Elastic buckling and second-order behaviour of pitched-roof steel frames

The aims of this work are two-fold: (i) to present the results of a study concerning the elastic in-plane stability and second-order behaviour of unbraced single-bay pitched-roof steel frames and (ii) to propose, validate and illustrate the application of an efficient methodology to design this type of commonly used frame. After (i) characterizing the relevant frame buckling modes and P-Δ second-order effects, and (ii) addressing the exact and approximate calculation of the associated bifurcation loads and secondary bending moments, the paper deals with the incorporation of these concepts in the definition of an efficient design procedure. In particular, it is clearly shown that, due to the rafter slope, the geometrically nonlinear behaviours of orthogonal beam-and-column and pitched-roof frames are qualitatively different. Finally, the proposed concepts and methodologies are illustrated through the presentation and discussion of numerical results involving fixed and pinned-base frames.     

Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections

The objective of this paper is to propose a simplified approach to the evaluation of the critical buckling load of multi-story frames with semi-rigid connections. To that effect, analytical expressions and corresponding graphs accounting for the boundary conditions of the column under investigation are proposed for the calculation of the effective buckling length coefficient for different levels of frame sway ability. In addition, a complete set of rotational stiffness coefficients is derived, which is then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, featuring semi-rigid connection at their near end as well as the eventual presence of axial force, are considered. Examples of sway, non-sway and partially-sway frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with the finite element results, while the application of codes such as Eurocode 3 and LRFD leads to significant inaccuracies.     

Review on the modelling of joint behaviour in steel frames

Steel portal frames were traditionally designed assuming that beam-to-column joints are ideally pinned or fully rigid. This simplifies the analysis and structural design processes, but at the expense of not obtaining a detailed understanding of the behaviour of the joints, which in reality, have finite stiffness and are therefore semi-rigid. The last century saw the evolution of analysis methods of semi-rigid joints, from the slope-deflection equation and moment distribution methods, to matrix stiffness methods and, at present, to iterative methods coupling the global and joint structural analyses. Studies agree that in frame analysis, joint rotational behaviour should be considered. This is usually done by using the moment-rotation curve. Models such as analytical, empirical, experimental, informational, mechanical and numerical can be used to determine joint mechanical behaviour. The most popular is the mechanical model, with several variances (e.g. Component Method). A summary is given of the advantages and disadvantages and principal characteristics of each model. Joint behaviour must be modelled when analysing semi-rigid frames, which is associated with a mathematical model of the moment-rotation curve. Depending on the type of structural analysis required, any moment-rotation curve representation can be used; these include linear, bilinear, multilinear and nonlinear representations. The most accurate representation uses continuous nonlinear functions, although the multilinear representation is commonly used for mechanical models. This article reviews three areas of steel joint research: (1) analysis methods of semi-rigid joints; (2) prediction methods for the mechanical behaviour of joints; (3) mathematical representations of the moment-rotation curve.     

Behaviour of semi-rigid steel beam-to-beam joints under bending and axial forces

This paper presents an analysis of semi-rigid beam-to-beam end-plate bolted joints that are subjected to bending and tension or a compression axial force. Usually the influence of axial force on joint rotational stiffness is neglected. According to EC3, the axial load, which is less than 10% of plastic resistance of the connected member under axial force, may be disregarded in the calculation of characteristics of a joint. Actually, the level of axial forces in joints of structures can be significant and has a significant influence on characteristics of semi-rigid joints. One of the most popular practical methods permitting the determination of rotational stiffness and moment resistance of a joint is the so-called component method. The extension of the component method for evaluating the influence of bending moment and axial force on the rotational stiffness and moment resistance of a joint are presented in the paper. The numerical results of calculations of characteristics of joints and calculations of steel framework are presented in this paper as well.     

钢框架栓焊梁柱连接节点的抗震设计

节点设计是整个钢结构设计的重要环节,提高钢框架梁柱连接节点的抗震性能是整个钢结构抗震设计的重要内容.本文主要介绍了提高钢框架栓焊梁柱连接节点的抗震设计的主要措施,主要方法包括:通过加腋和加盖板对节点进行加强,提高节点承载力;对梁局部削弱,使塑性铰从节点区外移至梁上;改进节点区焊接孔构造形式,缓解局部应力集中;妥善处理弧板和垫板,减少焊缝缺陷.     

