one 



frame spacing (L-rp). 



A stress intensity cr. was then computed using the Hencky-Von Mises 



30 



