薄壁框架节点中的翘曲扭转传递:运动、建模及结构响应

在梁的有限元分析中,采用简化运动模型模拟翘曲扭转约束及其在框架节点中的传递。简要说明薄壁杆件的扭转性能,建立运动模型,模拟翘曲扭转在2个以上U型或I型杆件交汇的框架节点中的传递。为了说明本模型的应用及有效性,列出数值结果,并进行讨论。将梁元与壳元的有限元结果进行对比,验证了本模型可考虑节点的翘曲扭转性能。     

曲线箱梁桥的地震反应分析

根据薄壁箱梁的翘曲扭转理论,建立了可以考虑截面翘曲和偏心影响的3维空间曲线箱梁桥的位移模式和能量泛函,利用有限元列式建立了动力方程。并编制了相应的程序。最后通过算例说明了翘曲扭转对曲线箱梁桥影响较大,不可忽略。     

Warping and bimoment transmission through diagonally stiffened beam-to-column joints

For beam-to-column rigid joints with a diagonal stiffener, the warping degrees of freedom at the beam-to-column joint have been taken to be continuous in some current literature. A new warping transmission model is presented for this type of joint in this paper, in which the bending deformation and twisting of the diagonal stiffener are considered and the restraining of the web in the joint panel zone to the twist of the diagonal stiffener is taken into account. Comparison with FEA using shell elements demonstrated the high accuracy of the proposed model, while the results with the continuous warping assumption have greater deviation with the finite element results. The suggested model can be implemented simply though modifying the traditional thin-walled beam element matrix at the joints. The proposed model is applicable for solving combined flexural and torsional problems of frames composed of thin-walled members.     

Global buckling analysis of plane and space thin-walled frames in the context of GBT

This paper reports research work concerning the use of Generalised Beam Theory (GBT) to analyse the global buckling behaviour of plane and space thin-walled frames. Following a brief overview of the main concepts and procedures involved in the performance of a GBT buckling analysis, one presents in detail the formulation and numerical implementation of a GBT-based beam finite element that includes only the first four (rigid-body) deformation modes — namely, one describes (i) the kinematical models developed to simulate the warping transmission at frame joints connecting two or more non-aligned U- and I-section members, (ii) the procedures adopted to handle the effects stemming from the non-coincidence of the member centroidal and shear centre axes (cross-sections without double symmetry), and (iii) the definition of joint elements, which involves providing a relation between the connected member GBT degrees of freedom and the joint generalised displacements. Finally, one presents and discusses numerical results that make it possible to illustrate the application and show the capabilities of the above GBT-based finite-element formulation and implementation. For validation purposes, the GBT-based results (critical buckling loads and mode shapes) are also compared with values yielded by shell (mostly) and beam finite element analyses carried out in the code ANSYS.     

A model for warping transmission through joints of steel frames

A simple approach is developed in this paper which considers the effect of partial warping continuity through the joints of thin-walled steel frames when using beam finite element analysis. Using a condensed stiffness matrix for the joint generated by the substructuring technique, warping springs are introduced to represent the condition of partial warping restraint at intersections between members. The performance of the proposed model is demonstrated through a number of numerical examples. Excellent agreement is achieved between the results of beam finite element analysis using the suggested joint model and accurate shell finite element analysis.     

考虑圣维南翘曲变形的初始扭转薄壁梁单元刚度矩阵

基于传统薄壁直梁力学模型,对初始扭转薄壁梁有限元数值模型进行系统的分析与研究。首先基于初始扭转梁的几何变形微分关系,导出初始扭转薄壁梁圣维南翘曲应变。根据传统薄壁直梁有限元力学模型,考虑初始扭转梁圣维南翘曲变形,建立其有限元单元刚度矩阵。最后,通过椭圆截面初始扭转梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的考虑圣维南翘曲变形的初始扭转薄壁梁单元刚度矩阵具有良好的精度。     

Modeling distortional shear in thin-walled elastic beams

In this paper, the theoretical background and the numerical analyses of an advanced beam finite element that relaxes the hypothesis of the cross-section non-deformability are presented. The corresponding new modes, called distortional modes, are added to the modes describing the behavior of a classical thin-walled beam: tension/compression, bending and torsion. For instance, a load acting in a cross-sectional plane of a beam is considered to induce not only bending and torsion but also distortion. The distortion produces non-uniform shear and axial stresses together with a non-uniform warping of the cross-section. These resulting effects, significant for very thin-walled open profiles (and thin-walled closed profiles with high distortional loadings), are shown in this paper to be important when compared to bending and torsion stresses even in simple loading cases.     

