Keywords: local buckling, square steel tube member, multiple yield surfaces, softening, thermodynamics, plastic dissipation, beam element.

For the collapse behavior of the structures composed of a square steel tube member, it is necessary to evaluate local buckling. In order to economically analyze a large structural model with member local buckling, a special simplified method such as the simple plastic hinge model or the multi spring model were proposed and the strength degradation resulting from the local buckling was taken into account. The elements indeed involve characteristics of local buckling, but the theoretical background and validity of the mechanics in its treatment are not clear.

In a previous paper, we proposed a consistent and convenient analytical method to evaluate the post buckling behavior involving local buckling for an H-section steel member [1]. In this method, we regard the effect of the local buckling as the softening, that is, the multi yield surfaces in the space of (M_i,M_j,N) are moving according to the local buckling evolution. Then in this paper, we extend this method for H-section member to a square steel tube member, and propose a useful beam element based on the thermodynamics for square steel tube member involving local buckling.

In this formulation, we introduce effective plastic-buckling components and effective elastic components of the nodal relative displacement. Then we consider the free energy with respect to this effective elastic displacement. The Clausius-Duhem inequality which corresponds to the second law of thermodynamics gives the elastic constitutive equation and inequality fort 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 the H-section beam, we evaluate the influence of local buckling as softening. In this method, multi-surfaces for yielding and buckling behaviour are considered in the space of (M_i,M_j,N). Each surface corresponds to the yielding and buckling strength of each buckling flange. Using the hypothesis of stress block, we get the yield function involving local buckling. Then we investigate the elastoplastic buckling behavior of a plate model and we obtain a consistent softening property caused by buckling.

Furthermore we show that the numerical implementations to determine nodal forces for the local buckling and examine the validity and the usefulness of our method through some numerical examples.

1

T. Ohtsuka, S. Motoyui, "Analytical Evaluation of Local Buckling Behaviour of H-Section Steel Members", in Proceedings of the Seventh International Conference on Computational Structures Technology, B.H.V. Topping, C.A. Mota Soares, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 150, 2004. doi:10.4203/ccp.79.150

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)