Page 179 - Reliability and Maintainability of In service Pipelines

Case Studies on the Application of Structural Reliability 163

M s ; V s ; F cr and a o are flexural stress, shear stress, crack control limit and con-
crete cover The formulae presented by design codes for the resistance modes
have stationary formats; while in the case of corrosion, the wall thickness of the
pipe is a time-dependent parameter (i.e., decreases within the time). Hence, the
time-dependent format of each formula is given in the last column of Table 5.9.

Symbols

a depth of the equivalent rectangular stress block, (mm)
A the acid-consuming capability of the wall material
2
A s Area of tension reinforcement in length b, (mm /m)
b unit length of pipe, 1000 mm
B 1 crack control coefficient for effect of spacing and number of layers of reinforcement
c the average rate of corrosion (mm/year)
crack control coefficient for type of reinforcement
C 1
d distance from compression face to centroid of tension reinforcement, (mm)
diameter of rebar in inner cage, mm
d b
[DS] dissolved sulfide concentration (mg/L)
0
f design compressive strength of concrete, (MPa)
c
design yield strength of reinforcement, (MPa)
f y
F crack width control factor
F c factor for effect of curvature on diagonal tension (shear) strength in curved components
F d factor for crack depth effect resulting in increase in diagonal tension (shear) strength
with decreasing d
F N coefficient for effect of thrust on shear strength
h overall thickness of member (wall thickness), (mm)
i coefficient for effect of axial force at service load stress
k acid reaction factor
J is pH-dependent factor for proportion of H 2 S
w the width of the stream surface
P’ perimeter of the exposed wall
M s service load bending moment acting on length b, (Nmm/m)
M u factored moment acting on length b, (Nmm/m)
N s axial thrust acting on length b, service load condition (1 when compressive, when
tensile), (N/m)
N u factored axial thrust acting on length b, (1 when compressive, when tensile), (N/m)
s is the slope of the pipeline
t elapsed time
u is the velocity of the stream (m/sec)
basic shear strength of length b at critical section
V b
Φ the average flux of H 2 S to the wall
strength reduction factor for flexure
[ f
strength reduction factor for shear
φ v
Δ reduction in wall thickness due to corrosion, (mm)
maximum permissible reduction in wall thickness (structural resistance or limit), (mm)
Δ max
The four limit states (i.e., Eqs. 5.33a 5.33d) can be classified in the two main
categories of failure modes, namely serviceability limit states and ultimate