314 REPORTS ON THE STATE OF SCIENCE, ETC. 
An approximate investigation by Leon! shows that the maximum stress at the 
central point of the circular contour is 2 p where p is the stress applied in a very wide 
plate, but the boundary conditions are not fully satisfied. It is, perhaps, easier to form 
a rough idea of the stress distribution obtained by considering a very wide tension 
member under a stress of intensity p with a central hole of radius a, for which there 
is an exact solution. Taking one half of the member when divided by a central 
longitudinal plane, upon which latter stress systems are imposed corresponding to 
those which the other half of the member produced before the division took place, 
we have at the circular contour a varying stress of 3 p at A, fig. 1, falling to zero stress 
at B when 0=30°, and becoming a compression of value —p at C, while along the free 
side C D we have to annul a normal stress 
i= 49 (168 (1498) 
having a value —pat ©, zero atr=a¥V 3 and afterwards rising to a small tensional value 
before it ultimately disappears. There is also a radial stress rr along this edge, which is 
zero at C, and increases slowly to its full value of p in a manner so much resembling 
that actually found in a notched tension member of this kind that it may be considered 
to represent this latter approximately. The main effect is, therefore, to estimate the 
effect of annulling 06 along the vertical edge. We shall then have zero stress at C, and 
presumably a somewhat smaller change along the contour A C as the distance from C 
increases, so that we may expect to find a stress at A somewhat greater than 2 p, 
which experiments show to be correct. 
For example, in the case of the notched transparent member shown in the lower 
part of fig. 1, where the stress distribution is experimentally determined, we find a 
maximum stress of 1,340 lbs. per sq. in. across the minimum section, due to a mean 
applied stress p,,—734 lbs. per sq. in., from which latter it is necessary to find the 
equivalent value of the stress p applied to an infinite plate from an approximate 
relation 
p.nalc —1)= |"“80.ar 
a‘ 
r’ 
where 66=54542 
and c a=the half-width of the plate and the expression for 00 has been assumed from 
Leon’s approximate investigation. 
This last equation gives p—620 lbs. per sq. in. approximately, so that the increase 
of intensity at the notch is 2°16 in this instance. 
The great variation of stress intensity across the minimum section, accompanied 
as it is by cross stress having here a maximum value of about 4 p, renders this form of 
specimen unsuitable for tension tests, since, if the material is approximately elastic 
up to fracture, the stress system is never simple tension, and, if it becomes semi- 
plastic or wholly plastic, it is still possible that there may be two principal stresses of 
the same sign at all points of the minimum cross-section except the ends, and, should 
the material fail in shear, the apparent strength obtained will then be greater than that 
of a simple tension member, as is often found to be the case. 
Standard test-bars for plates, as found in specifications for testing materials, can be 
derived from this form, by introducing a parallel length of the same width as the 
minimum cross-section between the notches, and the stress system produced when 
observed in circularly polarised white light is shown in fig. 2 for a transparent tension 
member, in which the stress in the central part is arranged to give an intensity repre- 
sented by a very sensitive purple-red field so that the somewhat higher stress near 
the form of the straight and curved sides, and represented by a blue field, is very 
apparent. 
As may be inferred, and is in fact proved by experiment, this marked increase of 
stress, at a point just beyond the central straight portion of the contour, may be 
multiplied almost indefinitely by increasing the curvature of the joining curves. 
Thus, for example, in a transparent model of a flat tension member with ends en- 
larged to 0°932 in. width from 0-460 in. at the centre, and a connecting curve of } in. 
radius, the stress increased from 1,200 lbs. per sq.in. to 1,480 lbs. per sq.in., or 23°4 per 
1 Osterrcichische W ochenschrift fiir den Offentlichen Baudienst, February 1908. 
