CIRCULAK CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 227 
Tr ^ /I 
+ 15—2S(-1) 
fJ.IT 0 
+ 
1 
{2n + 1)^ ' (271 + If 
. 2ii + Ivre . 2n + Ittz 
Sin-::- Sin 
(-!)■ [I,(») 
yu,7r“ 7 ( 2/1 + 1)^ I loC^) 
15 15 
8«2 
sin 
2c 2c 
2?i + l7rc . 27i + l7r:4 
Sin 
Je 
zc 
. (133), 
T 
- - log, 
IT 
TT 11 Z 
tan - — , 
4 4 c 
TT TTZ + e 
tan ( - — - — 
4 4 c 
+ 
ttT 
e (from 2 = 0 to 2 = c — f’) 
and 
c — z (from z = c — e to z = c) 
T X / I 
+ i5iv(_in/ 
“ TT 0 ' ' ■ 
1 \ . (2/1 -f l)7rc 271 + Ittz 
(2n + If ^ i2n + 1+) 2c 2c 
+ ■-2 
(-1)“ . 
Itfci) 
(2n + 1)' 
Vkl*) 
A _ A' 
~ ^ ~ - “ 8«2 ~ 8«‘5 
2« 
2i‘)i -|- lir^ 2/1 + 1 
sm --cos-- (134), 
2c 
Or 
where in the last 2 in both equations only a comparatively small number of terms 
need be taken. 
* 
31. Numerical Example. 
Values of the Coefficients and of the Displacement 
and Stresses. 
Take a cylinder such that 7ra/2c = 1, and let e = cl'2, so that the distribution ot 
stress is as shown in fig. 4. Then a — 2n + 1, and we find : 
J. / 9 T'/» 
V = - ■ [vq sin TTzj^c — i\ sin ^Trzj^c — iq sin bTrzj^c + sin 7ttzI2c + rq sin ^ttz/2c 
jJblT 
— iqsin llTTzj^c — . . .) 
2+2T 
TT 
(^0 
sin TTZ!'2c 
h sin Snzj’Zc 
.) 
2 /2T 
(f)Z —■ ""— ^ [sq cos 7r2/2c — 5^ cos 3TTzj2c — . . .) 
the law of the signs being obvious, and the v’s, t’s, and s’s being given below : 
2 a 
2 
