﻿1016 Prof, S. Timoshenko on the Distribution of 

 equal at all points, and two simple radial distributions : 

 2P cos 0! 2P cos 02 



77 p x ' 



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(3) 



I£ P = 2r, the corresponding normal and tangential stresses 

 at the points o£ the cylindrical surface of the radius r will be 

 approximately represented by the following series * : — 



w -=-^ (0-506 + 1-008 cos 20 + 0-443 cos 40 



7TIX 



-t 0-158 cos 60 + 0-0467 cos 80 + 0-0083 cos 100), 



^ 9P 



r6= — (0-749 sin 20 + 0*374 sin 40 



7T.K 



+ 0-141 sin 60 + 0-0460 sin 80 + 0*0133 sin 100). 

 Distributing on the inner rim of the ring (fig. 3) the tensions 



* The calculations have been made by the Bunge approximate method. 

 See Theorie und Praxis der JReihen, p. 153. From the calculations 

 made we may conclude that the error in stresses will not be higher than 

 | per cent, if we take the first six terms of the series only. 



