开口薄壁梁柱的空间稳定分析
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摘要
钢结构构件壁薄而修长,在外力作用下常易产生翘曲扭转变形,设计不合理将会导致空间失稳。针对翘曲变形,这种薄壁构件特有的变形形式,必须利用一套不同于实体构件的分析理论对其进行分析和计算。传统的“瓦格纳-符拉索夫理论”开创了相关理论的先河,至今仍影响着各国研究工作的进行。然而,随着传统理论复杂性带来应用上的困难问题逐渐显露,相继有学者提出了新的分析理论,“泛义弯曲理论”即为其中之一。该理论用更为宽松的“中直线假定”替代传统理论中的“刚周边假定”,相应的分析结果更符合实际。本论文基于新理论,对开口薄壁梁柱的空间稳定性进行研究,主要完成了以下几个方面的工作:
①以开口三板型截面薄壁梁柱为对象,对“泛义弯曲理论”的基本原理进行介绍,在验证其正确性的同时展示其巨大效益。新理论新创建了弯矩矢量和转角向径两大物理量,借此将构件的空间内力平面化、空间变形一维化;列出了薄壁构件内、外双力矩平衡方程,指出翘曲正应力和双力矩是薄壁构件的主导力因素;新建了薄壁构件截面内力和变形的速算法“动态坐标法”,该方法将构件发生的空间变形合成为绕转动中心轴的转动,将传统理论中四项应力叠加式合成为一项统一计算公式,极大地加快了计算速度;提出了薄壁构件构件层次的拉弯比拟法,指出自由扭转刚度在构件的一阶内力和变形的计算过程中可以暂时略去,如此可以全面移植“平面弯曲理论”中的相应成果,极大地简化了计算过程。
②基于“泛义弯曲理论”展开对开口薄壁梁柱空间屈曲问题的研究。首先,基于新理论,以转动中心为简化中心,导出了薄壁梁柱空间屈曲的控制方程,并反演出临界力统一公式及相应的转动中心坐标公式。由空间屈曲控制方程,结合历史上对瓦格纳效应及系数的定义的相关讨论,澄清了瓦格纳效应及系数的概念及计算思路,揭示了其具有的诸多力学特性和工程应用价值。其次,利用转动中心联线形成的转心三角形,揭示出临界力及相应屈曲模态的正交特性,该特性为后续二阶分析中变形的正交分解后单独进行放大再叠加的放大系数法的应用提供了理论基础。最后,对各种截面形式的开口薄壁构件进行大量的计算后绘制出临界力与长细比关系曲线和转心三角形,从中揭示出开口薄壁梁柱空间屈曲特性。
③确定开口薄壁梁柱二阶分析中将要涉及的重要参数,为后续二阶分析提供条件。类比平面初始缺陷的选取并结合薄壁构件的空间屈曲特性,提出薄壁构件空间稳定初始缺陷的选取方法。讨论了基于临界力及相应屈曲模态的正交特性如何把薄壁梁柱的初始变形和一阶变形正交分解为三个独立变形的方法。根据内、外双力矩的平衡方程导出相互独立的三种变形的转角放大系数,提出了统一放大系数的概念。从最基本的扭转问题出发,推导简单荷载作用下的考虑了自由扭转刚度的内力和变形计算公式,从中寻找出自由扭转刚度的二阶效应规律。初步提出计算薄壁构件截面二阶应力的方法,解决传统理论中无法将双力矩项正确引入二阶应力计算公式的问题。
④基于边缘屈服准则绘制开口薄壁梁柱空间稳定系数与长细比关系曲线,揭示构件发生空间失稳时的诸多特性。从柱子曲线理论的研究进程出发,从众多稳定判定准则中选取简单且实用者,即采用边缘屈服准则,对多种截面形式且考虑了空间初始变形的开口薄壁构件空间稳定承载能力进行计算,将计算结果绘制成曲线,从中揭示构件发生空间弯扭失稳时的诸多特性。特别指出了两板型截面构件特有的失稳模式——扭转剪切失稳产生的根本原因。最后,初步讨论残余应力和弹塑性对压杆空间稳定性的影响。
⑤利用ANSYS有限元软件对前述开口薄壁梁柱空间稳定分析结果进行验证。对多种截面形式的薄壁构件进行一阶分析和特征值屈曲分析结果表明,本论文提出的分析方法正确。在原有的特征值屈曲分析的模型中引入构件的几何初始缺陷,利用弧长法绘制荷载-位移曲线并获得压杆的极限承载力,将其与前文中的空间稳定分析的结果进行对比后发现:两板型截面短杆确实存在剪切失稳现象,但新方法中的压杆尤其是较短压杆空间稳定分析结果与有限元分析结果相比偏于保守,因此必须对新方法中的空间稳定校核公式进行修正,提出新的实用校核方法。
⑥将基于“泛义弯曲理论”的开口薄壁梁柱空间稳定分析结果在工程中进行初步推广应用。将基于边缘屈服准则的空间稳定校核公式变换为临界应力的表达形式,并类比平面稳定问题中的处理方式,提出合理的开口薄壁梁柱的空间稳定校核方法——虚拟弹性逆算初弯扭法。鉴于现今缺少构件空间初始缺陷的科学统计资料,初步提出实用计算方法——折算长细比法。使用该方法对T形截面钢压杆的空间稳定性进行讨论,消除传统校核公式和理论分析方法带来的分歧,并按照新方法对现行规范中存在的问题进行初步修正。
总的说来,本文所作的工作是:简述并验证统一计算理论、推导空间屈曲临界力及屈曲模态的统一计算公式、理顺基于边缘屈服准则的空间稳定系数的统一计算步骤和提出实用的空间稳定统一校核方法。当然,上述对开口薄壁梁柱的空间稳定性的研究目前只处于理论阶段,尚缺乏有关初始缺陷资料的积累,以及大量实际工程的检验。本文从理论方面为薄壁构件空间稳定研究开创一种新思路,供规范修订参考。
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.
