...
Eigenvalue
...
analysis
...
Please
...
note
...
that
...
Buckling
...
is
...
the
...
...
...
used
...
for
...
Eigenvalue
...
analysis
...
.
...
Eigenvalue
...
analysis
...
predicts
...
the
...
theoretical
...
buckling
...
strength
...
of
...
a
...
structure
...
which
...
is
...
idealized
...
as
...
elastic.
...
For
...
a
...
basic
...
structural
...
configuration,
...
structural
...
eigenvalues
...
are
...
computed
...
from
...
constraints
...
and
...
loading
...
conditions.
...
Buckling
...
loads
...
are
...
then
...
derived,
...
each
...
associated
...
with
...
a
...
buckled
...
mode
...
shape
...
which
...
represents
...
the
...
shape
...
a
...
structure
...
assumes
...
under
...
buckling.
...
In
...
a
...
real
...
structure,
...
imperfections
...
and
...
nonlinear
...
behavior
...
keep
...
the
...
system
...
from
...
achieving
...
this
...
theoretical
...
buckling
...
strength,
...
leading
...
Eigenvalue
...
analysis
...
to
...
over-predict
...
buckling
...
load.
...
Therefore,
...
we
...
recommend
...
Nonlinear
...
buckling
...
analysis.
...
Nonlinear buckling analysis
Please note that Static, Nonlinear with P-Delta
...
and
...
Large
...
Displacements
...
is
...
the
...
...
...
for
...
Nonlinear
...
buckling
...
analysis
...
.
...
Nonlinear
...
buckling
...
analysis
...
provides
...
greater
...
accuracy
...
than
...
elastic
...
formulation.
...
Applied
...
loading
...
incrementally
...
increases
...
until
...
a
...
small
...
change
...
in
...
load
...
level
...
causes
...
a
...
large
...
change
...
in
...
displacement.
...
This
...
condition
...
indicates
...
that
...
a
...
structure
...
has
...
become
...
unstable.
...
Nonlinear
...
buckling
...
analysis
...
is
...
a
...
static
...
method
...
which
...
accounts
...
for
...
...
and
...
...
...
(P-Δ
...
and
...
P-δ),
...
load
...
perturbations,
...
geometric
...
imperfections,
...
and
...
gaps.
...
Either
...
a
...
small
...
destabilizing
...
load
...
or
...
an
...
initial
...
imperfection
...
is
...
necessary
...
to
...
initiate
...
the
...
solution
...
of
...
a
...
desired
...
buckling
...
mode.
...
Important considerations
- The primary output of linear buckling analysis is a set of buckling factors. The applied loading condition is multiplied by these factors such that loading is scaled to a point which induces buckling. Please refer to the Analysis Reference Manual (Linear Buckling Analysis, page 315) for additional information.
- Since the deflections, forces, and reactions of linear buckling analysis correspond to the normalized buckled shape of a structure, users must run Nonlinear buckling analysis to obtain the actual displacements, forces, and reactions. Figure 1 illustrates the Nonlinear-buckling-analysis output of a column subjected to an initial imperfection where lateral load induces displacement equal to 0.6% of column height. Softening behavior indicates the onset of buckling.
Users may download the analytical model for this system through the P-Delta effect for fixed cantilever column test problem.
See Also
- Nonlinear buckling article