In this work, the focus is on the effect of the rigidity of springs (rotational and translational), positioned at the ends of an element (beam-column) vis-à-vis the stability analysis. The role of the springs is to model the nodal restraints of any element of a given structure. This formulation offers significant practical advantages in the elastic buckling analysis of such structures.

For this purpose, a versatile and efficient solution of the differential equilibrium equation of a beam-column element with arbitrary boundary conditions is derived [1,2]. The rotations and lateral displacements of the springs are taken into account within the evaluation of the boundary conditions of the element.

In this way, it is possible to compute at each step of the non-linear analysis, the stiffness of the nodes of each element and subsequently calculate a relative restraint factor at each end of the column, which are associated to actual rotations and lateral displacements of the element. This in turn, implies the computation of the factor K of the element. This approach offers the possibility to examine, during the non-linear analysis, the degree of sensitivity of the factor K as regards the degree of restraint at the ends of the element.

This approach is performed through a relationship to several parameters, such as the relative retention factors and the factor K. This relationship can be regarded as particularly reliable as justified by the good results achieved regarding the rupture of several buckling structures that were investigated.

1

R. Adman, H. Afra, "Analytical Solution of a Beam Element for Elastic Buckling Analysis", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 249, 2004. doi:10.4203/ccp.79.249

2

R. Adman, H. Afra, "Exact shape functions of imperfect beam element for stability analysis", Advances in Engineering Software, 38, 576-585, 2007. doi:10.1016/j.advengsoft.2006.08.020

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