In view of these considerations, it was decided for critical pressure 

 calculations to utilize only the nominal pipe dimensions supplied by the 

 manufacturer and an analytical expression which would combine simplicity 

 with fair accuracy. Such an analytical expression is the R. von Mises-^ 

 equation for buckling of monocoque cylinders equipped at their ends 

 with simple supports in the form of ring stiffeners or bulkheads (Equation 1] 



1 - a' 



n-' +^ - 1 



(n^ + a^)^ - 2/iT n^ + ^Hj 





Ail = 1/2 1 + (1 +a)pV^ 2 + (1 -CT)p| 



1 + (1 +2a)p - (1 -a2)(l + Y^ PJp- 



lXj = (^ - op) 



3D^ 



D h -o^ 



2t 



ttD 

 2L 



To solve Equation 1, one must find that whole number n of buckling 

 lobes on the cylinder which would make the collapse pressure p a minimum 

 for a given mean cylinder diameter D, wall thickness t, and length between sup- 

 ports L. Although this analytical expression is rather simple, time consuming 

 and repetitious calculations must be performed before that number n of 

 buckling lobes is determined which makesp a minimum for a given cylinder 

 under hydrostatic pressure. For this reason, several approximations of 

 Equation 1 have been developed"^ (Equation 2) which in conjunction with 

 the expression for long unstiffened cylinders'* (Equation 3) permit rapid 

 calculation of the collapse pressure for any cylinder. 



39 



