junctures to reduce the high longitudinal stresses; he also presents an 



analysis for determining the elastic behavior of these structural elements 



and gives results to indicate the degree of reduction which can be realized 



in these high stresses. 



FAILURE CRITERIA FOR AXISYMAIETRIC 

 COLLAPSE PRECIPITATED BY YIELDING 



We will now consider the question of how the biaxial stresses (defined 

 by Equations (15) through (20)) in a pressurized ring- stiffened cylinder can 

 combine to produce axisymmetric collapse precipitated by yielding of the 

 shell plating. Although these stresses are based on equilibrium con- 

 siderations only and do not reflect any buckling state, they can and do 

 predict good results when used in conjunction with appropriate theories 

 of failure even though, strictly speaking, axisymmetric collapse is 

 associated with an instability phenomenon. Formulas for predicting 

 axisymmetric collapse precipitated by yielding based on various theories 

 of failure are summarized in Reference 8. 



The simplest formula devised for the design of pressure vessels is 

 the so-called "boiler formula". This formula may have some merit in 

 predicting the bursting strength of internally pressurized unstiffened 

 cylindrical tubes, but it is unsatisfactory (for other than comparative pur- 

 poses) in the design of pressure hulls in which instability and the influence 

 of reinforcing ring frames play a dominant role. 



Equation (28) gives the pressure at which the circumferential 

 membrane stress in an unstiffened cylinder of mean radius R and 



31 



