# 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.

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:

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

1).