The pair of equations that when substituted for R. von Mises 

 expression permit rapid approximation of the collapse pressure due to 

 buckling are: 



P = 



2.42 E 



(1 -M 



2>0.75 



0.45 



(2) 



2E 



(1 



■|- \ 3 



(3) 



where L = length of cylinder between stiffeners, inches 

 D = mean diameter of cylinder, inches 

 t = wall thickness, inches 

 E = modulus of elasticity, psi 

 ^1 = Poisson's Ratio 

 p = collapse pressure, psi 



After solving both equations for the dimensions of a given cylinder, the 

 higher collapse pressure is utilized as the correct one. However, a more 

 desirable solution to Equation 1 would be a set of plotted nondimensional 

 curves that would permit the user in the field to determine immediately 

 the predicted collapse pressure for a given cylinder without involved calcu- 

 lations. Such a plot of Equation 1 has been prepared (Figure 40) in 

 nondimensional form. Because they are nondimensional, the graphs can 

 be used to predict the buckling collapse pressure of monocoque cylinders 

 between simple supports regardless of cylinder composition. 



A major problem encountered in the comparison of experimental 

 and analytical data is that test specimens and methods of test do not 

 exactly agree with the basic assumptions of the analytical expression. In 

 the experimental testing program of standard glass pipes with conical 

 flanges, three basic differences (see next paragraph) from the analytical 

 expression exist. The analytical expression is based on the assumptions 

 that: ( 1 ) the monocoque cylinder is of uniform wall thickness, (2) the 

 cylindrical radius is uniform throughout the length of the cylinder, (3) the 

 ends of the cylinder are simply supported, (4) the material is perfectly 

 elastic, and (5) the implosion of the cylinder is not initiated by failure of 

 the material, but by elastic instability of the cylinder. 



40 



