Keywords: local buckling, H-section steel member, elastic and elastoplastic buckling, softening, thermodynamics, plastic dissipation, truss element.

It is significant to analyze the collapse behaviour of designed structures. For the strength degradation behaviour of the structures composed of H-section member, it is necessary to evaluate local buckling. In order to evaluate the influence of local buckling, we usually use the finite element method with a discrete model. But it is very costly to evaluate the local buckling by using a discrete model because the model requires many elements to acheve accurate results. So far, to analyze a huge structural model economically, a special simplified method like the simple plastic hinge model and multi spring model were proposed, and the strength degradation by the local buckling was taken into account on their element. When we analyze truss members, we usually use a multi-spring model, and the influence of local and overall buckling is reflected in the load-displacement relationship. But a process to decide its restoring force characteristic is not systematic because the theoritical background and validity of mechanics in its treatment are not clear.

In previous papers, we proposed a consistent and convenient analytical method to evaluate the local buckling behaviour of an H-section beam-column under combined axial force and major-axis moment [1]. In this method, its formulation is based on thermodynamics and we regard the effect of the local buckling as the softening, that is, multi yield surfaces in the space of nodal force move according to the local buckling degree. This softening property is derived from the buckling property of the plate, corresponding to plastic dissipation.

Then in this paper, we propose a consistent and convenient truss element which is able to evaluate local and overall (minor-axis) buckling behaviour of H-section steel member. First of all, we describe plate buckling, and we get the softening property caused by buckling. That is, the effective yield stress is degradated according to the evolution of the buckling parameter even in elastic postbuckling. And the effective yield stress is satisfied as a function with respect to buckling parameter in plastic buckling. Secondly, for a thin-walled member, we describe the elastic buckling behaviour of the H-section truss member. It is impotant that we consider elastic buckling behaviour, because we usually regard the strength of an elastic truss member is not degraded though coupling the local buckling with the overall buckling to bring about strength degradation. Finally, we describe the plastic buckling for a member of usual slenderness ratio and width-thickness ratio. And by using the Clausius-Duhem inequality and the principle of maximum plastic dissipation, we obtain basic equations of elastoplastic buckling (elastic constitutive equation, moment balance equation, and evolution equation). Furthermore, similar to major-axis bending, we approximately apply the hypothesis of the stress block to the local buckling stress distribution, and get the yield function with local buckling. Its softening property is derived from the buckling property of the plate, corresponding to plastic dissipation.

1

Ohtsuka T., Motoyui S., "Analytical Evaluation of Local Buckling Behaviour of H-Section Steel Members", Proceedings of The Seventh International Conference on Computational Structures Technology, Topping, B.H.V., (Editor), Civil-Comp Press, Stirling, UK, paper 150, 2004. doi:10.4203/ccp.79.150

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