Influence of joint detail on the flexural/torsional interaction of thin-walled structures

For a structure formed from two thin-walled open members connected at 90°, torsion applied to one member can result in torsion as well as flexure in the second member, with the magnitude and direction of this torsion as well as flexure in the second member being determined by the type of joint used. Conventional structural analysis would normally assume the presence of only flexure in the second member. The results from a finite element study of structures formed from thin-walled channel sections connected by box, mitre and stiffened mitre joints is presented and an explanation for the behaviour of the different joint types is given. It is shown that for the box joint the warping deformation of the loaded member is the dominant factor in determining the magnitude and direction of the twisting of the second member, whilst this is determined for the stiffened mitre joint primarily by the St Venant rotation deformation of the loaded member. For the unstiffened joint it is shown that the warping and St Venant rotation deformation effects tend to cancel each other out.     

Frame mode method for thin-walled structures

The Rayleigh-Ritz method is extended to thin-walled structures on continuous supports by means of the combinations of frame modes transversely and continuous beam modes longitudinally. Effects of warping, distortion and shear-lag are considered simultaneously. The thin-walled structure problem is reduced to simpler plane frame and continuous beam problems. Numerical results are compared to the finite element and finite strip methods. The present method is advantageous over both the finite element and finite strip methods in the reduced number of generalised coordinates and its ability to use the existing frame programmes to analyse thin-walled structures. No new elements are required to be generated.     

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.     

Torsion analysis of thin-walled beams including shear deformation effects

The first part of the paper develops a theory for the torsional analysis for open thin-walled beams of general cross-sections which accounts for shear deformation effects. Statically admissible stress fields are postulated in agreement with those resulting from the Vlasov thin-walled beam theory. The principle of stationary complementary energy is then adopted to formulate the governing field compatibility condition under the stress fields postulated. The naturally arising boundary terms are found to relate the warping deformations to the internal force fields. A torsion beam example is solved using the new theory in order to illustrate its applicability to practical problems. The second part of the paper implements the solution numerically in a force-based finite element context. Two finite elements are developed by assuming linear and hyperbolic bimoment fields. The FEA solutions are shown to provide lower bound representations of the stiffness when compared to those based on conventional beam theories founded on postulated kinematic assumptions.     

梁柱节点翘曲位移传递的分析

考虑柱子和两个正交方向梁的翘曲自由度,再加上传统的节点位移和节点转动等6个自由度,空间框架中刚性连接节点的自由度应该为9个。对常用的梁柱刚性连接节点中的3个翘曲自由度之间的关系进行分析,得到了3个方向的翘曲自由度之间的关系,这些关系能够用于消去梁的翘曲自由度,从而保证一个节点仍然是7个自由度。采用ANSYS板壳有限元分析结果进行的验证表明,提出的公式是正确的。研究表明,目前各种通用软件中采用一个节点7个未知量的方法隐含的梁柱翘曲自由度之间的关系是不符合实际的。     

楼板对高层建筑核芯筒受力性能的影响

本文根据Vlasov的薄壁杆件翘曲理论,采用有限元和解析相结合的分析方法,研究了四周与楼板连接的开口薄壁核芯筒的扭转刚度,考察了楼板出平面刚度对核芯筒受力性能的影响,提出楼板有效宽度的概念,推导出相应的计算公式。在实际工程设计计算中,可考虑楼板对核芯筒约束扭转的制约作用。     

A beam model for large displacement analysis of flexibly connected thin-walled beam-type structures

This paper presents a beam formulation for large displacement analysis of beam-type structures with flexible connections. Within the framework of updated Lagrangian incremental formulation and the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping and the second-order displacement terms due to large rotations, the equilibrium equations of a straight beam element are firstly developed. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the internal torsion and bending moments, respectively. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends. To account for the flexible connection behaviour, a special transformation procedure is developed. The numerical algorithm is implemented in a computer programme and its reliability is validated trough several test examples.     

