292 
DR. G. B. JEFFERY ON PLANE STRESS AND 
from the straight edge. Here again, however, the maxima and minima are 
accentuated. The minimum at the central point has decreased and has become a 
compression numerically equal to 1'956T. 
It appears that for the range of values which we have investigated the maximum 
stress is on the circular boundary at the point of nearest approach to the straight edge. 
Its value for different values of the ratio of the distance of the centre of the hole from 
the straight edge to the radius of the hole, together with the stresses at the centre of 
the straight edge and at the most remote point of the circular boundary, is shown in 
Table III. 
Table III. 
«1- 
Ratio of distance 
of centre from edge 
to radius of hole. 
Stress at mid-point 
of straight edge. 
Stress at nearest 
point of circular 
boundary. 
Stress at most 
remote point of 
circular boundary. 
0-6 
1-185 
- 4-080T 
5-064T 
3-362T 
0-8 
1-337 
-1-956 
4-366 
3-266 
DO 
1-543 
-0-895 
3-919 
3-201 
1-2 
1-811 
-0-269 
3-609 
3-152 
1-4 
2-151 
+ 0-134 
3-396 
3-115 
1-6 
2-577 
0-405 
3-254 
3-087 
1-8 
3-107 
0-591 
3-162 
3-065 
2-0 
3-762 
0-721 
3-103 
3-048 
2 • 2 
4-568 
0-810 
3-065 
3-035 
2-4 
5-557 
0-871 
3-043 
3-025 
00 
OO 
1-000 
3-000 
3-000 
It will be noted that when the hole is very near to the straight edge, so that the 
two boundaries are separated only by a narrow connecting piece, the stress in this 
piece consists of a very large tension on the inside and a numerically slightly less com¬ 
pression on the outside. Hence, as might be expected from general considerations, 
the stress in this narrow connecting piece is a bending moment accompanied by a 
certain amount of tension. 
These results may 'be compared with some experimental results recently obtained by 
Prof. Coker and Messrs. K. C. Chakko and Y. Satake* by optical means. These 
deal with the stresses in a strip of finite width under tension with a circular hole 
centrally placed, whereas we have considered the case of a semi-infinite plate with a 
circular hole near its straight edge. The problems are therefore not quite comparable ; 
but as in each case the critical region will clearly be near the minimum section between 
the hole and a straight boundary, the two problems may be expected to exhibit the 
same general characteristics. For the strip of finite width it is found that there is 
maximum stress in the circular boundary at the points of nearest approach to the 
* ‘ Transactions of the Institution of Engineers and Shipbuilders in Scotland,’ vol. lxiii., Parc I., p. 33, 
ly 19. 
