errr 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 341 
In Specimens A6 and A13 the maximum value (underlined in Table VI.) of 
greatest stress-difference was found to correspond to the maximum of bending; 
and in B31, to correspond to the maximum of torque. It is clear that the 
maximum value of the greater principal stress in A6 and A13 must also corre- 
spond to maximum bending, because to obtain this principal strain we have to 
: 3 Pig 
take the numerical sum of 4a anda/ 2 > +9, and the latter of these two 
J€\~ 
; 3 : : é 
expressions, as well as the 4% happens to be a maximum at the maximum of 
bending moment. 
For B31, having regard to the relative values of e, and ¢, it appears that 
the maximum value of the greater principal strain is also at the maximum of 
bending. 
fielation between Maximum Shear Stresses and Greatest Strain-difference. 
An examination of Tables V. and VI. shows that the values of the maximum 
principal strains are not nearly so uniform as the maximum shear stresses; 
but they are not so widely divergent as the principal stresses (not tabulated). 
As might be expected, the values of the greatest strain-difference are rather 
more uniform, those for the combined tests appearing rather smaller than those 
for the separate tests. 
Fig. 14 has been plotted from Tables V. and VI. It will be noted that the 
solid specimens group themselves to the right for the reason that their calculated 
stresses are too large—i.e. more than the real stresses. Making use of a former 
result of one of the authors, that the stresses calculated for solid specimens 
(using formule true only for perfectly elastic conditions) are about 15 per 
cent. too high, the stresses of the solid specimens have been reduced in the 
ratio 422, and the reduced values have been plotted against the greatest strain 
difference in fig. 15. In fig. 15 the points corresponding to the hollow specimens 
appear in the same positions with respect to the axes as in fig. 14. Fig. 15 
illustrates also the relation between ihe magnitudes of the maximum shear 
stresses of the differently-tested specimens. 
VII. 
On Some Problems Relating to the Design of High-Speed Discs. 
By R. V. Sournwett, of the National Physical Laboratory. 
Recent investigations by Prof. H. Lamb and by the present author ! appeared 
to have some bearing on the practical problem of vibrations in turbine discs,? 
and the work has accordingly been continued at the National Physical Laboratory, 
with the assistance of Miss B. 8. Gough. The following summary of the progress 
made has been written in the hope that discussion will reveal the directions in 
which further extension could be most usefully directed. The accuracy of the 
calculations depends in every instance upon the validity of the theory of thin 
plates, as applied to the problems treated; and since the limitations of this 
theory are not as yet fully understood, comparative experiments will be of the 
greatest value. 
1 ‘The Vibrations of a Spinning Disc,’ Proc. Roy. Soc. (A), vol. 99 (1921), 
pp. 272-280. 
* Cf. K. Baumann, ‘Some Recent Developments in Large Steam Turbine 
Practice,’ Jour. Inst. Elect. Eng. (1921). 
