338 REPORTS ON THE STATE OF SCIENCE, ETC. 
TABLE V. 
BENDING OR TORSION SEPARATELY APPLIED. 
| 
. } | 
Range of Data from Maximum | Maximum’ \y4,;- | 
| * Strain. Dead-weight Test Greater Or ares 
Specimen | Kind of Test Orie on _| Principal | Toe Shear 
s fia stra: Stress | 
=H Pp,org ;R, or Ry Snes Difference Stress 
e e e e 
| tonsa” | om. o” | 
Al5 solid ... | Bending only 10-33 10:00 6-12 -00126 -00157 6-87 — 
All 5 ais? o ‘A 11-97 10-50 6-60 -00141 -00176 7-18 
| Al4 hollow ... | 3 ae 9-87 10-00 5:36 -00136 -00171 6-37 | 
IAG Ng adsl as x 8-18 10-00 5-13 -00118 00147 | 6:37 | 
A7 solid ve | Torsion only 14-67 5-00 7-01 -000975 -00195 7-65 | 
| ALO hollow ... | 35 ” 9-75 4-75 5-27 -000813 -00163 6:50 | 
| BBI2 wae a ees tT 1) 3 10-72 5-00 5-86 -000850 -00170 6-25 | 
|) DBZ Seve ge = 2 2 11-36 5°00 6-03 -000877 -00175 6-10 | 
Ferisesce Pee iy ee res ea 10-30 5-00 5°93 000805 | -00161 | 6-25 
| BST eto dae < 10-65 5-00 5-87 -000842 | -00168 | 625. 
Nove.—The data in the first five columns are taken from Tables 2 and 3, pp. 136-146, Proc. Inst 
Mech. Eng., January-May, 1917. 
It will be observed that the values of the greater principal strains are widely 
divergent. The values of the greatest strain difference are not so uniform 
as the maximum shear stresses, especially if account be taken of the enhanced 
values of the latter for solid specimens, which greater values are presumably due 
to the formula of calculation. 
It should be observed that the greatest strain differences for bending, in 
Table V., are calculated on the assumption that the minor principal strains ¢2 
are equal to @¢; where o is Poisson’s Ratio and ¢; is the (greater principal) 
strain. This would be exact if the stresses were elastic, but since there is 
a non-elastic element, the results for ¢, are approximate. The non-elastic ele- 
ment is, however, only about one-sixth (at most) of the total strain, so that the 
error in assuming that the greatest strain difference (bending tests only), 
Viz. €;—€2, is equal to ¢; +4 makes, at the most, an error of 4 per cent. in the 
greatest strain difference. 
To apply formule (3) and (4) to calculate the strain components for the 
combined tests, the assumption is made that these components are linearly 
distributed as in separately applied testing. The effect described on pp. 334 
and 335 with respect to decrease of one component strain when the other is 
increased may possibly be due to non-linear distribution of these strains. It is 
probable, however, that there will be no marked departure from linearity, and 
formule (3) and (4) have been used to evaluate the component strains for 
fracture ranges. 
Given two direct strains ¢; and e2 at right angles to each other, and a slide 
@ on planes parallel to e¢; and ¢2—which are the circumstances: corresponding 
to the localities of greatest stress in the specimens—then, if 8, and 8, are the 
principal strains, 
3=3 {ate Vee e 
and the greatest strain difference is 
3, —8,= V(e—2,)?-+ 4? 
where 
(5) 
310-5 
5,=3 {« Fey V (res)? +9? } 
} 
e¢j= at 
eX 
=— Ree "A3 x al] 
a “Ra” < 743 x 10 
and 
p= 2B x 9-27 x 10_ 
cR “A v 
