CIRCULAR CYIJNDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 157 
But clearly if 2:2 is to be zero all over the plane ends we must have 
Uq = - 
X * 2 li 
h = 
(2n + 1) 7!- 
2c 
and 
E = 0 
(27) , 
(28) , 
(29). 
The expressions for the displacements and stresses then reduce to the following, 
writing kr = p for shortness : 
u = 
\ . C T- ,,1 cos kz 
= UqV - t j Aili (p) + - pT„ 
k 
k 
rr = 2 (X + /x) Uq + \ii\^ 
+ - 1 “ ^ 2^ [(2X + 3p) + pAo] Iq (p) + 2p 
P 
— V 
22 = 
rz — pS 
where 
P- 
A + 2p 
C 
k ‘ 
2L' 
+ ^ 2 ) Ii (p) + T P^o (p) 
A/ K -T 
Over the surface of the cylinder r = «, we find 
(W/^)r=a =-X’ '^^’0 
(30) , 
(31) . 
CpH 
k _ 
(p) 1 cos kz. 
• (32), 
cos kz 
. 
■ (33), 
■ (34), 
. (35), 
~ (’^ + y) iij (''^) + (, + y“ )^i(“) 
A, 
+ A,[-(l-y) I, 3 (a)-y«I,(a)] 
-I >cos k' 
Aj[Ii(a) - yalo(a)] 1 
{rzlp.)r^„ = S ^ >sm 
+ A. [I^ (a) + yal^ (a)] J 
where y is written for and a for ka, 
A + 2p 
(36), 
(37), 
