COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS, 305 
The actual increase at this point is 4.5 per cent, of the difference between 
the displacement remote from the flange and at the flange, which approaches 
very closely the calculated value of 4.3 per cent. 
Tests have also been carried out on tubes of greater thickness and with 
broader flanges, the results obtained being very similar to those described 
above, but, as would be expected, the agreement of theory and experiment is 
not so close. 
The results of this investigation have an important bearing on the strength 
of steel pipes reinforced by steel bands, such as are occasionally used in pipe 
lines for hydro-electric installations. Experimental work in this connection is 
at present in progress. 
Radial Displacement, 
Distance from for Pressure 800 lb. per sq. in. 
Flange (ins.) Calculated Observed 
(ins. x 10°) (ins. x 10-”) 
0 10-60 -- 
025 11-53 12-05 
05 13-60 14-20 
075 15-94 16-30 
100 18-16 18-80 
+125 20°31 20-80 
+150 21-92 21-95 
“175 22°95 22-80 
-200 23-78 23-30 
*225 24-22 23-80 
250 24-46 23°85 
30 24-52 23-90 
35 24-32 23-70 
40 24-10 23-50 
45 24-06 23°35 
50 24-02 23°35 
IIL. 
On Stresses in Multiply-connected Plates. 
By Professor L. N. G. FILon, W.A., D.Sc., FBS, University College, London. 
1, It is a well-known theorem, due to Airy, that in a problem of plane strain, the 
axes of x and y being in the plane of the strain, the stresses can be expressed in terms 
of a single function E by the equations 
vy = -- » 4 
Wd ph Baby * vi 
ns denoting the stress, parallel to s, across a face perpendicular to n,. 
This result can be extended to the case where the stress zz normal to the faces of 
a thick plate vanishes throughout. In this case, P, Q, S$ denoting the mean stresses 
taken across the faces of the plate 
*°E iE ; 3-E 
f . See : : : 
bvdy ’ (2) 
In either case the function E, which is called Airy’s stress function, satisfies the 
equation 
v'E=0 : ; : ' 2 Paul 3) 
