## Buckling analysis

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:

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

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

3. 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

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. If the 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.

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.