Page 31 - Reliability and Maintainability of In service Pipelines

20 Reliability and Maintainability of In-Service Pipelines

δ 1 1
5 2 lining ð1:8Þ
2w l r r max
where:

δ 5 width of the crack
w c 5 thickness of mortar coating
w l 5 thickness of mortar lining
r 5 circular radius of pipe
r max 5 max radius
r min 5 min radius
Cracks are usually narrow and their width does not exceed the thickness of a
dime if the deflection of the pipe ring is less than 5%. As the pressure in the pipe
results in a rerounding of the pipe, and causes the cracks to heal, those remaining
are only hairline cracks which are distributed evenly throughout the pipe and heal
in moist environments.
Despite this measure, the best method to determine crack width is not observ-
ing pipe ring deflection but rather focusing on permanent deviations in radii of
curvature, which is a more reliable method.
A theory that involves a method on the basis of radii is longitudinal strain,
which supports the formula below:
r
σ z
5 ð1:9Þ
E R
where R is radius of longitudinal bend in pipe, r is radius of the pipe, and E is
modulus of elasticity.
Fig. 1.3 shows the compound yield of a pipe, it is devised that the yield stress
is slightly greater than the tensile strength, σ y , if both the longitudinal and ring
stresses hold the same sign (either tension or compression); conversely, the yield
stress is less than tensile strength, σ y , if the longitudinal and ring stresses hold
opposite signs.
Although yield stress is known to be a measure of performance limit in the
design of pipes, it is not always regarded as a failure condition, however in the
case of steel pipes, yield stress is biaxial in the worst cases. Yield stress is mea-
sured via the application of standard unaxial tension tests. An example of this is
shown in Fig. 1.3 which shows that steel pipes containing internal pressure, the
hoop tension stress is σ x , while longitudinal stress, σ z , causes biaxial stress.
Longitudinal stresses are associated with longitudinal bends in pipes, with tension
and compression acting on the inside and outside of the bend, respectively.
Therefore, it is safe to conclude that both hoop tension and longitudinal