COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 349 
the tensile circumferential stress is greater than would occur in a plain tube of the 
same thickness. It will further be seen from equation (7) that under these condi- 
_ tions an increase in the shrinkage allowance results in an increase in the tensile stress 
between the rings. Evidence of a similar effect was clearly shown by the experi- 
ments described in the previous paper, the stresses being increased by a constraint 
which would, at first sight, be expected to reduce them. 
Through the courtesy of the Chief Electrical Engineer to the Department of 
Public Service, City of Los Angeles, the author has been supplied with details of the 
dimensions of a reinforced pipe which forms part of the pipe line to the power 
station of that city, and it will be instructive to investigate the stresses which may 
occur in it under certain assumed conditions. 
The internal diameter of the pipe is 80 in., and the thickness 0-63 in. The 
reinforcing rings are 4:45 in. wide by 1-575 in. thick, and are spaced 11-05 in. centre 
to centre, leaving an unsupported length of pipe equal to 6-60 in. The working 
pressure is stated to be 642 ft. of water, or 278 lb. sq. in. For this case we have 
1-285 we N 
——= = 0-255, ml _ 9-841, H =0-800, M = 0-925. 
The circumferential stress which would be produced in a similar pipe without 
reinforcing rings would be 
ae = 17,900 Ib. sq. in. 
The actual maximum stress in the pipe, from equation (7), is 
s 
his 2 ese fi Sa 
qi=0°5 aes 0 re 
—_———--- = 
The stress gy in the ring is most readily obtained from equation (6); thus 
PR? 1 (= 
io. ) Mantis, Be 
Ee 
and I — "EF *) _ 9.490 ( 
Tt 
The author has no information regarding the amount of shrinkage allowed for the 
rings. The manner in which, according to this theory, the stress in the rings and the 
maximum stress in the pipe vary with the initial shrinkage is shown in Table I. 
TABLE I. 
Initial Shrinkage s | Stress in Rings qo Max. Stress in Pipe q? 
(in.). (Ib. sq. in.). | (Ib. sq. in.). 
0-000 8,780 9,450 
0-002 9,500 8,750 
0-004 10,230 8,060 
0-006 10,950 7,360 
0-008 11,680 6,670 
0-010 12,400 5,970 
0-013 13,490 4,930 
0-016 14,57 3,880 
0-020 16,020 2,490 
Assuming a maximum working stress of 6 tons per sq. in. in the rings, the 
_ shrinkage would require to be 0-013 in., but under these conditions the maximum 
stress in the pipe, viz. 4930 lb. sq. in., would appear to be unnecessarily small, The 
