Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

Cellular buckling in I-section struts

An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh–Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments.     

冷弯薄壁卷边槽钢轴压构件畸变与局部相关屈曲试验研究

对卷边尺寸不同的两类腹板中间设置加劲卷边槽形截面,共18个冷弯薄壁型钢固支轴压试件进行畸变屈曲与局部屈曲相关作用的静力试验研究。得到试件的屈曲模式、相关屈曲行为、破坏模式以及极限荷载。试验结果表明：畸变屈曲与局部屈曲的耦合相关对试件的变形和极限荷载有不利作用;畸变屈曲与局部屈曲的耦合相关作用存有较大的屈曲后承载力;畸变屈曲与局部屈曲的耦合相关顺序,即畸变屈曲 局部屈曲耦合相关、局部屈曲 畸变屈曲耦合相关,对试件的变形、非线性平衡路径、破坏模式以及极限荷载的影响有所不同。采用ABAQUS有限元软件对试件进行模拟分析,计算结果与试验结果吻合良好。     

方形钢管混凝土钢管壁弹性屈曲分析

对方形钢管混凝土钢管壁局部屈曲行为进行弹性分析,推导钢管壁发生局部屈曲时的屈曲系数、屈曲半波长及临界屈曲应力表达式,并与局部屈曲试验研究成果进行比较,提出更为合理的计算公式,为后续的进一步研究打下基础.     

方形钢管混凝土钢管壁弹性屈曲分析

对方形钢管混凝土钢管壁局部屈曲行为进行弹性分析,推导钢管壁发生局部屈曲时的屈曲系数、屈曲半波长及临界屈曲应力表达式,并与局部屈曲试验研究成果进行比较,提出更为合理的计算公式,为后续的进一步研究打下基础。     

Collapse analysis of regular and irregular tall steel moment frames under fire loading

This study is carried out to evaluate the progressive collapse of steel buildings under fire event. To this end, a 15‐story steel structure with moment‐resisting system and composite floors is considered. The effects of various parameters such as beam section size, gravity load ratio, vertical irregularity of resisting system, and location of fire compartments on collapse modes are investigated numerically. Different temperature‐time curves are defined across the composite floors according to the Eurocode 4. It is found that local collapse of the frames at the ground floor fire is triggered by the buckling of the interior heated columns at approximately 540°C. The redistributed loads by floors delay the global collapse at least 45 min. Increasing gravity loads accelerates the global collapse of the frames significantly. The heated columns of the middle floor buckle at higher temperature compared to the ground floor heated columns and no global collapse occur due to this scenario. In general, the potential of collapse of the regular and irregular frame due to fire in the edge bay is higher compared to the fire in the middle bay. It is also found that the local and global collapse of regular frames occur earlier than irregular frames.     

Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hooke's law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamilton's principle. In this paper the static solution has been obtained by Koiter's asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunov's orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.     

Interactive buckling and load carrying capacity of thin-walled beam–columns with intermediate stiffeners

The design of thin-walled beam–columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam–columns with central intermediate stiffeners under axial compression and a constant bending moment. The columns are assumed to be simply supported at their ends. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed by means of the transition matrix method and Godunov’s orthogonalisation. Instead of the finite strip method, the exact transition matrix method is used in this case. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The paper’s aim is to expand the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained, the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The calculations are carried out for a few beam–columns. The results are compared to those obtained from the design code and to the data reported by other authors.The results discussed in the present study represent the most important results obtained by the authors in earlier investigations devoted to central intermediate stiffeners (Int. J. Solid Struct. 32 (1995) 1501; Eng. Trans. 43 (1995) 383; Int. J. Solid Struct. 37 (2000) 3323; Int. J. Solid Struct. 33 (1996) 315; Thin Wall. Struct. 39 (2001) 649; Arch. Mech. Eng. XLVIII (2001) 29).     

