'cl 



^h/R (36) 



+a2rZ-3,P^]l/Z 



1 8 

 Lunchick working at the Model Basin derived another criterion of 



failure for predicting axisymmetric collapse which is based on the plastic- 

 hinge concept. He made use of the Hencky-Huber-Von Mises theory of 

 yielding, i.e., Equation (34), and allowed for the plastic reserve strength 

 after yielding begins in the shell plating at midbay. Lunchick developed a 

 formula for the pressure at which a complete plastic hinge has formed at 

 midbay. Since the combined stress gradients at the frame locations are 

 steeper than those at midbay so that complete plastic hinges form much 

 earlier at the frames, this TMB plastic-hinge theory, in reality, gives the 

 pressure at which the shell fails as a three-hinge mechanism. Although 

 this mechanism is not physically possible in the case of cylindrical shells 

 as it is for beams, it does lead to predictions of a collapse pressure (p^-g) 

 which agree well with experiment in certain ranges of geometry. A 

 complete discussion of this theory together with some comparisons to 

 experimental data may be found in Reference 18. For our purposes here, 

 it suffices to give the salient results which can be used for computation. 



It can be shown that the ratio of circumferential bending stress to 

 circumferential membrane stress and the ratio of longitudinal membrane 

 stress to circumferential membrane stress (all stresses considered at 

 midbay) can be expressed in the convenient- notation of Reference 8 and 



35 



