﻿Stresses in a Circular Ring. 1017 



which are equal and opposite to the tractions (3), and using 

 the solution of the case of a circular ring, the following- 

 expressions are obtained for the stresses at any point : — 



+ 0-4832| 4 )cos2^ + (0-3691^ 2 -0-6783^ 



+ 030*8-^ -0-0599 ? 4 )cos4^ + (o-06504^ 4 



-0-10026 ^ + 00041319 ~ 8 -0-00952~ > Ws 60 



+ (0-008758^ -0-01225^ + 0-00040795 ^° 

 \ h? R 8 p 10 



- 0-0010888 ^\ cos 80 + (Vo007880^ 



-0001037-g+0-00002960^ 2 



-0-00008475^° 



w 



R 10 \ -i 



-^>)coslO0j 



- 2P 



rr 



R 



2P r r 2 R 2 — o 2 / 



= .R I ' 606 ? W^ + (-2-268-0-4832 



-:- 2-752 -*\ cos 20 + ( -0-3691 |J + 0*2261^ " 



-O-O368^+O-1798^W40+(-O-O65O4:£ 

 A> p / \ R 4 



o 6 R 8 "R6\ 



+ 005013 £ - 0-0041319 - 8 f 0-01904 — cos 6(9 



+ (-0008758 -£? 



R 8 \ 



+ 0-0018146— 8 ) 



\ 



008758 £ + 0-007352 1! - 0-00040795 51° 



r 



1(5) 



I cos 80 + f -0-0007880 jf 

 \ R 8 



O io ft 12 



+ 0-0006911-^ -0-00002960^ 



R 10 \ n 



+ 0-0001265 - r A cos 10<9J, 



P/«7. Ma#. S. 6. Vol. 44. No. 263. Nov. 1922. 3 U 



