Page 108 - Buried Pipe Design

84 Chapter Three

Pipe stiffness terminology

Stiffness factor EI
EI EI
Ring stiffness (or sometimes )
r 3 D 3
F EI
Pipe stiffness 6.7
y r 3
where E modulus of elasticity, lb/in 2
I moment of inertia of wall cross-section per unit length of
pipe, in /in in 3
4
r mean radius of pipe, in
D mean diameter of pipe, in
F force, lb/in
y vertical deflection, in

The most commonly used terminology is pipe stiffness (F/ y). For a
given pipe product, this term is readily determined in the laboratory by
a parallel plate loading test. In this test, a pipe sample is placed between
two horizontal parallel plates in a testing machine. A compressive load is
applied and increased until the vertical deflection y reaches 5 percent
of the diameter. And F/ y is the load at 5 percent divided by the sample
length and divided by the vertical deflection y. Typical units for F/ y
are pounds per square inch. This is evident from the third equation, as
it is clear that F/ y has the same units as the modulus of elasticity E.
In summary, the three most important parameters for flexible pipe
analysis and design are (1) load, (2) soil stiffness, and (3) pipe stiffness.
Any design method that does not include a consideration of these three
parameters is incomplete.
For a flexible pipe, vertical deflection is the variable that must be
controlled by proper installation design. This deflection is a function of
the three parameters discussed above.

Spangler’s Iowa formula
M. G. Spangler, a student of Anson Marston, observed that the Marston
theory for calculating loads on buried pipe was not adequate for flexible
pipe design. Spangler noted that flexible pipes provide little inherent
stiffness in comparison to rigid pipes, yet they perform remarkably well
when buried in soil. This significant ability of a flexible pipe to support
vertical soil loads is derived from (1) the redistribution of loads around
the pipe and (2) the passive pressures induced as the sides of the pipe
move outward against the surrounding earth. These considerations, cou-
pled with the idea that the ring deflection may form a basis for flexible
pipe design, prompted M. G. Spangler to study flexible pipe behavior