The SPACE GASS buckling analysis module performs a rational elastic buckling analysis of a frame to determine its buckling load factors, buckling mode shapes and member effective lengths.

The buckling load factor is the factor by which the loads need to be increased to reach the buckling load. A load factor less than 1.0 means that the working loads exceed the structure’s buckling capacity.

For information about displaying buckling mode shapes and finding out where buckling is occurring, refer to "Buckling analysis results".

The buckling modes considered in the buckling analysis involve flexural instability due to axial compression in the members (also known Euler buckling) and should not be confused with flexural-torsional buckling (torsional instability due to bending moments) or axial-torsional buckling (torsional instability due to axial loads).

An accurate buckling analysis such as the one available in SPACE GASS looks at the interaction of every member and plate in the structure and detects buckling modes that involve one element, groups of elements, or the structure as a whole.

A buckling analysis is an essential component
of every structural design because it:

- Determines if the loads exceed the structure's
buckling capacity and by how much.

- Calculates the member
effective lengths for use in the member
design.

- Determines if the static analysis results
are usable or not.

Points 1 and 3 above highlight the fact that a buckling analysis must always be performed unless you are certain that the structure's buckling capacity exceeds the applied loads by a suitable factor of safety.

Important points

- The results of a static analysis will be incorrect if the structure's
buckling capacity has been exceeded (see point 3 above), and hence
one of the key roles of a buckling analysis is to ratify the static
analysis results.

- If you get buckling load factors that are below the minimum allowable
value (eg. shown as "<0.001" when the minimum allowable
value is 0.001), this could indicate an instability
problem rather than a buckling problem. It is even more likely to
be an instability
problem if the low buckling load factors occur in every load case.

- If the model contains instabilities, the buckling analysis may,
in some cases, give invalid results. In the absence of instability
or buckling messages from the static analysis, you should always check
the deflections to see if they are excessive or not.
__Excessive deflections are sometimes the only indicator of instabilities__.

- Spectral, harmonic and transient response load cases cannot be
included in a buckling analysis. Furthermore, if you perform a buckling
analysis on a combination load case that contains a mixture of static
with spectral, harmonic or transient load cases, only the static load
cases in that combination will be analysed for buckling. This means
that if you transfer member compression effective lengths from a buckling
analysis into a steel member design, any spectral, harmonic or transient
load cases considered in the design will not contribute to the calculation
of the compression effective lengths. You should therefore consider
specifying the compression effective lengths manually in those cases.

- The buckling analysis module gives you the choice of two theories.
The "Signcount Eigenvalue" theory is very accurate but does
not consider plate/shell buckling, whereas the "Classic Eigenvalue"
theory considers the buckling of members and plates/shells, but is
not quite as accurate as the Signcount theory and tends to overestimate
the buckling load factor in some circumstances. The "Classic
Eigenvalue" theory is the one typically used in other structural
analysis programs. In order to improve the accuracy of the "Classic
Eigenvalue" theory it is recommended that you subdivide members.

- The "Signcount Eigenvalue" theory will usually fail with
a very low buckling load factor if the model contains instabilities,
however the "Classic Eigenvalue" theory is not as good at
finding instabilities and may return reasonable looking buckling load
factors even if the model contains instabilities. Instabilities may
cause incorrect results and so it is important that they are found
before you accept the results. You should not rely on the buckling
analysis to find all instabilities and so you should check for instabilities
in other ways, such as looking for inappropriate or large deflections
(translations or rotations), ill-conditioning or lack of convergence
in the static analysis results.

- If your model contains cables then the "Signcount Eigensolver"
theory gives reasonable results, provided you follow the procedure
outlined in "Buckling
analysis with cable members". The "Classic Eigenvalue"
theory does not give accurate results when cables are present in the
model.

- If your model contains gap or fuse members, or variable spring, plastic, friction or one-way restraints, because they are inherently non-linear in the way they behave, they are not really suited to a buckling analysis that uses the "Classic Eigenvalue" theory or the "Linear" member axial force distribution. SPACE GASS will allow a buckling analysis with these settings, but all gap/fuse members and non-linear restraints will be treated in a simplified linear manner that may not give you the results you expect or want. Gap and fuse members will be treated like normal members with their tension and compression limits ignored. Plastic and friction restraints will be treated as fixed, while variable spring restraints will be treated as springs using a constant spring stiffness that corresponds with a zero deflection from its stiffness vs deflection table. One-way restraints will be treated a bi-directional.

Once the buckling load factors have been determined, a simple formula is used to calculate the member effective lengths as described in the next section. The effective lengths can then be automatically transferred into the steel member design modules.

The method that SPACE GASS uses to calculate the buckling factors (eigenvalues) and corresponding mode shapes (eigenvectors) is based on the theory presented by Wittrick and Williams (12).

Note that the magnitudes of the effective lengths or the effective length factors (k factors) from a buckling analysis cannot be used to determine if buckling is a problem or not. This can only be determined by looking at the buckling load factor.

Refer to "Static analysis buckling" for details of some simple buckling checks that are included in non-linear static analyses.

Refer to "Special buckling considerations" for details of items to be aware of when preparing your model for a buckling analysis.

Refer to "Buckling analysis results" for details and interpretation of the results of a buckling analysis.