On the buckling of axially restrained steel columns in fire

This paper describes the behaviour of restrained steel columns in fire. It follows the introduction of extra load into the column through the axial restraint of the surrounding cooler structure and the consequential buckling. Key to this understanding is the post-failure behaviour and re-stabilisation of the column, which is discussed with reference to a finite element model and an analytical model. Through bi-directional control of the temperature, the finite element model allows the snap-back behaviour to be modelled in detail and the effects of varying slenderness and load ratio are investigated. The analytical model employs structural mechanics to describe the behaviour of a heated strut, and is capable of explaining both elastic and fully plastic post-buckling behaviour.Through this detailed explanation of what happens when a heated column buckles, the consequences for steel-framed building design are discussed. In particular, the need to provide robustness is highlighted, in order to ensure that alternative load paths are available once a column has buckled and re-stabilised. Without this robustness, the dynamic shedding of load onto surrounding structures may well spread failure from a fire’s origin and lead to progressive collapse.     

Experimental study on semi-rigid composite joints with steel beams and precast hollowcore slabs

The concept of semi-rigid composite connection has been widely researched in the past; however, most of the researches are limited to composite joints with metal deck flooring and solid concrete slabs. Composite construction incorporating precast concrete hollowcore slabs (HCU) is a recently developed composite floor system for buildings. The research on the structural behaviour of the semi-rigid composite joints with HCU is new and without any previous experimental database. In this paper, eight full-scale tests of beam-to-column semi-rigid composite joints with steel beams and precast hollowcore slabs are reported. The variables are stud spacing, degree of the shear connections, area of the longitudinal reinforcement and slab thickness. The test set-up and instrumentation is described in detail. The experimental behaviour is analysed and based on the test data the structural behaviour of these semi-rigid composite joints is discussed. Based on the experimental data, a simplified method to predict rotation and moment capacity for this type of composite connection is proposed.     

Comparative study of the buckling of steel beams in Eurocode 3 and the Russian code

Lateral torsional buckling is the main limit state that must be checked for steel beams. Design codes provide different models for the analysis of this complex phenomenon. The present paper describes a comparative study of the interpretation of beam buckling of symmetrical sections in EN 1993-1-1 (EC3), its preliminary ENV-version and a Russian steel structure design code. In order to choose the nationally determined parameters in EC3, the impact of parameters on the safety level and overall design results has to be carefully studied. Modification factors, introduced in EC3, have moved the resistance for certain load distribution from ENV-based values closer to the Russian code.     

Statistical evaluation of the lateral-torsional buckling resistance of steel I-beams, Part 2: Variability of steel properties

The statistical evaluation of codified resistance models is a crucial step to ensure that the derived reliability targets are achieved. Experimental tests are seldom sufficient to provide a statistically representative sample so that nowadays numerical tests are accepted provided they accurately reproduce experimental results. The evaluation of the influence of the variability of steel properties on the lateral-torsional resistance of steel beams is presented in this paper, leading to the assessment of the required partial safety factor γ_M1 to ensure compliance with the EN 1990 reliability criteria. Results confirm that the choice of γ_M1=1.0 is appropriate.     

Exact and approximate solutions for the flexural buckling of columns with oblique rotational end restraints

This paper is concerned with the elastic flexural buckling of doubly symmetric columns with oblique restraints under concentric loading. Oblique restraints cause coupling between the principal axis deflections and rotations, and the flexural buckling mode involves simultaneous bending about both principal axes.The paper discusses the nature of oblique restraints, and presents exact and approximate solutions for the buckling loads of columns with rigid or elastic restraints against rotations at the ends. The exact solutions are obtained by solving the governing differential equations and boundary conditions, while the approximate solutions are based on energy solutions with assumed buckling displacements. The approximate solutions are sufficiently simple that they can be used in design, and are shown to be within 1% of the exact solutions.     

门式刚架轻钢结构支撑体系计算方法的探讨

分析比较门式刚架轻钢结构的支撑计算的三种方法，对支撑体系的计算提出合理的方案。     

On the incorporation of equivalent member imperfections in the in-plane design of steel frames

This work deals with the incorporation of equivalent member imperfections in the global analysis of steel frames and, in particular, is intended to clarify the Eurocode 3 (EC3) provisions involved in such procedure. In fact, these provisions stem from the well-known “European column buckling curves”, which means that they are based on the behaviour of simply supported isolated members under uniform compression (columns). First, one addresses the geometrically non-linear behaviour of isolated columns displaying arbitrary support conditions and different initial geometrical configurations. Then, the results obtained are used to propose a systematic and rational method to evaluate the appropriate “equivalent initial imperfections” that need to be incorporated in the second-order global elastic analysis of a frame or isolated compressed member. This method (i) is fully consistent with the EC3 column buckling curves and (ii) adopts critical buckling mode shape initial imperfections with amplitudes determined by means of closed-form analytical expressions. In order to enable a better grasp of the concepts involved and also to illustrate the capabilities of the proposed methodology, several numerical examples are presented and discussed throughout the paper.     

