A New Criterion for Column Buckling Based on Four Flexibility Restraint Indices

In the current study, a criterion of stability capable of predicting an impending failure by elastic buckling is proposed. The K factor represents an important parameter vis-á-vis the buckling analysis. It can easily translate the critical buckling load by using a single formula covering all situations of boundary condition. The K-factor methods, whose calculation is normalized in the Eurocodes is to date an analysis tool widely used by engineers because of its flexible approach, especially when dealing with structures perfectly braced. However, in the case of unbraced structures, the relations allowing the evaluation of the factor K remains as proposed by the Eurocodes empirical. In this study, the rigidities at the ends of a beam-column element are modelled using rotational and translational springs. The role of the springs is to model the nodal restraints of any element of a given structure, knowing that it is a well-established fact that the rigidity of the joints influences the behaviour of the K factor. This formulation offers significant practical advantages in the global elastic buckling analysis of such structures. This approach is performed through a relationship to several parameters, such as the relative retention factors and the effective length factor K. The approach was applied in analysing the buckling of a number of structures and good results were obtained, thus justifying its reliability. In determining the effective length factor K, a marked difference was noted between the results obtained using the Eurocode approach and that proposed by the current study, particularly in the case of non-braced structures. This performance is achieved through the formulation of a rigorous stiffness matrix based on indexes of flexibility that reflect its actual original nodal boundaries. Finally, this result offers to the finite element approach the required tool of accuracy required besides the simplicity of the method.