Page 145 - Buried Pipe Design

Design of Gravity Flow Pipes 119

This type of bending frequently occurs when pipes are bent to con-
form to direction changes. Such bending can cause ring buckling.
Reissner 41 has also provided an equation for calculating the radius of
curvature that will cause ring buckling as follows:
D
R b (3.24)
1.12 t/D

Shear loadings. Shear loadings often accompany longitudinal bend-
ing. The cause can usually be attributed to nonuniform bending or dif-
ferential settlement. Forces can be large, highly variable, and localized
and may not lend themselves to quantitative analysis with any degree
of confidence. For this reason, shear force must be eliminated or min-
imized by design and proper installation.

Fatigue. The fatigue performance limit may be a necessary consider-
ation in both gravity flow and pressure applications. However, normal
operating systems will function in such a manner as not to warrant
consideration of fatigue as a performance limit, although some fatigue
failures have been reported in forced sewer mains.
Pipe materials will fail at a lower stress if a high number of cyclic
stresses are present. Pressure surges due to faulty operating equip-
ment and resulting water hammer may produce cyclic stress and
fatigue. Cyclic stresses from traffic loading is usually not a problem
except in shallow depths or burial. The design engineer should consult
the manufacturer for application where cyclic stresses are the norm.

Delamination. Reinforced and laminated products may experience
delamination when subjected to ring deflection. Delamination is
caused by radial tension and interlaminar shear. In the design of rein-
forced products, the radial strength is often neglected and radial rein-
forcement is omitted. However, the resulting radial strength may be
adequate if deflections are controlled. Radial tension is given by

r T/[t (R y)]
y
T
da
–c
where
r radial tension stress
t wall thickness
R radius
y distance from neutral axis to point in question
c t/2

stress in tangential direction as function of position in
wall (My/I)
da (dy) (unit length)