Page 68 - Reliability and Maintainability of In service Pipelines

Pipeline Inspection and Maintenance 57

Buckling limit state can be presented in the form of Eq. (2.8).

GP; P cr ; tð Þ 5 PtðÞ 2 P cr ð2:8Þ
in which buckling strength (i.e., PtðÞ) can be calculated by Eq. (2.9) (Moser and
Folkman, 2008).

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 EI
P 5 32R w B E s ð2:9Þ
0
S f D 3
m
and the critical value for buckling suggested by Moser and Folkman (2008) is as
Eq. (2.10).
W c P s
P cr 5 R w 1 ð2:10Þ
D m D m
Flexure: Excessive bending can result in flexural failure which is an ultimate
failure. If the flexural stress on the pipe exceeds the flexural strength, pipe fails
structurally. Flexure limit state function can be presented in the form of Eq. (2.11).

GM n ; F y ; t 5 M n tðÞ 2 f y ð2:11Þ
For steel pipes the equation to calculate flexural capacity suggested by Gabriel
(2011) is as follows:
2D f EΔYy 0 S f1
M n 5 ð2:12Þ
D 2
m
The critical threshold for flexure failure is f y which is yielding strength of pipe
material.
Shear: If a pipe loses its shear strength it is completely failed. Therefore shear
failure mode is considered as the ultimate strength limit state function, which can
be presented as Eq. (2.13).

GV b ; V s ; tð Þ 5 V b tðÞ 2 V s ðtÞ ð2:13Þ
The formulation for shear strength for a reinforced concrete pipe suggested by
ASCE 15 98, 2000 is as follows:

q ffiffiffiffi
A s F d F N
0
V b 5 0:083b[ v dF vp f c 1:1 1 63 3 ð2:14aÞ
bd F c
N u
F N 5 1 1 ð2:14bÞ
3:5bh
If the shear stress (i.e., V s ðtÞ) exceeds the shear strength of a pipe (i.e., V b ðtÞ),
then failure happens.