2000 2500 £g Cm* 



FIG. 5. Relationship 

 between K and y. 

 which the buckling pressure p is obtained 



11 



were to be substituted in the otherwise unaltered 

 Euler buckling formula. We have employed this 

 expression for E in Eq. (13) for the conversion 

 of y into k f or k ^ 1900, y * 0.000809, and 

 thereby obtained the k-scale for the unelastic 

 region. The relation between y and k is repre- 

 sented in Fig. 5. 



The application of the graphs is as follows. 

 For the given value of the ratio, wall thickness 

 to diameter, i.e. h/a, we seek the corresponding 

 ordinate, as well as the corresponding polygon, 

 for the given ratio of the radius to effective 

 length a/1. The ordinate of the intersection of 

 these two lines gives the value of y or of k from 



P " 



E 



2h 



i^r- 



= 2h k 

 a K 



(16) 



If no lines exist for the exact ratio given, y can be determined by interpolation. 

 In any event, the graph indicates the number of lobes, n, which is determinative 

 for the given case. For a known n, it is then not difficult to compute the exact 

 value of y by equations (6), (7), or (8). 



The following numerical table was obtained by readings from the graph. It 

 is valid both below and above the proportional limit, providing the cylindrical 

 shell is manufactured from medium steel plate. 



Table I. 



Critical pressure p in kg/cm 2 for various v/all-thickness ratios, 

 h/a, and length ratios, a/1. 



v _ira 



CC--Y 



a/1 



1000 h/a 



0.5 



1.0 



1.5 



2.0 



2.5 



3.0 



3.5 



4.0 



2 



0.637 



0.045 



0.23 



0.6 



1.3 



2.2 



3.6 



5.3 



7.4 



4 



1.273 



0.080 



0.46 



1.3 



2.6 



4.6 



7.4 



10.9 



15.3 



6 



1.910 



0..125 



0. 72 



2.0 



4.0 



7.2 



11.5 



14.2 



17.2 



8 



2.546 



0.175 



1.0 



2.7 



5.6 



9.6 



12.5 



15.4 



18.3 



10 



3.183 



0.22 



1.2 



3.5 



7.2 



10.3 



13.2 



16.1 





12 



3.820 



0.26 



1.5 



4.2 



8.0 



10.9 



13.8 







14 



4.456 



0.31 



1.8 



5.1 



8.4 



11.2 









16 



5.093 



0.37 



2.1 



5.8 



8.7 



11.6 









18 



5.730 



0.41 



2.4 



6.0 



9.0 











20 



6.366 



0.45 



2.8 



6.2 



9.2 