Loss-of-stability induced progressive collapse modes in 3D steel moment frames

This paper deals with the progressive collapse analysis of a tall steel frame following the removal of a corner column according to the alternate load path approach. Several analysis techniques are considered (eigenvalue, material nonlinearities, material and geometric nonlinearities), as well as 2D and 3D modelling of the structural system. It is determined that the collapse mechanism is a loss-of-stability-induced one that can be identified by combining a 3D structural model with an analysis involving both material and geometric nonlinearities. The progressive collapse analysis reveals that after the initial removal of a corner column, its two adjacent columns fail from elastic flexural-torsional buckling at a load lower than the design load. The failure of these two columns is immediately followed by the failure of the next two adjacent columns from elastic flexural–torsional buckling. After the failure of these five columns, the entire structure collapses without the occurrence of any significant plastification. The main contribution is the identification of buckling-induced collapse mechanisms in steel frames involving sequential buckling of multiple columns. This is a type of failure mechanism that has not received appropriate attention because it practically never occurs in properly designed structures without the accidental loss of a column.     

An experimental investigation of distortional buckling of steel storage rack columns

An experimental investigation on the behavior of steel storage rack columns subjected to compression is presented. Members of different lengths are tested, but special attention is focused on the behavior of the specimens having lengths that make them subject to distortional buckling. This mode of buckling can be observed in moderately long specimens; namely, longer than the stub columns used for the determination of the local buckling strength, but short enough to avoid the effects of global buckling. The deformation experienced by these specimens is measured, and it is observed that there is a range of member lengths where the failure mode is a combination of distortional buckling and global buckling modes. Furthermore, it is verified that, although the effect of the interaction between these modes on the member strength is not large, the accuracy of the current design procedures improves if it is considered in the calculations.     

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns,Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.     

冷弯薄壁型钢双肢拼合构件轴压承载力研究

目前我国相关规范对冷弯薄壁型钢组合截面构件的承载力设计方法比较粗略。基于已有的卷边槽形截面构件和由其组成的组合箱形截面构件的轴心受压承载力试验研究结果,通过有限元模拟和理论分析研究了此类构件拼合前后的受力性能的差异。分析了安装误差和连接件间距对拼合构件承载力的影响。提出了针对组合箱形和工字形截面构件的轴心受压承载力设计方法。研究表明,组合箱形截面构件的整体屈曲和畸变屈曲承载力较单肢截面构件有一定提高,而组合工字形截面构件仅整体屈曲承载力有一定提高。设计承载力与试验结果的比较表明,所提出的建议设计方法基本合理,可为相关规范的编制提供参考。     

Mode interaction in thin-walled equal-leg angle columns

This paper presents and discusses numerical results, obtained through Ansys shell finite element analyses, dealing with the post-buckling behaviour (mostly elastic, but also elastic–plastic), ultimate strength and failure mode nature of fixed-ended and pin-ended thin-walled equal-leg angle steel columns with coincident critical flexural-torsional and minor-axis flexural buckling loads (i.e., experiencing very strong coupling effects between these two global instability phenomena) – for comparative purposes, columns that are buckling in pure flexural-torsional and flexural modes are also analysed. Since the main aim of the work is to investigate the column imperfection-sensitivity, the analyses concern otherwise identical columns containing initial geometrical imperfections with different shapes and amplitudes, combining the competing critical buckling modes – particular attention is paid to the sign of the minor-axis flexural component. The results reported consist of column (i) elastic equilibrium paths and the corresponding peak loads and deformed configurations and (ii) elastic–plastic collapse loads and mechanisms, making it possible to assess how they are influenced by the initial geometrical imperfections.     

Local–global mode interaction in stringer-stiffened plates

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global buckling mode and the strongly stable local buckling mode is highlighted. Highly unstable post-buckling behaviour and a progressively changing wavelength in the local buckling mode profile are observed under increasing compressive deformation. The analytical model is compared against both physical experiments from the literature and finite element analysis conducted in the commercial code Abaqus; excellent agreement is found both in terms of the mechanical response and the predicted deflections.     

