# TR.37.4 Buckling Analysis

## General Format

PERFORM BUCKLING { ANALYSIS (MAXSTEPS f1) | EIGEN } (PRINT print-options)

print-options = { LOAD DATA | STATICS CHECK | STATICS LOAD | BOTH | ALL }

See TR.37.1 Linear Elastic Analysis for details.

Without this command (or any of the analysis commands
described earlier), no analysis will be performed. These
`ANALYSIS` commands can be repeated if multiple analyses
are needed at different phases.

Where:

Parameter | Description |
---|---|

EIGEN |
if specified the analysis will perform the eigen method, otherwise the iterative method will be used |

MAXSTEPS f1 | the maximum no. of iterations desired (default value of n = 20). 15 is
recommended. For use with the iterative (ANALYSIS) method
only. |

- the iterative method:
`PERFORM BUCKLING ANALYSIS` - the eigen method:
`PERFORM BUCKLING EIGEN`

## Iterative Method

- Solving the static case.
- Re-forming the global joint stiffness matrix to include the Kg matrix terms which are based on the computed tensile/compressive axial member forces and inplane plate stresses..
- Solving simultaneous equations for displacements;
- Repeat b) and c) for the number of required additional iterations; either until convergence or until MAXSTEPS is reached.

If the loads must be in the opposite direction, STAAD.Pro will stop solving that case at 1 iteration. The results for the case will be outputted; then STAAD.Pro will continue with the next case.

Convergence occurs when two consecutive buckling factors in the iteration are within 0.1% of each other.

Results are based on the highest successful Buckling Factor estimate that was calculated; as if the original applied loads times the buckling factor had been entered.

## Eigen Method

A Buckling Analysis will correctly reflect the secondary
effects of a combination of load cases only if they are defined using the
`REPEAT LOAD` specification (TR.32.11 Repeat Load Specification). Buckling will not be performed for
`LOAD COMBINATIONS` cases.

Buckling Kg matrices are computed for frame members and plate elements only. They are not calculated for solid elements or curved members. The results are based on "P-large & small Delta" effects (refer to Option 1 in TR.37.2 P-Delta Analysis Options).

Buckling Analysis solves for Buckling Factors. These are the amounts by which the load case must be factored for the buckling shape to occur. Only the last buckling case will be presented in the post processing. However, the buckling factors of all buckling cases will be written to the output.

If the loads must be in the opposite direction, STAAD.Pro will compute negative buckling factors.

Results are for the normalized buckling shape not as if the original applied loads times the buckling factor had been entered.