Page 121 - Pipeline Rules of Thumb Handbook

108 Pipeline Rules of Thumb Handbook

In a section of unrestrained pipe at B, the longitudinal
stress caused by only internal pressure will be half the hoop
stress.

s H
s LB = psi (3)
2
The associated strain will be made up of a

(i) Temperature effect

a T
e TE =D
(ii) Pressure effect

s LB s H
e PR = =
Figure 4. Sectional plan for anchor block design. E 2 E
(iii) Poisson effect

us H
e PO =
E
The net longitudinal strain at Point B will therefore be

s H
D
e B = a T + (12 - ) . (4)
u in in.
E
Figure 5. Sectional elevation for anchor block design.
The transition of stress and strain between points A and B
is assumed to vary as a linear function of length as shown in
section A–B is a transition from fully restrained to Figure 2.
unrestrained and beyond point B is unrestrained. (Fully In order to establish the length L over which the transition
restrained is taken to be a condition of zero longitudinal occurs, the longitudinal resistance of the soil needs to be
strain.) known. For this part, it is assumed that any tendency to
Analyzing a short section of fully restrained pipe, subject to move will be counteracted by constant and opposite soil
1
internal pressure and a temperature change, there is a tensile force. Wilbur has recommended a design value for average
stress due to a Poisson effect of soils of
2
PDi Ê D o ˆ
.
s PO = us H where s H = F s = 80 Ë 12 ¯ lbf ft (5)
t 2
and a compressive stress due to a temperature change of Between A and B equilibrium of forces exists and
therefore,
D
s TE = E a T
FL = A m (s LB -s LA )
s
The net longitudinal stress therefore at Point A will be
From which
s LA = us H E a Tpsi (1)
-
D
A m (s LB -s LA )
L = ft (6)
and the strain at point A, being fully restrained, will be F s
zero
Total movement at B will be average strain between A and
e A = 0 (2) B over length L or