Robustness of multi-storey car parks under vehicle fire

While recent studies on structures subject to fire have focused on individual structural members, sub-frames, or entire structures, issues of robustness due to the possible loss of columns exposed to fire have received less attention. This paper is concerned with the realistic modelling of a multi-storey car park under a vehicle fire scenario occurring near an internal column, where emphasis is given to the robustness and ductility response of the floor systems subsequent to column buckling. To address this, a detailed heat transfer analysis according to the proposed fire scenario is conducted to obtain realistic temperature distributions within the structure. For the subsequent structural analysis, two structural models with different modelling sophistications are established, namely, a detailed slab model and a simplified grillage model. Dynamic analysis is performed to trace potential dynamic effects, where the inelastic joint response is considered in detail for the purpose of robustness assessment. Based on the undertaken nonlinear analysis, three major failure modes, specifically single-span failure, double-span failure, and shear failure, are identified which can potentially trigger progressive collapse. Finally, the significance of dynamic effects along with column buckling under fire is evaluated, where it is found that the actual ductility demands fall between two idealised extreme cases, namely ‘static column loss’ and ‘sudden column loss’.     

高强度钢材箱形截面轴心受压短柱局部稳定试验研究

针对高强度钢材焊接箱形截面柱的局部稳定受力性能,对4个Q460钢材等边箱形短柱进行轴心受压试验。根据试验结果分析试件的局部屈曲应力、极限应力随板件宽厚比的变化规律,并将试件的局部屈曲应力、极限应力与我国、美国、欧洲钢结构设计规范以及陈绍蕃建议的相应设计方法和计算公式进行对比分析。结果表明,钢板的宽厚比越大,试件截面的利用率越低,局部屈曲后强度越富余;我国钢结构设计规范中对于试件的局部屈曲应力的计算公式不适用于等边箱形短柱;对于等边箱形短柱的极限应力,美国、欧洲钢结构设计规范和陈绍蕃建议的设计方法的计算结果较为接近,且均略高于试验结果,这3种设计方法都是可行的。进一步修改已有的计算公式,以适用于计算Q460高强度钢材等边箱形短柱的局部屈曲应力;建议采用陈绍蕃建议的设计方法,并进一步修改欧洲钢结构设计规范的计算公式,以适用于计算Q460高强度钢材等边箱形短柱的极限应力。     

Influence of load-non-uniformity and eccentricity on the stability and load carrying capacity of orthotropic tubular columns of regular hexagonal cross-section

The paper contains an analysis of the influence of non-uniformity and eccentricity of compressive loads on global and local buckling, on interactive buckling, and on the load-carrying capacity of thin-walled columns. Isotropic and orthotropic tubular columns of regular hexagonal cross-section have been examined. Equilibrium equations for the first and the second order non-linear approximation have been solved using the asymptotic Byskov–Hutchinson method. Numerical calculations have been performed for numerous different loading modes of isotropic columns and also for several loading modes of orthotropic columns. The results are presented in diagrams with some conclusions.     

Q690高强钢焊接箱形轴压构件整体稳定研究及设计建议

为研究Q690高强钢焊接箱形轴心受压构件的整体稳定性能,给出适合该类构件的设计建议,通过对3根Q690焊接箱形截面试件的残余应力试验,得到了箱形截面的残余应力分布模型。设计并制作了5根Q690焊接箱形柱,并对其两端铰支条件下进行了轴压试验研究,试验前分别对试件的几何初始缺陷和初始偏心均进行了测量。轴压试验中,所有试件破坏形式均为整体失稳破坏。基于试验结果,分析了该试件的整体稳定性能,采用直接分析法建立了数值模型,并校验了数值模型的准确性。同时,采用该数值模型对箱形轴压构件进行了参数分析,基于试验和参数分析结果,给出了Q690焊接箱形轴压构件的一阶弹性设计建议。     

On the local and global buckling behaviour of angle,T-section and cruciform thin-walled members

This paper reports the results of an investigation aimed at providing fresh insight on the mechanics underlying the local and global buckling behaviour of angle, T-section and cruciform thin-walled steel members (columns, beams and beam-columns). Due to the lack of primary warping resistance, members displaying these cross-section shapes possess a minute torsional stiffness and, therefore, are highly susceptible to buckling phenomena involving torsion – moreover, it is often hard to distinguish between torsion and local deformations. Almost all the numerical results presented are obtained by means of Generalised Beam Theory (GBT) analyses and, taking advantage of its unique modal features, it is possible to shed some new light on how to characterise and/or distinguish the local and global buckling modes of the above thin-walled members. Finally, some comments are made concerning the development of a rational and efficient (safe and economic) approach for their design.