When attempting to do a Second-Order analysis and the analysis is unsuccessful, a common error message states that you must check for instability. A good method of determining the location of the instability is to do a Buckling analysis.
You can use a buckling analysis to calculate the safety factors for structural instability due to buckling. This can be demonstrated by loading a simply supported column with the Euler Critical Load. In the following example, a 220x220 concrete section was used as the column section. The height of the column is 3m.
The column is loaded with a single point load equal to the Euler Critical Load and a buckling analysis is done. The buckling factor is calculated as 1.000:
If the overall buckling factor of a structure is between 0 and 1, it is an indication that the structure is unstable. Since a second-order analysis takes the effect of sway into account, the analysis won’t be successful if the structure is unstable (buckling factor between 0 and 1).