Page 162 - Buried Pipe Design

136 Chapter Three

3
and solve for EI/R .
2

EI r (1 ) 1 ft 3 2
120 36 (0.84) 2.1 lb/in
3
R 3 1728 in 3
Pipe stiffness is
f EI 2
6.7 3 14 lb/in
y R

It is possible the bending stress will exceed the yield strength before buck-
2
ling takes place. The maximum moment in the ring is M (P x r )/4, and
bending stress is given by
Mc M

y
I I/c
Solve for I/c.

I M

c
y

( r) r 2 r 3 120 (36) 3
M 810 in lb/in
4 4 1728 4
Assume the following:

y 110,000 lb/in 2
c distance from neutral axis to outer fiber 1.7 in
I 810 3
7.36 10
c 110,000
Therefore,
4

in
2
3
I 7.36 10 (1.6) 1.18 10
in
Thus, a little ring stiffness makes a big difference in the stability of a flex-
ible ring on a sloped trench wall (sidehill).
For most pipes, the ring stiffness required for installation is ade-
quate if it complies with the familiar rule of thumb according to which
minimum cover is D/2. For a pipe parallel to a sloped trench wall in
cohesionless soil, minimum cover is one-half a diameter to the sloped
surface of the trench wall.