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Relationship between Second Order & Buckling Analysis

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 220×220 concrete section was used as the column
section. The height of the column is 3m.

analysis img_12
Figure 1: Simply supported column loaded with Euler Critical Load.
analysis img_13
Figure 2: Euler Critical Load for example column.

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:

analysis img_14
Figure 3: Buckling Analysis result.

Any load larger than the Euler Critical Load will cause the column to be unstable. A buckling
factor larger than 1 indicates that the structure is stable whereas if the buckling factor is
less than 1, the column unstable (a negative value indicates that the column is in tension
and will not buckle).
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