COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 303 
In the limiting case in which displacement at the flange is entirely prevented 
the increase in stress may thus amount to 4.3 per cent. of the normal stress. 
The elastic deformation at the flange will reduce this figure, but it is sufficiently 
great to be measurable experimentally. 
A tube of mild steel was accordingly machined accurately to an internal 
diameter of 1 in. and an external diameter of 1.05 in., a collar being left 
on the tube having an external diameter of 1.5 in. and a thickness of 
.038 in. Connections were provided at the ends for attachment to a pump 
and gauge, and the tube was free to take up the longitudinal stress produced by 
the internal pressure applied. The increase in diameter was measured by an 
instrument specially designed for the purpose, and similar in principle to that 
previously used in another connecticn® by the author and Professor Robertson. 
An outline sketch of the instrument is shown in fig. 8. A light frame A is 
held on the cylinder by means of two flat springs B so that the steel point P, is 
set at one end of the diameter whose extension is to be measured. In contact 
with the cylinder at the other end of the diameter is a second steel point P, 
carried by a level L, which is free to turn about the knife edge D, and is held in 
position by the light spring 8; (consisting of a rubber thread). Between 
V’s in the outer end of the lever L and a vertical bar E supported as shown 
in the sketch from the frame A, is held a small diamond-shaped rocking piece 
R possessing two knife edges, one edge resting in the V’s, and the other against 
Fie. 8. 
the flat surface of the vertical bar E. The rocking piece carries on the con- 
tinuation of its axis a mirror M, and a counterpoise. The angular rotation of 
this mirror is proportional to the change in diameter between the steel points 
P,P2, and is measured by means of a telescope and scale. A mirror M, (not 
shown in the right-hand view) fixed to the vertical bar E serves to detect any 
displacement of the instrument as a whole. In these experiments the scale 
was placed at a distance of 15 feet from the mirrors, and by using a telescope 
having a linear magnification of about 25, and a fine cross wire, the scale could 
easily be read to 0.i mm. Successive readings of the scale for the same 
pressure range differed by not more than 0.1 to 0.2 mm. on a total reading 
(for parts of the tube remote from the flange) of about 40 mm. The lever 
ratio being 2.85, and the rocking piece being 0.25 in. broad, diametrical exten- 
sions could be measured to an accuracy of the order of 10% in. To secure 
this degree of accuracy it was found necessary to mount the apparatus on a 
massive pedestal supported by felt pads to damp out small tremors, and to 
Maintain a constant temperature. It was not possible to take accurate 
measurements within half an hour of handling the instrument. 
The pressure gauge used was a standard steel-tube test gauge made by 
the Budenberg Gauge Co. 
In the test the increase in diameter was measured at various distances from 
the flange when the pressure was raised from 100 to 900 Ib. per sq. in., 
and the results are tabulated below, together with the values calculated by the 
theory described above. For the latter purpose an accurate determination 
5 Mngineering, December 15, 1911. 
