Page 327 - Buried Pipe Design

298 Chapter Six

2
Solving for the area yields A 0.96 in /ft. One should use 12-gage steel that
2
has an area of 1.356 in /ft.
A check on ring deflection would predict a ring deflection of less than 3
percent at a soil density of 90 percent.
The ring flexibility factor (handling factor) is adequate.

Three-dimensional FEA modeling of a corrugated steel pipe arch. Finite
element modeling of a corrugated structure presents special problems
that must be addressed if a solution is to be meaningful. If the struc-
ture is to be used as an underground shelter, it must be designed to
withstand very large longitudinal forces. These forces are developed
from large dynamic pressure loads acting on the shelter’s concrete end
walls, which in turn transmit a longitudinal load to the side of the cor-
rugated arch.
The modulus of elasticity and shear modulus of steel are material
properties that are usually considered to be independent of geometry.
In the case of corrugated pipe, the corrugations behave somewhat as
springs and allow structural deformation in addition to material elas-
ticity. The combined structural and material deformation may be
determined such that an equivalent modulus of elasticity and shear
modulus can be defined. The use of equivalent properties allows the
structural analysis to be completed by assuming orthotropic plate con-
ditions. The equivalent properties determined here represent analyti-
cal approximations that depend upon hypothetical boundary and
loading conditions. The purpose of these approximations is to assist in
the simplification of design.
Two separate finite element analysis (FEA) models were created for
determining the extensional elastic modulus and shear modulus of cor-
rugated plates. These models were created using the preprocessing
graphics capabilities of CAEDS finite element software. Then nodes
and elements were transported to NASTRAN for computer analysis.
Each computer model was run multiple times to provide results for
various material thicknesses of a 6 2 corrugation. The same basic
geometry was used for each of the different thicknesses. Uncoated
material thicknesses were used for all analyses.
The extensional elastic modulus of the corrugated plate was deter-
mined by applying increasing forces to one end of a finite element corru-
gation model one wavelength in length and 1 in wide. Load-deflection
curves were then constructed from the FEA results. The equivalent
extensional elastic modulus of the corrugation may be calculated from
the slope of the load-deflection curve in the linear region

force/area
E /
elongation/length