Page 143 - Buried Pipe Design

Design of Gravity Flow Pipes 117

only brittle, composite, or highly filled materials have installation
designs which are controlled by strain.
Strain described in this section refers to total circumferential strain,
which is made up of bending strain, ring compression strain, hoop
strain due to internal pressure, and strain due to Poisson’s effect. For
gravity sewer pipe, the bending strain is largest, and other compo-
nents may be small in comparison.

Bending strain. The bending strains can be calculated using the fol-
lowing equation. The equation requires ring deflection y/D and the
dimension ratio D/t. The equation is based on the pipe’s deforming into
an elliptical shape. The assumption of an elliptical shape has been
shown to be a very close approximation for most solid wall pipe.

t
3 y/D
(3.19)
D
1 2 y/D
where maximum strain in pipe wall due to ring bending (can be
assumed to occur at crown or invert of the pipe)
t pipe wall thickness
D pipe diameter
y vertical decrease in diameter
For example, if t 0.132, d 4, and the ring deflection is 10 percent,
the bending strain is calculated as follows:

0.132
3 (0.10)
0.0124 or 1.24 percent strain
1 2 (0.10)
4
The following simplified equation for calculating maximum strain
due to ring deflection has been proposed.
t y
ε b 6 (3.20)
D D
This equation predicts strains that are too high for low ring deflections
and does not work well for solid wall pipes. However, it is the preferred
equation for profile wall pipes. The two equations predict the same
bending strain when y/D is 0.25.
Ring compression strain

P v D
ε c (3.21)
2tE
Hoop strain (due to internal pressure)
PD
ε p (3.22)
2tE