Keywords: structural stability, thin-walled beam-type structures, flexible connections, space beam element.

In order to predict the behaviour of complex structures the response of all components, including connections of members, must be evaluated. Real framework connections exhibit a flexible or semi-rigid behaviour which falls in between the idealized pinned and rigid connection behaviour [1]. The flexible connection behaviour is the result of a complex interaction among various components of the connection construction itself. Therefore, conventional numerical analysis procedures must be modified in order to replace the idealized connection approach with a flexible connection one, which improves the accuracy of the structural analysis. Various standard and technical construction codes define guidelines for design process of framed structures based on connection geometrical and mechanical properties.

Connection characteristic are numerically modelled by curve-fitting experimental data in order to enable their integration in finite element method analysis procedures [2]. Connection characteristic can also be obtained by modelling connections using shell or beam finite element models. For an initial stability analysis only the initial slope of the load-deformation connection characteristic needs to be modelled by defining the initial connection stiffness [3]. A nonlinear analysis requires the modelling of the entire connection characteristic which introduces parameters such as the ultimate load capacity and shape coefficient of the connection.

This paper presents a finite element model for the initial stability analysis of thin-walled beam-type structures with flexible connections. The equilibrium equations of a buckled space beam element are derived by applying linearized virtual work principle, Vlasov's assumption and the nonlinear displacement field of thin-walled cross-sections, accountng for large rotation effects. Structural material is assumed to be homogeneous, isotropic and linear elastic. The internal moments are calculated by engineering theories.

The stability analysis is performed using a two-node beam element with seven degrees of freedom per node. The elastic and geometric matrices of a straight and prismatic two-nodded beam element are derived using a linear interpolation for axial displacement and a cubic one for deflections as well as twist rotations. In this, due to the nonlinear displacement field, the geometric potential of semi-tangential moment is obtained for all the internal moments, ensuring that the joint moment equilibrium conditions of adjacent non-collinear elements [4]. Flexible connections are taken into account at element nodes by modifying the tangent stiffness matrix of a conventional beam element using a special transformation procedure. On this basis a computer program is developed and validated through test problems.

1

A. López, I. Puente, M.A. Serna, "Direct evaluation of the buckling loads of semi-rigidly jointed single-layer latticed domes under symmetric loading", Engineering Structures, 29 (1), 101-109, 2007. doi:10.1016/j.engstruct.2006.04.008

2

W.F. Chen, E.M. Lui, "Practical Analysis for Semi-Rigid Frame Design", World Scientific Publishing Company, Singapore, 2000.

3

W. McGuire, R.H. Gallagher, R.D. Ziemian, "Matrix Structural Analysis", John Wiley & Sons, New York, 2000.

4

G. Turkalj, J. Brnic, "Nonlinear stability analysis of thin-walled frames using UL-ESA formulation", International Journal of Structural Stability and Dynamics, 4 (1), 45-67, 2004. doi:10.1142/S0219455404001094

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