Keywords: H-section truss element, elastoplastic buckling behavior, local buckling behavior, thermodynamics, plastic dissipation, softening.

The post-buckling benaviour of slender member like a chord of truss structures generally implies extremely strength degradation. So the peculiar n-u curve given from experimental results and so on is usually used as the axial force-stretch relation of members when we analyze such truss structures. At this case, however the theoretical background and validity in its treatment are not clear in view of thermodynamics.

Even if the member's slenderness ratio is the less, the member is composed of H section and so on, its strength degradation benaviour become much more extremely because of local buckling. In order to evaluate the influence of local buckling, we usually use the finite element method with discrete model, but it is very costly to evaluate the local buckling by using the discrete model because the model requre many elements to acheve a accurate result.

So far, to analyze the elastoplastic local buckling benaviour, the simplified method like the simple plastic hinge model, multi spring model were proposed. But similary above mentioned method using the peculiar curve, the theoritical background of these model are not clear and its application to the member subjected to high axial force is inappropriate. On the other hand, for the high axial loading member, we use the generalized plastic hinge model. But this model is not applied to local buckling benaviour.

In previous papers, we proposed a method [1] based on the thermodynamics to analyze the post buckling benaviour of elastoplastic compression member, and from investigation into the buckling benaviour of truss beam [2], we suggested a beam element [3] involving local buckling by regarding the effect of the local buckling as the softening in resultant stress space .

Then in this paper, we will extend the foreging method and propose a new consistent convenient analytical method to evaluate the post buckling benaviour involving local buckling for H-section slender member.

In this formulation, we consider the Helmholtz free energy involving local buckling energy term for simplified buckling model. And the Clausius-Duhem inequality which means the second law of thermodynamics gives the elastic constitutive equation, the balance of moment at the rotary spring and the plastic dissipation term. Here, the principle of maximum plastic dissipation is introduced to the post-buckling benaviour subjected to the yielding condition with local buckling. Then we can obtain the evolution equations. Considering local buckling mode, the yielding function with local buckling is expressed in the form of softening.

Furthermore, we show the numerical implementations to calculate axial force for the elastoplastic buckling with respect to axis, and examine the validity and the useful of our method through numerical examples for the buckling with respect to and axis concretely.

1

Motoyui, S., Ohtsuka, T., "Analytical Method for Truss Element Involving Elastoplastic Buckling Benavior", Proceedings of The First International Conference on Steel & Composite Structures (ICSCS'01), Vol. 2, pp.1421-1428, Pusan, Korea, June 2001

2

Motoyui S., Ohtsuka T., "Beam Element for Truss Girder Involving Member's Elastoplastic Buckling Benaviou", Proceedings of The International Symposium on Theory, Design and Realization of Shell and Spatial Structures, TP069, Nagoya, Japan, 2001

3

Ohtsuka, T., Motoyui, S., "Beam Element for H-section Steel Member with Local Buckling", Proceedings of The International Symposium on Theory, Design and Realization of Shell and Spatial Structures, TP070, Nagoya, Japan, 2001

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