expanded leads to an equation from which the buckling pressures can be 

 determined. This system of equations has been programmed on the 

 Model Basin IBM-7090 computer for purposes of numerical computations 

 and verification of the analysis. 



In lieu of this rather complicated mathematical solution, which is 

 necessary for a complete analysis and insight into the phenomenologic 



C Q 



aspects of the problem, Blumenberg developed some convenient 

 empirical formulas for design purposes on the basis of test data he and 

 Reynolds obtained. He adapted the well-known Levy ring formula to the 



present problem by redefining the geometric parameters as follows: 



3 

 /Pcr^cLeN 



where it is assumed that 



/Pcr-PB\ 

 L ~Lf -h(Lp-L,£) (166) 



^ \ Px-Pb / 



for the range where p„ >^ P^r — Pb* Al^o* ^^^ following additional defini- 

 tions are used: 



I is the moment of inertia of the heavy-frame- shell 



section, 

 p is the critical pressure of the actual cylinder including 



all the frames. 

 R^ is the radius from the cylinder axis to the centroid of the 



heavy-frame -shell section. 



104 



