﻿1018 Prof. S. Timosbenko on the Distribution of 



2P 



r *=S[( 2 - 



268-3*1624-0-4832 



W 



\ 



W 



+ 1*376— 2 )sin 20+ (0-3691^-0-4522^ 



R 6 R 4 \ / n 4 



••03680 - 6 + 0-1198 -4 J sin 4(9 + (0-06504-^ 



0-07520 4 -0-0041319 „ + 0*01428 ~] sin Q0 

 R b p 8 pV 



/ D 6 o 8 R 10 



(0008758^-0 009802 |g- 0-00040795 — 



0-0014517 — ) sin 8(9 -f I 0-0007880 ^1 

 p 8 / \ R 8 



-0-0008638^-n -0-00002960 ~ 



+ 0-0001054 



,10 



R 10 

 R 10 



R 12 



12 



' 10 \ ~1 



[loJBinlO^J, 



(6) 



where p denotes the distance from the centre. 



Superposing the stresses (4), (5), (6) on the stresses (1) 

 and (2) above, we obtain the stress-distribution in the com- 

 pressed ring of fig. 1. The normal stresses on the vertical 

 and horizontal cross-sections of the ring have the following- 

 values : — 



(0d) e=o =^ 0-5-0-506^ ^ 4-2-268-5-955 

 7rR L p 2 R j — r l 



R 2 



-0-6133^-0-0915^-0 01146^8 -0-00104 ^ 10 



T?4 136 T)8 T310 



+ 0-4233^+0-02728^ +0*003043 — 8 + 0-0003232-^ 

 p 4 p b p 8 p lu 



+ 0*0000296^1 (7) 



w-^i-'iffiF 



i-5 



2R J 



(R 2 + P 2 ) 



0-506 



r 2 R 2 + p s 

 o 2 R 2 -r 2 



-2268 



+ 6-693 ^ -0-7433 £ 4 +0*1090 |- 6 -0*01304^ 



+ 0*001037- 

 rv 



+ 0-000492 7 ^ - 0-00002960 — r J 



r>4 T?6 OS 



5431 4 + 0*04632^-0*005221— s 

 p 4 p 6 p 8 



(8) 



