Keywords: continuous beam, elastic intermediate restraint, deformation response, buckling problem, non-linear analysis.

Individual bracings or bracing systems are widely used by engineers in a practical design to prevent lateral deflection of structures. Here the computational modelling of a laterally braced element subjected simultaneously to an axial force and a bending moment is considered. The buckling analysis and design of elements considering axial compression as one of the effects that makes it essentially a non-linear problem, in which axial force participation in the flexural response needs to be considered [1]. The proposed computational method is based on the solution of an appropriate differential equation. It shows how the influence of the axial force on the bending moment can be incorporated directly into the governing differential equation. In the most cases, the additional restraint is not completely rigid, but elastic. Thus, the solution of the buckling problem of the element with the intermediate elastic restraint under bending and compression is, therefore, of practical interest. There are, however, solutions for buckling problems for the laterally braced elements for some cases dispersed in the literature. The most common structural models dealt with are of the compression element with the intermediate elastic restraint and of the structural element subjected simultaneously to the axial load and the bending moment with inelastic intermediate restraint. The general calculation model encompasses previously described cases for the boundary conditions and presents the possibility of an appropriate superposition procedure. The developed method is used to derive the governing equations and the governing parameter termed the slenderness parameter. The numerical examples show the correctness of the computational method. Subsequent analysis with the commercial finite element software using a nonlinear solver determines the errors. The errors obtained are within the desirable limits of the accuracy. The developed method can be used for predicting the deformation response of the restrained element subjected simultaneously to axial force and bending moment. Furthermore, it is appropriate to analyse the influence of the elastic restraint and the deflection dependent lateral load on the elastic stability of the element considered. The limiting value of the restraining stiffness [2] used contributes to the prediction of significant changes in the deflection shape and the extreme values of the bending moments.

1

E. Bayo, A. Loureiro, "An efficient and direct method for buckling analysis of steel frame structures", Journal of Constructional Steel Research, 57, 1321-1335, 2001. doi:10.1016/S0143-974X(01)00040-2

2

N.S. Trahair, M.A. Bradford, D.A. Nethercot, L. Gardner, "The Behaviour and Design of Steel Structures to EC3 (Fourth edition)", Taylor & Francis Press, New York, US, 2008.

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