303 
1912-13.] Plane Strain in a Wedge. 
where 
m = 8 cos a sin 3 a , 
In Case II. 
2 sill a sin 2a , c 9 = COS a + 3 cos 3a 
'2 /xu = 
2 / AU = Q — 
4 m l 
k^j) {Sl + h){h 2 ' + y2) _ Sl(/ ‘ 2 * x2) + s * y2 ] ■ } 
A + 2a , v 
0/F“ + S 2/ — S 2 
2m 2 L2(X + /4) 
xy 
(38) 
where 
^ = - 8 sin a cos 3 a , gj ■•= 3 sin 3a - sin a , t> 2 = sin a + sin 3a . 
If the results of the above two cases are added, the displacements 
due to pressure Pr on 0 = a will be obtained. 
When \ = /u the results are as follows : — 
P p 
2 /xu — - — -(cos a + 2 cos 3a )(h - x)y - - — [sin a (h 2 - x 2 + y 2 ) + 4 sin 3a?/ 2 ] , 
2 m 4 m 1 
p 
2 [xv - - — [cos a( 3/? 2 - 2 hx -x 2 + y 2 ) - 4 cos 3a(/?. - £c)asl 
4m 
4- - — (2 sin 3a - sin a) #?/ . 
2 TWj 
(39) 
In Case III. 
Pg 
i/x 
{ „ A . \( cos /? /i 2 - a; 2 sin , 7 * \ 
\ 2(A + /x)J \cos 2 a 2 sin 2 a v / 
+ ( A +V 3e0 B*a)^£ , 
\2 (A + /x) / cos 2 a 2 
4/xLVi 
A 
/d_\2(A + /*) 
A + 2/x 
2(A + /x) 
cos , sin B y 2 
Cl xy 4- — 
cos 2 a sin 2 a 2 
(40) 
3 sin 2 a 
sin /3 h 2 — x 2 
+ cos z a - 
A \ sin (3 
2(X + fi) 
-«)*]. 
sin 2 a J 
(15) It is of considerable interest in the present case to have some definite 
notion as to the extent of the motion at any point of the base. It is at 
once obvious that, as the base forms a considerable portion of the whole 
boundary, any serious movements of the base would somewhat discount the 
value of the foregoing results in their application to masonry dams resting 
on rock. The movements for the case of a wedge of 2 a = 36°, having the 
front face vertical, have been calculated for the extreme points of the base, 
which have been taken to be ^ = 100 feet and y = dz 32 - 49 feet, the dam 
being thus 105T5 feet high. 
The movements have been calculated for the three cases already stated 
in § (14). 
