Keywords: thin-walled framed structures, nonlinear stability, beam element, updated Lagrangian formulation, flexible connections.

Stability limit state evaluation of frame-type structures is frequently carried out under the assumption of ideal frame connections, i.e. two extreme idealisations for connections are used: fully (perfectly) rigid and frictionless (ideal) pinned [1]. Such models simplify the stability analysis significantly, but often cannot represent the real structural behaviour because real connections exhibit a flexible or semi-rigid behaviour which falls in between the two idealised cases. The behaviour of flexible connections is the result of a complex interaction among various components of the connection construction itself [2]. Therefore, conventional numerical analysis procedures must be broadened by incorporating real connection characteristics in order to replace the idealized connection approach, which improves the accuracy of the structural analysis [3,4].

This paper presents a two-node (14 degrees of freedom) beam element for the numerical simulation of nonlinear stability behaviour of flexibly connected space frames composed of the straight and prismatic thin-walled beam members. The equations of equilibrium are derived using the updated Lagrangian incremental description and the nonlinear displacement field of thin-walled cross-sections. Force recovery is performed according to the external stiffness approach [5]. Internal moments are calculated by the Euler-Bernoulli-Navier theory for bending and the Timoshenko-Vlasov theory for torsion. As a result of the applied displacement field which includes second-order displacement terms resulting from large rotations, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Material non-linearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at the ends of the finite elements and for this a corresponding plastic reduction matrix is applied [6]. Flexible connections are allowed to occur at finite element nodes by modifying stiffness matrices of a conventional beam element. A special transformation matrix is derived for that purpose. On the basis of this, a computer program called THINWALL v.2 is developed and validated using test problems.

1

W. McGuire, R.H. Gallagher, R. Ziemian, "Matrix structural analysis", John Wiley & Sons, New York, 2000.

2

M. Ivanyi, C.C. Baniotopoulos, "Semi-rigid connections in structural steelwork", Springer-Verlag, Wien, 2000.

3

G.E. Blandford, "Stability analysis of flexibly connected thin-walled space frames", Computers & Structures, 53(4), 839-847, 1994. doi:10.1016/0045-7949(94)90372-7

4

S.L. Chan, P.P.T. Chui, "Non-linear static and cyclic analysis of steel frames with semi-rigid connections", Elsevier, Amsterdam, 2000.

5

G. Turkalj, J. Brnic, J. Prpic-Orsic, "Large rotation analysis of elastic thin-walled beam-type structures using ESA approach", Computers & Structures, 81(18-19), 1851-1864, 2003. doi:10.1016/S0045-7949(03)00206-2

6

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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