Page 389 - Pipeline Risk Management Manual Ideas, Techniques, and Resources

364 Pipe Strength Determination
P,xD External loadings
Gm,, = -
2xt External forces require complex calculations both in determin-
where ing actual loadings and the pipe responses to those loadings.
0 ma^ = maximum stress (psi) Soil loads, traffic loadings, buoyancy, and the pipe weight are
P, = internal pressure (psig)
D = outside diameter (in.) typical loadings. For offshore and submerged pipelines, the
t = wall thickness (in.). effects of water pressure, currents, floating debris (producing
impact loadings), and changing bottom conditions must also be
considered. An equation given to calculate required wall thick-
This equation specifically calculates the tangential or hoop ness to resist buckling due to a static uniform external pressure
stress of a thin-walled cylinder of infinite length (Figure C. 1).
It assumes that the wall thickness is negligible compared to is [55]:
the diameter. Normally the outside diameter is used in the
equation (rather than the average diameter) to be slightly t = D X d q
more conservative. An exception is concrete pipe, in which
the internal diameter is used in the calculation [55]. This where
allows for concrete’s minimal tensile strength. Barlow’s for-
mula is not theoretically exact, but yields results within a few t = wall thickness (in.)
percent of actual, depending on the Dit ratio. (Higher D/t D = diameter(in.)
yields more accurate results, lower yields more conservative p = uniform external pressure (psi)
= pipe modulus of elasticity (psi).
E
results; see [55].)
Many plastic pipe manufacturers refer to a standard dimen- This equation does not consider the soil-pipe interaction that
sion:
is a critical part of the buried pipeline system. A rigid pipe
must directly withstand the external loads applied. On over-
DO
SDR= - stressing, typical failure modes are shear and crushing.
t A flexible pipe, however, deflects under load, allowing
Thus we have the surrounding soil to assist in the support ofthe load. Ifthis
deflection or bending becomes excessive, ring deflection
may be the failure mode causing buckling of the flexible
pipe.
where Ifthe external load has a velocity component associated with
it, this must also be considered. Highway traffic, rail traffic,
SDR = standard dimension ratio and aircraft landings are examples of moving or live loads that,
Do = outside diameter (in.) in addition to their static weight, carry an impact factor due to
t = pipe wall thickness (In.) their movement. This impact factor can magnify the static
IS maX = maximum stress (psig) effect of the vehicles’ weight. Design formulas to calculate
PI = internal pressure (psig) loadings from moving vehicles can be found in pipeline design
manuals.
Calculations can he done to estimate buckle initiation and
buckle propagation pressures for subsea pipelines. It is usually
appropriate to evaluate buckle potential when the pipeline is in
the depressured state and thereby most susceptible to a uni-
formly applied external force.

Longitudinal stresses
While the primary stress caused by internal pressure is hoop
stress, stresses are also produced in other directions. The longi-
tudinal stress produced by internal pressure can be significant
in some pipe materiais. The amount of restraint on the pipeline
uu in the longitudinal direction will impact the amount of longitu-
/#- PDl2T dinal stress generated in the pipe. If the pipe is considered to be
completely restrained longitudinally, the magnitude of the lon-
gitudinal stress is directly proportional to the hoop stress. The
proportionality factor is called Poisson k coefficient or ratio.
Some values of Poisson’s ratio are:
Steel 0.30
1 - -1 Ductile iron 0.28
Diameter (D)
PVC 0.45
Figure C.1 Barlow’s formula for internal pressure stress. Aluminum 0.33