Thin-Walled Cylinders 



Table 1. Out-of- Roundness Parameters for 

 16-Inch OD Cylinders (Ref 2,4) 



t/Do 



^tmin/t 



ARj/t 



AR^/t 



0.03'' 



0.12 



0.12 



0.12 



0.06^ 



0.06 



0.06 



0.06 



0.13^ 



0.03 



0.03 



0.03 



0.19^ 



0.02 



0.02 



0.02 



" Thin-walled cylinder. 



Border between thin- and thick-walled 

 cylinder. 



'^ T-hick-walled cylinder. 



Thin-walled cylinders are 

 divided into two categories : moder- 

 ately long cylinders and long cylin- 

 ders. Moderately long cylinders 

 are influenced by end-closures 

 which restrain the cylinder from 

 instability failure. Long cylinders 

 are not influenced by end-closures 

 and behave as infinitely long cylin- 

 ders. In Reference 8, thin-walled 



cylinders included another category called short cylinders, but in this 

 report the thick-walled cylinder category encompasses short cylinders 

 (Figure 3) . 



The same approach used in Reference 8 is used herein. Donnell's 

 equation is applied to moderately long cylinders and Bresse's equation 

 to long cylinders. An empirical plasticity reduction factor, r\, is used 

 in both equations to account for inelastic behavior of concrete and 

 specimen out-of-roundness. The new data permit an n relationship to 

 a. /{' to be determined with far greater accuracy than previously. 



Empirical n values were determined by calculating the elastic stress 

 at buckling and dividing this stress into the experimental stress at 

 implosion . 



The elastic buckling stresses were calculated as follows: 



Donnell's Equation 

 0.855 E 



(-im^D 



(1 - V ) 



2.3/4 \R/ L 



(4) 



