Page 317 - Buried Pipe Design

288 Chapter Six

The ring compression method specifies that the ring compression
thrust P D/2 must be less than the allowable thrust, which is the
v
allowable strength of longitudinal seam per unit length of pipe. This
method assumes that the vertical soil pressure on the pipe is P and
v
that the soil completely supports the ring radially.
A modification of the ring compression concept includes wall crushing
and wall buckling in addition to seam strength as performance limits.
The computed stress is S P (D/2A) (see Fig. 6.2), and the ultimate
v
stress f is the crushing strength of the wall (yield point stress), the buck-
c
ling strength of the wall, or seam strength. Again, it must be assumed
that the soil is precisely as compressible as the ring cross-section.
Actually soil is not precisely as compressible as the ring cross-section,
and so the soil pressure on the ring is not exactly P . But another prob-
v
lem arises also. Which wall strength, crushing or buckling, actually con-
trols performance and so limits design? At one extreme, if the soil could
resist all ring deflection, crushing would control and f would be the
c
yield point stress. At the other extreme, if the soil were fluid, (i.e., could
resist no ring deflection), buckling may control. Of course, soil is some-
where between the two extremes and is compressible.
Still other theories are based on a predicted stress S in the pipe wall
as calculated by classical formulas such as

P Mc
S
A I
where P ring compression thrust, that is, P P D/2
v
A area of wall cross-section
M moment on the wall
I moment of inertia of wall
c distance from neutral axis to most remote fiber
R radius of curvature
i
R original pipe radius
o
S total stress
bending stress
bending strain
Mc
E
I

t 1 1
R i
bending
2R t R R
o i o
Thus

EI EI EI t 1 1
M ⇒ R i
c t/2 t/2 2R t R i R o
i