﻿Stresses in a Circular Ring, 1019 



The results of these calculations are represented on fig. 4. 

 As a measure of the accuracy of these calculations, we have 

 R 

 (00) _.^=-0'5022P, .... (9) 



f 



so that the error is smaller than i per cent. 



If the corresponding calculations are made for the vertical 

 cross-section, we obtain 



R jj 



f ^>.=« d P= * °' 996 C1Q) 



This must be compared with the result 



& 2P . . , , . P 



1 — cos 9 sin (bdd)= — , 



r it it 



corresponding to a' simple radial distribution (fig. 5). We 

 have again an error smaller than \ per cent. 



The method outlined here may be applied to the more 

 general case of a circular ring subjected to any forces acting 

 on its external rim. It is only necessary to use the corre- 

 sponding solution for a disk *. 



* A. E. H. Love, ' Treatise on the Theory of Elasticity,' p. 216. 





3 U 2 



