Page 329 - Buried Pipe Design

300 Chapter Six

angular deformation of the square element. The 100-lb force
was divided by the area of the side to determine the shearing
stress .

F

The shear and extensional elastic moduli and Poisson’s ratios deter-
mined may be used to formulate equivalent orthotropic elements for
use in large FEA models of corrugated structures. The elastic limit
may be used as one criterion of failure in corrugated arch structures
subject to end loading.
The NASTRAN finite element analysis program was used to
complete a three-dimensional analytical model of the arch. The
extensional modulus, shearing modulus, and Poisson’s ratio were
used to create equivalent orthotropic plate elements that would
approximate the actual corrugated plate, use far fewer elements
and computer time, and allow for easier failure analysis of the
structure.
An arch support structure was analyzed using finite element mod-
eling. Rather than model the corrugated geometry in detail, equiva-
lent orthotropic plate elements were derived from the material
properties obtained from smaller analytical models of the actual cor-
rugated geometry. The analysis included a simulation of structural
restraints, load distributions, soil interaction assumptions, material
properties, and other parameters. The application of the model results
is obviously dependent upon the proper characterization of the model
parameters.
Quarter symmetry may be utilized to reduce the number of finite
elements and thus the computer runtime for the model. This was pos-
sible since loading on either end was assumed equal, and the loads
were applied symmetrically at the faces. Appropriate boundary condi-
tions were used to constrain the deflecting elements from violating
boundaries of symmetry.
The three-dimensional finite element with model parameters, as
defined, using equivalent properties works well. These equivalent
material properties (see Tables 6.1 and 6.2) were determined by
assuming orthotropic plate conditions. The combined structural
and material deformation may be determined such that an equiva-
lent modulus of elasticity and shear modulus can be defined. The
equivalent properties determined here represent analytical
approximations that may be used to assist in the simplification of
design.