Page 159 - Buried Pipe Design

Design of Gravity Flow Pipes 133

y yield strength of pipe
DR dimension ratio D/t for plane pipes
8
t 3

P y y for plain pipes (3.30)
3 D
For plain pipes, the moment that produces a fully plastic hinge is 1.5 times
the moment that produces yielding. Therefore the fully plastic load is
3
t
P fp 4
y (3.31)
D
The approximate vertical ring deflection at plastic hinging can be cal-
culated as follows:
y 0.02PfpD 3
≈
D EI
where y/D ring deflection
P vertical pressure on ring
D circular pipe diameter
EI wall stiffness per unit length of pipe

Sloped trench walls
Figure 3.30 shows a flexible pipe in cohesionless soil for which the
slope is angle of repose ≈
. Pressure distribution on the ring is trian-
gular, as shown. Maximum moment at A can be found by Castigliano’s
equation. However, it is sufficiently accurate to find the equivalent
moment M A Pr /4 for average uniform pressure P x r .
2

P y = 0 P x = g r

Figure 3.30 Trench wall sloped at the angle of repose (soil is stable). The
flexible pipe requires sufficient pipe stiffness or minimum cover to prevent
collapse.