An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3.     

Imperfections in steel girder webs with and without perforations under patch loading

In this paper, the problem of stability of web plates with imperfections, subjected to patch load, is studied. The aim is to give some insights about the best way to take into account real imperfections in non-linear stability analyses of plates with and without perforations. In this context, the study is developed on the basis of the measured imperfections or numerically deriving the deformed model (theoretical imperfections). The influence of the patch load length, out-of-plane imperfection amplitude, dimension and position of the hole on stability behaviour and buckling strength are studied comparing some theoretical deformed configurations corresponding to different modal shapes. The results obtained with a three-dimensional model of the whole real beam with stiffeners, with experimentally measured imperfections, and each corresponding single web panel are compared and discussed obtaining some insights about the accuracy of the simplified (and conservative) model of the single panel.The main insights of this work are as follows. The deformed shape, corresponding to the first buckling mode, can be assumed as the initial configuration of the panels with and without holes to study post-critical behaviour until ultimate condition. The shape of the imperfection does not severely change the critical buckling stress. A longer patch load reduces the ultimate stress in the panel. An initial imperfection amplitude of less than 1% of the height of the panel does not reduce the ultimate load by more than about 5%.     

Buckling analysis of a cooling tower shell with measured and theoretically-modelled imperfections

Geometrical imperfections were measured using photogrammetric techniques on an existing reinforced concrete cooling tower shell. The imperfections, related to the radii of such a real shell, were used as input data to create a real shape of the cooling tower. Numerical analysis was carried out for three models: (P) perfect shell of revolution, (M) shell with measured imperfections, (T) shell with a theoretical imperfection corresponding to the primary buckling mode under dead load. The buckling analysis was related to the linearized eigenvalue problem of elastic shells. The shell midsurface was approximated by eight-node quadrilateral isoparametric finite elements. Computations were carried out using the ANKA computer code. Critical values of the load parameter enable confirmation of a partial correlation between existing imperfections and buckling modes under dead load. The most disadvantageous direction of the wind load application on the real shell was found, in order to evaluate the decrease in the load-carrying capacity of the cooling tower shell against buckling. Theoretically modelled imperfections give rather unrealistic values of buckling loads of the real shell.     

Loss of stability of thin, elastic, strongly convex shells of revolution with initial imperfections, subjected to uniform pressure. A probabilistic approach

This paper presents an attempt to evaluate theoretically the influence of initial geometric imperfections in the shell surface on the value of the upper critical load of a strictly convex shell of revolution which is subjected to uniform pressure. Pogorelov's geometric method for nonlinear stability problems of thin shells is applied to obtain an analytical formula for the upper critical load, dependent on the initial imperfections. A probabilistic solution of the problem is presented. As a result, the stochastic influence of the initial deviations in the shell surface on the probability density function of the critical load and on the shell reliability are estimated and presented graphically. An example is given for an ellipsoidal shell of revolution.     

单层组合加肋拱支网壳的稳定性

介绍了某相贯单层组合加肋拱支网壳结构在竖向荷载及风荷载作用下的整体稳定性。采用有限元软件MIDAS,在两种荷载工况下分别进行了此网壳结构的特征值屈曲、几何非线性屈曲分析,初始缺陷对网壳结构的整体稳定性影响分析。结果表明:网壳结构对初始缺陷较为敏感,初始缺陷会明显降低结构稳定性;不同的荷载工况下,失稳的情况亦不同且网壳结构稳定临界系数随着荷载的增大而降低。     

Finite element techniques for the analysis of cooling tower shells with geometric imperfections

Two finite element methods for analysing geometrically imperfect cooling tower shells are presented. In the first the geometry of the imperfection is modelled by the elements; in the second the imperfection is represented by an equivalent load on the shell. Axisymmetric and general shell elements have been considered.Results are given which show that the first approximation to the equivalent load is sufficiently accurate and that it is possible to represent local imperfections by axisymmetric imperfections which require less computation. It is also shown that axisymmetric elements should be used wherever possible, because of their greater efficiency, following the geometry of an axisymmetric imperfection but representing local imperfections by equivalent loads.     

华能大厦单层柱面网壳的设计及分析

以某低矢跨比的单层柱面网壳分析与设计为例,分析该网壳在各种荷载作用下的受力特点;讨论网壳支承刚度对网壳的受力影响;介绍网壳的设计和节点构造方法;并着重研究网壳的整体稳定性。得出：低矢跨比单层柱面网壳的整体稳定对支承刚度和初始几何缺陷较敏感;考虑塑性影响后,低矢跨比柱面网壳的稳定承载力相对弹性稳定承载力有大幅度降低;不同...     

Der Einfluss von Imperfektionen in dünnwandigen geschweißten Rechteckquerschnitten unter Druckbeanspruchung

On imperfections in thin‐walled welded rectangular hollow section compressive members. This contribution presents the results of a research project analysing some aspects of stability failure of thin‐walled RHS compression members that are likely to exhibit combined global and local buckling. In particular the influence of various imperfections, namely residual stresses due to weld‐ing and local as well as global geometrical defects, on the load‐carrying capacity is subject to detailed experimental and numerical investigations. The insight into the structural behaviour leads to recommendations for standardized imperfections that should be used in the context of the numerical modelling of class‐4 square and rectangular hollow section members subjected to compression.     

