Page 222 - Buried Pipe Design

196 Chapter Four

Pressure pipes may also have longitudinal stresses induced by pres-
sure and temperature which should be given proper consideration by
the engineer responsible for installation design.

Poisson’s effect. Engineers who deal with mechanics of materials
know that applied stresses in one direction produce stress and/or
strains in a perpendicular direction. This is sometimes called the
Poisson effect. A pipe with internal pressure p has a circumferential
. The associated longitudinal stress is given by the follow-
stress p v
ing equation:

v p
where v longitudinal stress

Poisson’s ratio for pipe material
p circumferential stress

The above equation is based on the assumption that the pipe is
restrained longitudinally. This assumption is valid for pipes with rigid
joints or for pipes with extra-long lengths even if joined with slip joints
such as rubber ring joints. Studies have shown that soil-pipe friction
can cause complete restraint in approximately 100 ft. For shorter
lengths with slip joints, since the restraint will not be complete, the
longitudinal stress will be less than predicted by the above equation.
For reference, some values of Poisson’s ratio and Young’s modulus E
are listed in Table 4.4.

Temperature effects. Expansion or contraction due to temperature
increase or decrease can induce longitudinal stress in the pipe wall. As
with the Poisson stresses discussed above, these stresses are based on
longitudinal restraint. The longitudinal stress due to temperature is
given by the equation
T ( T) E

TABLE 4.4 Material Properties
Material Modulus, lb/in 2 Poisson’s ratio
Steel 30 10 6 0.30
Ductile iron 24 10 6 0.28
Copper 16 10 6 0.30
Aluminum 10.5 10 6 0.33
PVC 4 10 5 0.45
Asbestos-cement 3.4 10 6 0.30
Concrete 57,000 (f c ′) 1/2 ∗ 0.30
* f c 28-day compressive strength.