365 
1911-12.] The Elastic Strength of Flat Plates. 
L. The curve cuts the horizontal ordinate at _p = 46. 
(1) f x — 30,700 
(2) /J§ 27,300 
The average of these results gives 
(1) f 1 = 31,900 
(2) / 2 = 28,600 
No. (2) being corrected for m. 
Again it appears that No. (2) is closer to the actual yield stress than 
2 r ^ 
No. (1), and that the formula /=-- 9 . p is the more correct one. 
3 t 
The Question as to the Elastic Strength of the Plate . 
The circular plate fixed at the edge and under uniform load on its area 
is an example of material under two principal stresses, circumferential and 
radial. At the circumference, where these are greatest, they are in the 
ratio of unity to Poisson’s ratio. The maximum principal stress is therefore 
equal to the radial stress at the circumference. 
The radial strain at the circumference is affected by the circumferential 
stress acting at right angles to the radial fibres. The strain thus induced 
by the combined action of the two stresses, if multiplied by Young’s 
modulus, gives a measure of the elastic strength of the plate on the 
assumption that the maximum principal strain determines it. 
The two theories then give for the plate 
(1) Maximum stress 
(2) Maximum strain 
, 3 r 2 
h=- iT ,-v, 
2 r 2 
f-2 = ~ zl yP 
the latter being true if m = 3. In the present case, with m = 3T9, the 
formula must be multiplied by 1*01. 
The results stated above seem clearly to indicate, in the author’s 
opinion, that the second of these is the more correct one, namely, that the 
elastic strength of the plate is a function of the maximum strain. He 
therefore arrives at the conclusion that, for a circular flat plate fixed at the 
circumference and uniformly loaded upon its area, the analysis as given in 
Thomson and Tait and elsewhere is correct and verified by experiment, 
and further, that of the two elastic strength theories, that of the principal 
strain more nearly accords with experimental results. 
