Page 328 - Buried Pipe Design

Steel and Ductile Iron Flexible Pipe Products 299

A condition of plane strain as opposed to plane stress was assumed
to represent the corrugated structure. Consequently, the plane strain
2
elastic modulus was considered to be E/(1 ), where E is the plane
stress modulus of elasticity.
An equivalent Poisson’s ratio was found for the corrugated geome-
try by determining the change in width of the small representative
strip and dividing it by the original width to find e 2 and by the original
length to determine e 1.Poisson’s ratios were then calculated from the
equation

e 2
12
e 1
Poisson’s ratio 21 was then determined by the relation between the
orthotropic elastic moduli in the 1 and 2 directions:

21 E 1 12 E 2
Material nonlinearities occur when the steel corrugation reaches
its yield strength (33 ksi). At that point, the displacements are no
longer directly proportional to the applied forces. This point is
interpolated from the load-displacement curves where the curve is
no longer linear. The force at which this occurs divided by the
cross-sectional area of the corrugated plate is equal to the elastic
limit.
A nonlinear finite element analysis was used to determine the
corrugation elastic limit. To accomplish this, NASTRAN applied a
fraction of the total static load to the geometry, formed a new stiff-
ness matrix using the deformed geometry and changing material
properties, and then applied the remaining force in the same itera-
tive manner. When equivalent orthotropic elements are used in a
corrugated arch structural analysis, the elastic limit may be used as
a criterion of failure in the case of stresses caused by longitudinal
loading.
A square corrugated plate 6 in on a side was used for the 6 2 cor-
rugation. These models were attached to ground at each corner by very
soft springs and then a 100-lb shearing force was applied to each edge
around the perimeter.
Forces were distributed evenly across the straight edge and pro-
portionate to the lineal distance between nodes on the corrugated
edges of the model. Iterations on spring strength showed the
springs must have a minimum strength to provide model stability.
Shear modulus was calculated from the displacements output
by NASTRAN for the given geometry and material thickness. The
displacements divided by the length of the sides determined the