356 REPORTS ON THE STATE OF SCIENCE, ETC. 
IX. 
The Stresses in Cylinders and Pipes with Eccentric Bore. 
By G. B. JEFFERY, W.A., D.Sc. 
In a recent paper! the auther developed a general method for tke solution of 
two-dimensicnal elastic problems in which the stresses are given over two circular 
non-intersecting, non-concentric boundaries. One of the problems which most 
readily yields to this method of solution is that of a cylinder or pipe, whose internal 
and external sections are both circular but not concentric, in stress under a uniform 
hydrostatic pressure either internal or external. The problem is soluble in finite 
terms and reference may be made t) the original paper for a discussion of the stress 
distribution. These results may be applied to the determination of the diminution 
in the strength of a pipe or vylinder due to a small error of centring as between the 
external surface and the bore. If the radius of the bore is 7, and that of the 
external surface 7, and if the distance between their centres is d the maximum 
stress when the pipe is under an internal pressure P is on the internal surface at 
the thinnest part if d<3r, and is of magnitude. 
“SE i ae Ra a 
(72+ 72)(72—7,7 —27,d — a?) 
This depends only upon the ratios of7,, 7,, d, and we may therefore take a=ratio of 
mean thickness of cylinder wall to internal diameter, 8 = ratio of centre distance 
to mean thickness of cylinder wall, or 
a=(r,—7)/27, B=a](7.-7)) 
The maximum stress them becomes 
P [21+ 20)? { (1 +2a)?+1—4aB—da"B*} | 
{14 (1+ 2a)?} {Cl + 2a)?— (1 + 208)} 
In the appended tables the maximum stress in the material is given in lbs. per 
sq. in. per 1000 lbs. per sq. in. internal pressure for values of a, 8 lying between 0 
and ‘2 in each case. 
! Plane Stress and Plane Strain in Bi-polar Co-ordinates. Phil. Trans, Royal 
Society, Vol. 221 A, p. 265. 
