COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 339 
TABLE MV 
ComMBINED TEsTs. 
Novre.—For tests at 90° phase angle the greatest values of the strain components and of the Greater 
Principal Strains and Greatest Strain Difference are given both for (2) Maximum Bending and Zero 
‘Torque, and (6) Maximum Torque and Zero Bending 
. 
ag Width of 20 
| 5&8 z Hysteresis | Strain Components | Greater |aq| 2 
| as | _ Loop. ae Serr <0 a 
Speime: | $5 |Z  Cm.on Seale} Principal Eis a 
} mea | 28 |_—————_|______ : Strain gg 3S 
aa | £  |Bend-| Tor- | _,,, | 4 : beacaell ae) 
fax] RN | ing stan, | eLX 10: px1loe | | En 
“a To neice i Ee simile: Vas 
| | ) | @) 092) @ 0-06 | (a) 0-92 | 
AG | 6-05 | 675 | 0-42 | 0-36 | — 575 |. 
hollow | (b) 0-064 (b) 1-12 (b) 0-58 (3 
RS | (a) 1-115 (a) negligible! (a) 1-115 | (a) 1:39 |ja 3 
Pi} eeJAls | $85 | 9-35 | 1-22 | 0-17 | ; ele is | 48 || fe 
BEF solid | | | (b) 0-154 (b) 1-20 (b) 0-67 (b) 1-22 l\as | 
: | |B | 
| * | (a) 1-10 (@) 0-26 (a) 1-11 | (a) 1-40 | a | 
| B31 /10-50 (15-90 | 1-02 | 2-68. | — 6-94" |/ BS | 
| solid | / | (6) 0-106 (6) 1-55 (b) 0-815 | (6) 1:55 \ 33 | 
| — Bue 
Biya fas |eo2 | 747} — | — | ror |  o965 117. | 1:59 | 720 | | 28 | 
|o8] solid | Sr} 
aN | | BS | 
—|fe2 | | | [jes | 
"a Bly | G90 | 770 | — | — | 0-843 | + 1-025 seh] aan ebg-gol |S | 
’ solid | | | '¢ 
The values of 6, and 6,—4, taken in Table VI. have becu calculated from formule (5),. 
Since o has been taken as = we have 
3 
€; +e act 
€;— e3 
5 
ae 
4° 
and formule 5 reduce to 
wah (3, -~4 2B gee eo POG 
3)= (48 a ae +9) and B= 4/249 
In working out the values of 5, and 6,—6, for the specimens tested with 
phase angle 90°, it has been kept in mind that the maximum strain of bending 
will coincide with only the residual (or hysteresis) strain at zero torque, and 
vice versa. These hysteresis strains could not be measured, but the width of 
hysteresis loop may be taken (since the non-elastic element is, at most, only 
about one-sixth of the total strain) as the difference between the range of strain 
measured and the range that would have existed if the material had remained 
elastic. Considering two loops, one for bending and the other, differing in 
phase by 90° from the first, for the torsion, it is possible to correlate exactly 
only four points of the one loop with four points of the other. These four 
‘points are, of course, the maximum of strain of one kind with the strain 
at zero stress of the other. If the strains were elastic, and therefore simple- 
harmonic like the stresses, any one point of the one stress-strain curve could 
‘of course be correlated with its corresponding point on the cther curve. To 
find the position of crank, which gives a maximum for the greatest strain differ- 
ence, a simple calculation was made on the assumption that the strains were 
simple-harmonic. On this assumption the maximum for this quantity comes 
out to be at either maximum bending or maximum torque. Since the residual 
(hysteresis) strains are small (see Table VI.), the one or the other of these two 
epochs has been assumed to be that of the maximum of greatest strain-difference. 
The values of this quantity have been calculated for both these epochs, and 
are given in Table VI. 
