CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 195 
Q 
U'q = - - 
h{l — 7 ) + 2g'y 
f, /, + ( 27 - 1 )/+ 2 ^ (47-1) . 
All the constants • are therefore absolutely determinate and the solution is 
complete. 
§ 16. Expressions for the Stresses. 
The reduced expressions for the four stresses are given below : 
rr = ixE 
-{ffr- |aV + |#yc‘} +r=|(l +y)^-(4y+ 1)| 
+ 2^ X 2y [2c® — a®] — r^ 
12 
+ rh^ (4y + 1) - 2y2 
16ac^ 
+ =^Ay + 1) ! // (- 1,_ 
1 n%{a.) \ p 
COS 
nirz 
( 101 ). 
4c-a-7 *(-!)" 
■> ^ o 
77" 1 
+ l)« + -(8y+l) Ii-(8y+4)I, 
ya- (V - Ir) - Ir 
f" + 1) Up)-( f + - pli (p)l<=os'/ 
L \ -*^1 / \ -*^1 7 / P J 
- - Q 
+ /rE ' _ j27^1 _XA<^ 2 y+iy\ +E- 
2 ^3 
- 2»-(|(2y + - ««)- r*^.f - 2,-V + |(2y + l)-4 
, J_ T \ V 1-1)" Io(p) nTT- 
+ + 1) s — COS 
1 # Il(«) 
( 102 ). 
4 
4t“«®7 * ( — !)'■* _ 
O o 
TT'' 1 n" 
(2y 4- 1)« + -( 8 y + 1) Ii - ( 8 y + 4)1 
7«4V-lF)-If 
«I 
b 
- 2 
niTZ 
COS 
12 
«4 4 +^2 _ j ) 
— (4y — 1)31 + 2 y 22 ( 2 m — ce^] 
->■*(-//")+ r¥(4y-l)-2y:‘ 
- 4®‘'"’(2y + i)s 
TT’ ^ 1 Jl-’ pll(«) C 
4iC~a?y * ( — 1)" 
O ^ 0 
TT*' 1 
4 
2 y + i)a + -(8y + l) Ii-( 8 y + 4)Io 
7^41/ - I/) - 1/ 
1 
. P \ b 7 
2 c 2 
+ r. - io(p) L, “ 1 
1 
7 
a7r2 
COS 
C y* 
( 103 ). 