GBT buckling analysis of thin-walled steel frames: A state-of-the-art report

This paper presents a state-of-the-art report on the use of Generalised Beam Theory (GBT) to assess the buckling behaviour of plane and space thin-walled steel frames. After a very brief overview of the main concepts and procedures involved in performing a GBT buckling analysis, one addresses the development and numerical implementation of a GBT-based beam finite element formulation that is able (i) to unveil local, distortional and global buckling modes, (ii) to handle arbitrary loadings (namely those causing non-uniform member internal force and moment diagrams) and (iii) to incorporate the presence of several frame joint configurations and arbitrary end and/or intermediate support conditions (including those associated with the modelling of bracing systems). In particular, one describes the procedures employed to establish the frame linear and geometric stiffness matrices – special attention is paid to the constraint conditions adopted to ensure the local displacement compatibility at the frame joints. The paper closes with the presentation and discussion of a number of numerical results that make it possible to illustrate the application and show the potential of the GBT-based approach to perform frame buckling analyses – they concern both plane and space frames. In order to validate and assess the numerical efficiency and accuracy of the GBT analyses and results (critical buckling loads and mode shapes), the frames are also rigorously analysed in the commercial code Ansys – both the members and joints are discretised by means of fine shell finite element meshes.     

A beam finite element for non-linear analyses of thin-walled elements

The aim of the present paper is to investigate a theoretical and numerical model which is able to study the behaviour of thin-walled beams with open cross section in presence of large torsion. The presented model takes into account for large torsion, linear and non-linear warping currently named shortening effects, pre-buckling deformation and flexural–torsional coupling. In numerical analysis, a 3D beam with two nodes and seven degrees of freedom per node is adopted. The equilibrium equations and the material behaviour are derived in discrete form without assumption on torsion angle amplitude. Due to large torsion context, all the equilibrium equations are non-linear and highly coupled. The linear behaviour is made possible by disregarding non-linear terms. For non-linear behaviour and stability, the tangent stiffness matrix is carried out. Due to large torsion context, new matrices are present. The element is incorporated in a homemade finite element code. Newton–Raphson iterative methods are used with different control parameters. In order to prove the efficiency of the model many examples are presented in linear and non-linear behaviour with presence of bifurcations.     

薄壁曲线箱梁空间分析的梁段单元

广义符拉索夫薄壁梁理论耦合有限元技术 ,推导出一种能模拟拉压、弯曲、扭转、扭翘、剪切和剪力滞效应的薄壁曲线箱梁梁段单元。单元为两节点九自由度 ,除了常规梁单元的六个自由度外 ,还有三个分别考虑扭翘、剪切和剪力滞效应的自由度。利用变分原理在曲线坐标系下推导了单元刚度矩阵的显式及其等效结点荷载列阵。并在推导中考虑了曲线箱梁横截面剪心与形心不重合的影响。算例表明了本单元的有效性和准确性。     

An experimental investigation of the behaviour of thin-walled box beams

The purpose of this paper is to present the results of an experimental investigation of the behaviour of four types of thin-walled box beam and to compare the results with those obtained from theoretical analyses.Three steel models consisting of a straight single cell cantilever, a curved single cell cantilever and a simply supported twin box have been constructed, in addition to a continous prestressed concrete two-span double cell beam.Details are given of the methods of construction, instrumentation and experimental procedure for all the models.The behaviour of the individual models has been studied, with particular attention being given to the torsion and distortion of the box sections, the cross-sectional distributions of the longitudinal and transverse bending stresses and the deflections. Appropriate experimental results are presented, therefore, and are compared with those obtained from the specially developed thin-walled box beam finite element which has been presented previously in this journal.     

单室薄壁箱梁考虑偏载影响的活载加载计算分析

采用一种考虑约束扭转的空间薄壁箱梁单元 ,对大跨度连续刚构桥进行汽车活载加载计算。考虑荷载的横向偏载效应 ,对空间薄壁箱梁七个自由度 (三个线位移自由度、三个转角位移自由度以及一个翘曲位移自由度 )方向的影响线加载进行计算 ,求出梁部截面翘曲双力矩、横向弯矩、扭矩的极值曲线。应用此方法 ,对一实际的大跨连续刚构桥———靖远三滩黄河大桥进行计算分析 ,方法简单可靠 ,可为单室薄壁箱梁结构考虑荷载的横向分布提供新的设计思路。     

考虑翘曲变形的复合材料叠合梁几何非线性的有限元分析

提出了一个用于复合材料叠合梁结构分析的有限元模型,梁结构具有几何非线性性能,包括扭转翘曲变形。采用一个考虑了改进拉格朗日法和广义位移控制法的公式对结构的变形进行计算。采用二次等参有限单元对梁横截面进行离散化,以确定梁的弯扭特性。利用两结点的Hermitean三维有限梁元对结构进行离散化,其中每结点具有7个自由度。运用数个实例,分析了层的取向对结构性能的影响。