350 REPORTS ON THE STATE OF SCIENCE, ETC. 
weight per foot of the reinforced pipe is 1090 lb. The thickness of a plain pipe 
designed to carry the same pressure with a stress of 6 tons per sq. in. would be 0-842 
in., and its weight 722 lb. per foot. 
If a working stress of 6 tons per sq. in. be assumed for both the pipe and the rings, 
the working pressure may be 408 Ib. sq. in., and the shrinkage necessary 0-0014 in. 
To sustain this pressure a plain pipe would weigh 1059 lb. per foot, which is still 
lighter than the reinforced pipe. It is, of course, evident that for a given maximum 
stress and pressure a plain pipe must have the advantage in weight owing to the 
fact that the stress is uniformly distributed through the material. 
The possibility of allowing a higher working stress in the rings than would be safe 
for the pipe does, however, enable a reinforced pipe to be made lighter than a plain 
pipe, provided that the rings are sufficiently close together. Thisis shown by Table II., 
which gives the results of a calculation based on the dimensions of the Los Angeles 
pipe, assuming a stress of 10 tons per sq. in. for the rings and 6 tons per sq. in. for the 
pipe. In this table the pressure and the initial shrinkage required to produce these 
stresses are given for various distances apart of the rings, and the weights per foot 
of the reinforced pipe and a plain pipe to carry the same pressure with a stress of 
6 tons sq. in. It will be seen that the spacing of the rings must be less than 12 in. 
in order to obtain a lighter pipe. 
TaBeE II. 
Distance Initial Workin Weight pera 
| between Rings Shrinkage Seer Ee | | 
| le } LAr 7 d ‘4 = | | | 
| uoentd Beg a ‘ (Ib. sq. in.) Reinforced Pipe’ Plain Pipe 
| (in.) (in.) 
| (Lb.) |, % (libs) | 
—}— — — = _ | ——— ee | 
| 3-0 0-0122 720 Ly” 1850 E77 en 
5-0 0-0131 628 1180 1645 
| 6-6 0-01.45 541 1085 | 1410 
9-0 0-0187 448 | 988 | 1170 
| 12-0 0-0258 345 905 : 896 
| 18:5 0-0394 209 | 800 | 536 
25-1 0-0425 175 740 450 
43-0 0-0395 209 | 595 | 536 
| | | > 
IL. 
On the Graphical Determination of Stress from 
Photo-Elastic Observations. 
By Prof. L. N. G. Fmon, -M.A., D.Sc., F.R.S., University College, London. 
1. In the 1914 Report of this Committee various methods were given by Prof. 
Coker and the author for obtaining the stresses in a plate of transparent material 
strained in its own plane from the ‘ isochromatic ’ and ‘ isoclinic’ lines (B.A. Report, 
1914, pp. 201-210). It was there shown that the isoclinic lines, together with the 
conditions at the boundary, theoretically determine the stress-system completely. 
Before, however, this determination can be carried out, it is necessary to fit exact 
functional relations to these isoclinic lines, and this is a very difficult matter in practice. 
In the same report a method was given whereby the stresses xa, yy, xy could be 
derived from a knowledge of both the isoclinic and the isochromatic lines. If P, Q 
are the principal stresses at any point, and the stress P makes an angle @ with the 
a-axis, then 
zy = (P — Q) sin ¢ cos @ : ; : ; «Ly 
and is thus known everywhere. 
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