Keywords: local buckling, H-section steel member, multiple yield surfaces, softening, thermodynamics, plastic dissipation, beam element.

It is important to analyze the collapse behavior of designed structures. For the strength degradation behavior 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 using a discrete model because the model requre many elements to acheve accurate results. So far, to analyze a huge structural model economically, 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. These elements indeed involve characteristics of local buckling, but the theoritical background and validity of mechanics in its treatment are not clear.

In previous papers, we proposed a useful beam element for truss beam involving elastoplastic buckling of chord members [1]. In this method, we regard the effect of the chord member's buckling as the softening, that is, multi yield surfaces in the space of are moving according to the chord member's buckling degree. Then in this paper, we extend this method for truss beam to H-section member, and propose a useful beam element based on the thermodynamics for H-section steel member involving local buckling.

In this formulation, we introduce an effective plastic-buckling components and an effective elastic components of the nodal relative displacement. Then we consider free energy with respect to this effective elastic displacement. And the Clausius-Duhem inequality which means the second law of thermodynamics gives the elastic constitutive equation and the plastic dissipation. Here, the principle of maximum plastic dissipation is introduced to the elastoplastic local buckling behavior subjected to the yielding condition according to the yielding or buckling reference point. Then we obtain the evolution equations. Similar to truss beam, we evaluate the influence of local buckling as softening. In this method, multi-surfaces for yielding and buckling behavior are considered in the space of . Each surface corresponds to the yielding and buckling strength of each buckling flange. And by using the hypothesis of stress block, the effect of local buckling behaviour evaluates as the softening behavior for only a couple of surfaces corresponding to the buckling flange. But this buckling behavior of plate is more complicated than the buckling behavior of chord member. Then we investigate the elastoplastic buckling behavior of flange plate model and we obtain a consistent softening property caused by buckling.

Furthermore we show the numerical implementations to calculate nodal forces for the local buckling and examine the validity and the useful of our method through some numerical examples under monotonic and cyclic loading.

1

Motoyui, S., Ohtsuka, T., "Beam Element for Truss Beam with Chord Member's Elastoplastic-Buckling Behavior", The Eighth East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-8), pp.1-6, Singapore, December, 2001

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