Spatial Stability Analysis On Thin-Walled Beam-Columns With Open Cross-Section

Because of its thin wall and slender length, the steel member often yield warping and torsional deflection under external force. Unreasonable design would lead to the spatial buckling of member. In view of distortion, one kind of unique deformation of thin-walled member, there would be an analysis theory, which was different with the plane bending theory, to carry on the analysis and computation with it. The traditional Wagner-Vlasov Theory was the ancestor in this aspect and now influences the research in many countries. However, because it's difficult to apply the traditional theory, some scholars have advanced several new analysis theories. General Bending Theory was one of them. In General Bending Theory, the rigid perimeter assumption was substituted by the straight midline hypothesis. So, the theoretical analysis results were according with the reality. Based on the General Bending Theory, This paper conducts the research to the spatial stability analysis on thin-walled beam-columns with open cross-section. Mainly the following related works have been carried out:①Object to the thin-walled beam-columns with 3-plate-section, the basic principle of General Bending Theory is introduced, and the great benefit of the new theory is revealed by proving the theory. Firstly, the two physical quantities, moment vector and radius vector rotation, are founded. Take advantage of those quantities, the spatial internal force changes into the planar one and the spatial deformation changes into the one-dimensional one. Secondly, the inside and outside bimoment balance equation of thin-walled member is listed. It is pointed out that the warping normal stress and bimoment are the key force factors of thin-walled member. Thirdly, dynamic coordination method, the quick calculation of the internal force and deformation of the cross-section is newly built. By this method, it is carried on that the spatial distortion synthesis to the rotation circling the rotation center and the four stress superimposition in traditional theory synthesis to the unification formula, so the computation process is simplified and the computation speed is enhanced mostly. It is proposed that the tension-bending analogue of the thin-walled component level and pointed out that the free torsion rigidity can be neglected temporarily in the process of first-order analysis. So, the related achievement in the Plane Bending Theory can be transplanted generally and the computation process can be simplified greatly.②Based on the General Bending Theory, Spatial buckling of thin-walled beam-columns with open cross-section is researched. Firstly, based on the General Bending Theory, take the rotation center as the simplified center, the governing equation of the spatial buckling is derived, and the conversion of the critical force unification formula and the corresponding rotation center coordinates formula is carried on. Secondly, by the spatial buckling governing equation, combining the historical related discussion of the Wagner effect and the Wagner coefficient, it is clarified that the concepts, computation path, many mechanics characteristics and project application value of the Wagner effect and the Wagner coefficient. Thirdly, by the rotation center triangle which comes from the junction of rotation centers, the orthogonal characteristic of the critical force and the corresponding buckling mode is disclosed. That characteristic provides the theoretical basic for the application of the amplification coefficient method in the following second-order analysis. Finally, the massive computations of thin-walled member with many kinds of open cross-section are carried on, then the relation curves of critical force and slenderness ratio and the rotation center triangle are drawn up, and the related characteristic of the spatial buckling of member is disclosed.③The important parameters in the second-order analysis of thin-walled beam-columns with open cross-section are determined, that is providing facilities for the subsequent work in the second-order analysis. By analogy with the selection of plane initial flaw, combining with the spatial buckling characteristic of thin-walled member, the selection method of spatial initial flaw is proposed. It is discussed the orthogonal decomposition method of the initial deformation and first-order deformation turned to be three independent deformation. Based on the balance equation of inside and outside bimoment, the rotation angle magnification factor of three independent deformations is derived and the conception of uniform amplification coefficient is put forward. Embarking from the most basic torsion problem, the calculation formulas considering the free torsion rigidity of the internal force and the deformation of member under simple load are deduced. From those formulas, the second-order effect rule of free torsion rigidity is sought for. The computation method of second-order stress of thin-walled member is proposed initially. Then the question introducing correctly the bimoment to the calculation formula of second-order stress is solved.④In terms of the external fiber yielded criteria, the relation curves of spatial stability coefficient and slenderness ratio are drawn up. According to those curves, many characteristics of member with spatial flexural-torsional buckling are disclosed. From the research advancement of column curves, in terms of the external fiber yielded criteria, the spatial stability bearing capacity of thin-walled members with many kinds of section and considering the spatial initial deformation are computed. The results are drawn up to curves, and from them, many characteristics of member with spatial flexural-torsional buckling are disclosed. A new instability mode in steel member, the torsional shearing instability which is an especial phenomenon in Bi-plate-type section, is pointed out. The influence of residual stress and elastic-plasticity on the spatial stability is discussed initially.⑤By ANSYS, one kind of finite element software, it is proved that the former results of spatial stability of thin-walled beam-columns are valid. The results of the first-order analysis and the eigenvalue analysis indicate that the analysis method proposed in this paper is correct. The geometry initial flaw of member is introduced in the model of former eigenvalue analysis, and the limit bearing capacity of member is obtained by the load-displacement curve from the arc length method. Contrasting the limit bearing capacity with the result of spatial stability analysis in former chapters, it is discovered that the limit bearing capacities of struts particularly short ones in new method are too conservative than those in ANSYS. Therefore, the thing must be done is revising the check formula of spatial stability in the new method, and proposing a new practical check method.⑥The spatial stability analysis results of beam-columns with open cross-section are applied to the practice preliminarily. Transforming the spatial stability check formula based on the external fiber yielded criteria into the expression form as critical stress, and by analogy with the processing way in plane stability, the inverse calculation method of the initial flexural-torsional flaw in the hypothesis elasticity strut, which is the rational check method of the spatial stability of the thin-walled beam-columns with open cross-section, is proposed. In view of the fact that the scientific statistical data of members'spatial initial flaw are lack nowadays, the reduced slenderness ratio method, one kind of practical calculation method, is proposed preliminarily. Using that method, the discussion of the T-strut's spatial stability is carried on, and the differences brought by the traditional check formula and traditional theoretical analysis method are eliminated. According to the new method, the preliminary revisions of the existing problems in the present code are done.In general, the work completed in this paper is as following: summarizing and confirming the uniform computation theory, deducing the uniform computation formula of the critical force and buckling mode of the member in spatial buckling, Straightening out the uniform computation step of the spatial stability coefficient based on the external fiber yielded criteria, and proposing the practical uniform check method of spatial stability. Certainly, the research at present is only in the stage of theory, the data of related initial flaw and the practical verifications are lack. The purpose of this paper is finding a new path from the theoretical side for the research of thin-walled member's spatial stability to provide reference for code revision.