J 
) 
) 
: 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 357 
theoretical example should be constant ; but these discrepancies might be plausibly 
. for by the fact that the theoretical distribution of load is not accurately 
realised. 
The real test of the validity of the method lies in the agreement between the 
values of P and Q obtained at the same point by integration along lines of principal 
stress belonging to different (i.e. orthogonal) systems. 
In order to apply such a check, the value of Q at = 1-5”, y = 0, where the line 
of principal stress marked c in fig. 4 begins, was interpolated from Table II. and found 
to be —1-845 in our units. Q and P were then computed for various values of > 
along the line c from the data given in Table III., each successive entry in the fifth 
column being obtained by adding to the preceding the arithmetic mean of the two 
corresponding entries in the fourth column. 
TaBLeE III. 
” 
CALCULATION OF P anp Q ALONG THE Linz ‘‘c” oF PRINCIPAL STRESS. 
(P — Q) cot y 
> ¥ Bi" x arc 5° Q P 
0° 90° 2-25 0 —1-85 0-40 
5° 67° 2-33 0-086 —1-89 0-44 
10° Bie 2-38 0-135 —2-00 0-38 
15° 47° 2-53 0-206 —2-17 0-36 
20° 41° 2-70 0-271 |; —2-41 0-29 
25° BY ie 3°30 0-471 | —2-78 0-52 
30° 29° 4-00 0-630 | —3°33 0-67 
35° 24-5° 4-70 0-900 —4-09 0-61 
40° 18° 5-50 1:477 —5-28 0:22 
| 
SS SSS ss ss eee 
Finally, if we estimate the values of » at the four intersections Ac, Bc, Cc, De, 
and compare the values of P and Q obtained from Tables II. and III. by interpolation, 
we obtain Table IV. below. 
TABLE LY. 
CROSS-CHECK OF STRESSES. 
¢ Point P (II) P (III) Q (II) QU) 
ae era eed | 
6°5° Ac 0:45 0:43 —1-91 —1-92 | 
15° Be 0:42 0-36 —2-08 ile A 
23-5° Cc 0-47 0-45 —2-64 2-66 | 
33° De 0:64 0-63 —3-79 —3-79 | 
| 
The slight difference shown in the values of P — Q in the above is due to the fact 
that the values of P and of Q were interpolated for separately. 
Looking at these values, however, the agreement is singularly good, and may be 
looked upon as a remarkable confirmation of the accuracy of the method. 
It appears, therefore, that it is practically feasible to obtain the complete stress 
system in a transparent model from purely optical observations and without reference 
to the elastic properties of the material. 
The best thanks of the author are due to Mr. H. T. Jessop, M.Sc., of University 
College, London, who actually annealed the specimen of bakelite used in these 
observations and who obtained the tracings of the isoclinie and isochromatic lines. 
