Page 137 - Buried Pipe Design

Design of Gravity Flow Pipes 111

limit can be made by comparing the ring compression stress with yield
and/or ultimate strengths.

Wall buckling. Buckling is not a strength performance limit, but can
occur because of insufficient stiffness. The buckling phenomenon
may govern design of flexible pipes subjected to internal vacuum,
external hydrostatic pressure, or high soil pressures in compacted
soil. (See Fig. 3.22.)
The more flexible the conduit, the more unstable the wall structure
will be in resisting buckling. For a circular ring in plane stress sub-
jected to a uniform external pressure, the critical buckling pressure is

3EI
P cr (3.13)
R 3
For a long tube in plane strain, E must be replaced by

E
E
1 2
Also I may be replaced by
t 3
I 1
12

in Eq. (3.13). Then
Et 3
P cr (3.14)
2
4 (1 ) R 3
For buckling in the inelastic range (materials with pronounced yield
points), the critical buckling pressure in terms of the yield point
y is

t
y
P cr (3.15)
2
2
R 1 4
y R /(Et )

Figure 3.22 Localized wall buckling.