Bending of Thin Shells. 



501 



couples applied to the edges ; so that the tangential shearing 

 stresses and the torsional couples are zero. 



Fig. 3. 



whence 



Let a. be the semi-vertical angle of the cone, r the distance 

 of any point on OADB from 0, Then 



Pi l== Pi =co '> P2 = ® \ p2= r tana; 



G- 2 = fw7i 3 Er- 1 cot a, 



G 1 =-^n7i\l + 'E)^coU. 



The equations of equilibrium are 



£(V)-T 2 =0, 



^- 2 +N lC os«=0, 

 d(p 



Jr (N 2 r)smct+ _i-T s cosa = 0, 



d&i . 



-^r +N 1 rsin« = 0, 



S 



Let 



then 



whence 



whence 



and therefore 



-fnA 3 (l + E)cota = &, 



N 2 =-£A> 2 , N 1= =0, 

 T 2 = k tan a/r 2 , 

 T A & tan a 



(8) 



where A is the constant of integration. 



From these equations we see that all the stresses are per- 



