Buckling is a failure mode which requires compressive stresses in a structure where a large increase in deformation occurs with a small in crease in load. It is a failure mode since the buckled structure can no longer support the loads. Three analysis methods are available.
Elastic Buckling
A buckling analysis is performed using elastic stress analysis without any geometric non linearities to determine prestress in the component with a minimum design factor and loading combinations.
Elastic Plastic Buckling
A buckling analysis is performed using elastic plastic stress analysis with geometric non linearities to determine prestress in the component with a minimum design factor and loading combinations.
Collapse Analysis
A collapse analysis can be performed using elastic or plastic material behavior and includes geometric imperfections where the design factor is built in to the load combinations.
Conclusion
Buckling can be a catastrophic failure mode that must be checked per the ASME code.