Analysis of Locally/Distortionally Buckled Beams

The paper describes the derivation of a seven degrees of freedom beam finite element which enables the effects of local/distortional buckling deformations to be accounted for. The development of local/distortional buckling reduces the rigidity of the section against axial straining, minor and major axis flexure, as well as twisting. The reduction in rigidity can be determined by increasing the level of axial strain, minor axis curvature, major axis curvature or twist, and at each level of deformation subjecting a single or a few local/distortional buckles to small changes in axial compression, minor and major axis bending, and torsion. This analysis is performed prior to the frame analysis and produces arrays of tangent rigidities ((EA)t, (EIz)t, (EIy)t, (EIw)t) and other tangential stiffness terms for increasing values of generalised strains (, , , x z y x     ). Incorporating the reduced rigidities in the beam element formulation requires
changes to the tangential stiffness matrix.
The seven degree of freedom element is developed in the framework of the OpenSees software. The paper sets out the tangential stiffness matrix for a locally/distortionally buckled element and shows that close agreement can be obtained between the beam analysis which incorporates reduced rigidities and analysis using full shell finite element discretisation. The purpose of the developed element is to make beam-element analyses readily available for analysing the structural response of locally/distortionally buckled frames. This is particularly relevant for determining the additional second order moments resulting from the increased sway induced by the reduction in flexural and warping rigidity. This effect is becoming increasingly important to quantify as cold-formed steel sections are being produced in increasingly thinner gauges and subject to local/distortional buckling in the ultimate limit state. Yet, the associated additional
second order moments are presently not considered in the AISI S100-2007 Specification for the design of cold-formed steel structural members.

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