①以开口三板型截面薄壁梁柱为对象,对“泛义弯曲理论”的基本原理进行介绍,在验证其正确性的同时展示其巨大效益。新理论新创建了弯矩矢量和转角向径两大物理量,借此将构件的空间内力平面化、空间变形一维化;列出了薄壁构件内、外双力矩平衡方程,指出翘曲正应力和双力矩是薄壁构件的主导力因素;新建了薄壁构件截面内力和变形的速算法“动态坐标法”,该方法将构件发生的空间变形合成为绕转动中心轴的转动,将传统理论中四项应力叠加式合成为一项统一计算公式,极大地加快了计算速度;提出了薄壁构件构件层次的拉弯比拟法,指出自由扭转刚度在构件的一阶内力和变形的计算过程中可以暂时略去,如此可以全面移植“平面弯曲理论”中的相应成果,极大地简化了计算过程。
②基于“泛义弯曲理论”展开对开口薄壁梁柱空间屈曲问题的研究。首先,基于新理论,以转动中心为简化中心,导出了薄壁梁柱空间屈曲的控制方程,并反演出临界力统一公式及相应的转动中心坐标公式。由空间屈曲控制方程,结合历史上对瓦格纳效应及系数的定义的相关讨论,澄清了瓦格纳效应及系数的概念及计算思路,揭示了其具有的诸多力学特性和工程应用价值。其次,利用转动中心联线形成的转心三角形,揭示出临界力及相应屈曲模态的正交特性,该特性为后续二阶分析中变形的正交分解后单独进行放大再叠加的放大系数法的应用提供了理论基础。最后,对各种截面形式的开口薄壁构件进行大量的计算后绘制出临界力与长细比关系曲线和转心三角形,从中揭示出开口薄壁梁柱空间屈曲特性。
③确定开口薄壁梁柱二阶分析中将要涉及的重要参数,为后续二阶分析提供条件。类比平面初始缺陷的选取并结合薄壁构件的空间屈曲特性,提出薄壁构件空间稳定初始缺陷的选取方法。讨论了基于临界力及相应屈曲模态的正交特性如何把薄壁梁柱的初始变形和一阶变形正交分解为三个独立变形的方法。根据内、外双力矩的平衡方程导出相互独立的三种变形的转角放大系数,提出了统一放大系数的概念。从最基本的扭转问题出发,推导简单荷载作用下的考虑了自由扭转刚度的内力和变形计算公式,从中寻找出自由扭转刚度的二阶效应规律。初步提出计算薄壁构件截面二阶应力的方法,解决传统理论中无法将双力矩项正确引入二阶应力计算公式的问题。
④基于边缘屈服准则绘制开口薄壁梁柱空间稳定系数与长细比关系曲线,揭示构件发生空间失稳时的诸多特性。从柱子曲线理论的研究进程出发,从众多稳定判定准则中选取简单且实用者,即采用边缘屈服准则,对多种截面形式且考虑了空间初始变形的开口薄壁构件空间稳定承载能力进行计算,将计算结果绘制成曲线,从中揭示构件发生空间弯扭失稳时的诸多特性。特别指出了两板型截面构件特有的失稳模式——扭转剪切失稳产生的根本原因。最后,初步讨论残余应力和弹塑性对压杆空间稳定性的影响。
⑤利用ANSYS有限元软件对前述开口薄壁梁柱空间稳定分析结果进行验证。对多种截面形式的薄壁构件进行一阶分析和特征值屈曲分析结果表明,本论文提出的分析方法正确。在原有的特征值屈曲分析的模型中引入构件的几何初始缺陷,利用弧长法绘制荷载-位移曲线并获得压杆的极限承载力,将其与前文中的空间稳定分析的结果进行对比后发现:两板型截面短杆确实存在剪切失稳现象,但新方法中的压杆尤其是较短压杆空间稳定分析结果与有限元分析结果相比偏于保守,因此必须对新方法中的空间稳定校核公式进行修正,提出新的实用校核方法。
⑥将基于“泛义弯曲理论”的开口薄壁梁柱空间稳定分析结果在工程中进行初步推广应用。将基于边缘屈服准则的空间稳定校核公式变换为临界应力的表达形式,并类比平面稳定问题中的处理方式,提出合理的开口薄壁梁柱的空间稳定校核方法——虚拟弹性逆算初弯扭法。鉴于现今缺少构件空间初始缺陷的科学统计资料,初步提出实用计算方法——折算长细比法。使用该方法对T形截面钢压杆的空间稳定性进行讨论,消除传统校核公式和理论分析方法带来的分歧,并按照新方法对现行规范中存在的问题进行初步修正。
总的说来,本文所作的工作是:简述并验证统一计算理论、推导空间屈曲临界力及屈曲模态的统一计算公式、理顺基于边缘屈服准则的空间稳定系数的统一计算步骤和提出实用的空间稳定统一校核方法。当然,上述对开口薄壁梁柱的空间稳定性的研究目前只处于理论阶段,尚缺乏有关初始缺陷资料的积累,以及大量实际工程的检验。本文从理论方面为薄壁构件空间稳定研究开创一种新思路,供规范修订参考。
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.
引文
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