混凝土楼板对钢框架梁柱节点抗震性能影响的试验研究

为了研究节点区混凝土楼板对钢框架梁柱节点抗震性能的影响,完成了4个不同构造形式的节点试件在低周循环荷载下的破坏试验,分析了节点构造与混凝土楼板配筋率等因素对节点承载力、转动刚度、极限转动能力、耗能能力、延性和极限破坏状态的影响。对节点破坏模式和滞回曲线的分析表明,保证焊接质量是避免节点脆性破坏的重要措施。采用长焊接孔的节点,使钢梁发生了局部屈曲破坏,既可减少局部应力集中,又可提高节点的延性,提高配筋率可以显著增强节点的抗弯承载力。另外,混凝土楼板的存在使节点在构造上存在不对称性,应该在节点设计中给予考虑。     

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.     

Eccentrically patch-loaded steel I-girders: The influence of patch load length on the ultimate strength

The ultimate strength of steel I-girders is reduced when the loads are applied at an eccentricity relative to the center of the section, compared with the centric case, for which the loads are applied in the plane of the web. Current expressions for the strength reduction coefficient for eccentrically patch-loaded steel I-girders do not account for the length of the patch loading. In this paper, the effect of patch load length is investigated using a substantially larger data set than was available in the past. The length of the patch load is found to have a significant influence on the strength reduction coefficient for small ratios of flange thickness to web thickness, t_f/t_w.     

The semi-rigid behaviour of three-dimensional steel beam-to-column steel joints subjected to proportional loading. Part II: Theoretical model and validation

The component method proposed by the Eurocode is an excellent and versatile analysis tool, which can be applied to a wide variety of joints. However, it lacks appropriate components to predict the behaviour of minor-axis and three-dimensional joints. In this paper, a new component for laterally supported plates in bending (applied here to the column web and to the additional plate in bending) is presented and applied to minor-axis joints. Also, complete elastic models for both major- and minor-axis three-dimensional joints are presented. The proposed models take into account the effects on the elastic behaviour of each component caused by proportional loading along both axes.     

带填充墙钢框架结构抗侧力性能试验及理论研究

介绍了7榀钢框架及带填充墙钢框架结构的水平静力及低周反复加载试验。通过测试有墙和无墙钢框架试验模型在侧向力作用下的变形全过程,得到了墙体对钢框架结构强度和刚度的影响,了解了节点的破坏特征及墙体本身的工作性能,得到了有墙及无墙钢框架结构的滞回性能。试验中发现,填充墙体和钢框架之间的连接性能很好,墙体和框架可以共同工作。通过参数分析,给出了结构抗震弹性层间角位移的建议取值为1/350。在理论分析的基础上,提出了填充墙框架体系抗侧刚度简化公式,得到了试验结果的验证。     

Experimental analysis on the cyclic behaviour of beam-to-column joints in steel storage pallet racks

Design rules for steel storage pallet rack systems have recently been developed for static loading. The proposed approaches require monotonic tests to evaluate the behaviour of the key components of racks and to assess the main parameters governing their performance. By means of analysis of test data, rack design is based on use of the state-of-knowledge developed and codified for traditional cold-formed structural systems. As far as racks in seismic zones are concerned, no research activities have recently been carried out and only the Specifications developed by the Rack Manufacturing Institute (USA) provide practical design rules, while the European standard for the earthquake resistance of structures does not refer to rack systems.A study is currently in progress at the Department of Structural Engineering of the Politecnico di Milano (I) on the development of simplified rules for the design of steel storage pallet rack systems in seismic zones. This paper deals with the first part of the research, which consists of an experimental analysis aimed at investigating the behaviour of beam-to-column joints. Key features of tests are discussed and the main parameters characterising the joint moment–rotation curve under cyclic reversal loading are singled out.     

Advanced analysis of steel framed buildings using the Brazilian standard and Eurocode-3

In this paper, a refined plastic hinge approach is modified to account for the tangent modulus model, as recommended by the European buckling curves for steel columns, which are the same as the strength curves for columns specified in the Brazilian code for steel buildings-NBR-8800. The computational programme was developed on the basis of the inelastic stability function of the beam-column element, and it can be used to assess the steel frame behaviour, including gradual yielding associated with residual stresses, second-order effects, geometrical imperfections and the flexibility of beam-to-column connections. The numerical results obtained are verified by comparison with the plastic zone approach, as previously presented by other researchers. The proposed analysis is to be applied in the Brazilian context. It has large advantages over conventional linear elastic procedures and our findings indicate that it is a reliable tool to use in daily design practice.