348 REPORTS ON THE STATE OF SCIENCE, ETC. 
and the stress q1 at the centre is given by 
aj ed 
1 a 
_PR_4,/PR_ 1 | cPR*—cEsh + 1-55 PRA ) 
t ( ¢ x ct-+h)+1-55tHViR  } 
ne PR _ Mch PR Es 
ict h). A: “ab EAB (P oa) (7) 
ne Pett 
oe 
rel, LIN Po 
2) Ney 
aa lUSSReORSeCOne 
—4 il 
(7983.84 
Fie. 2 
The values of M and H are plotted in fig. 2 on a base of al Given the radius R and 
thickness ¢ of the pipe, and the distance apart / of the rings, 
mw teh ee 
JiR 
the values of M and H may be read off from fig. 2, and the maximum stress gq! readily 
obtained from equation (7). 
The stress that would be produced in a pipe of the same dimensions without 
PR : : ‘ 
reinforcing rings is equal to aa and it would appear, therefore, in order that the rings 
should have any strengthening effect, that M must have a positive value greater than 
zero. It will be seen from fig. 2 that this is only the case when Mig less than 2-36, 
or 1<3-66V/R. 
This limiting length is independent of the amount of shrinkage given to the rings. 
When / is greater than 3- 66/, tR and less than 8-54/tR, M has a negative value, and 
. Ti uk oe 