板片结构稳定性分析的改进随机缺陷法

初始几何缺陷对板片结构体系稳定性的影响是板片结构计算和设计中的一个关键问题。提出一种考虑初始几何缺陷的改进随机缺陷法 ,它弥补了一般随机缺陷法人工计算量大的缺点 ,也回答了设计临界荷载和一致缺陷法得到的临界荷载的可靠性问题。实例为一试验模型 ,通过理想模型、一致缺陷法、改进随机缺陷法以及试验结果的对比 ,得出一些对板片结构体系设计和研究有益的结论。     

大矢跨比单层球面网壳动力试验模型弹塑性稳定分析

为了解水平地震作用下具有不同失效机制的单层球面网壳结构在静力荷载作用下的弹塑性稳定性能,利用有限元软件ANSYS,对两个矢跨比为1/2的单层球面网壳结构试验模型进行双重非线性全过程分析,获得结构的弹塑性极限承载力,比较二者的失稳模态,初步了解二者之间的差异。考察结构杆件屈曲、初始缺陷等因素对结构稳定性能的影响,并分析各因素对结构极限承载力的影响规律。结果表明,地震作用下,具有强度破坏特征的网壳结构在静力下的失稳模式表现为结构的整体失稳,而发生动力失稳破坏的结构则表现为局部失稳破坏。杆件失稳和初始缺陷使结构的临界荷载大幅度降低,且地震作用下属于强度破坏的单层球面网壳结构在静力下对初始缺陷的敏感性大于动力失稳破坏结构。     

Reliable and accurate prediction of the experimental buckling of thin-walled cylindrical shell under an axial load

Reliable and accurate method of the experimental buckling prediction of thin-walled cylindrical shell under an eccentric load is presented. The experimental arrangement and specimens are discussed in detail, including the measurement of the geometric imperfections of the specimen's surface using a coordinate measuring machine. Different FE models, in terms of complexity, are used to simulate the experiment arrangement in an attempt to get a good agreement with the experimental buckling loads and study the effect of measured initial geometric imperfections, load eccentricity, load eccentricity position along the shell's circumferential direction and different experimental arrangement that influence the boundary conditions. It has been demonstrated that FE models with simplified rigid support conditions overestimate the prediction of the experimental buckling load even though these models included the effects of the measured initial geometric imperfections and load eccentricity. By contrast, FE models with realistically modeled support conditions achieved the best result. The average deviation −1.59% from the experimental buckling loads was achieved using the FE model simulating the mounting devices as elastic bodies and with surface-to-surface contact interaction behavior on the support. The presented work also demonstrated the strong influence of the eccentric load position along the imperfect shell's circumferential direction on the buckling of the thin-walled shell.     

The design of perforated cold-formed steel sections subject to axial load and bending

The uprights in a typical pallet rack are typically singly-symmetrical cold-formed sections subject to axial load together with bending about both axes. They usually contain arrays of holes in order to enable beams to be clipped into position at heights that are not pre-determined prior to manufacture. Their slenderness is such that their behaviour may be influenced by the three generic forms of buckling, namely local, distortional and global (lateral torsional). In practice, these members have generally been designed on the basis of expensive test programmes. This paper addresses the problem of how they might be designed analytically. The basis of the investigation is a comprehensive set of test results on upright sections in compression which embraces both stub column tests, in which the load position was varied along the axis of symmetry, and longer columns. The test results were analysed using both finite elements and a version of “Generalized Beam Theory” (GBT) which incorporated systematic imperfections. Consideration was also given to the design procedures proposed by the “Federation Europeene de la Manutention” (FEM) and recent research into the influence of perforations on the performance of cold formed steel sections. It is shown that GBT can be modified to take account of perforations so that the lower bound results give a sufficiently accurate column design curve, which takes account of local, distortional and global buckling, thus making extensive testing unnecessary.     

Effects of geometric imperfections on stress distributions in cooling towers

The effect of geometric imperfections on the static stress distributions in cooling towers is investigated. The antisymmetric imperfections as well as the axisymmetric ones are assumed to be localized band imperfections at some height in a tower. Analyses are carried out for the self weight, seismic lateral load and wind load. Hoop stress and meridional bending moment are strongly influenced and the quantitative effects are summarized in simple figures.     

Collapse analysis of steel jacket structures for offshore oil exploitation

This work describes the formulation of finite-element based numerical methods for global nonlinear collapse analyses of three-dimensional steel framed structures. Particular emphasis is dedicated to the reassessment and determination of residual strength of steel jackets that support offshore oil exploitation platforms. Two main aspects are considered: (1) the formulation for a three-dimensional geometric and material nonlinear frame element, and (2) the implementation of specialized techniques for the solution of the nonlinear problem. The formulation of the element combines a co-rotational approach to represent geometric nonlinearities, providing an accurate treatment of finite rotations, with the plastic hinge approach to represent material nonlinearities. The stiffness reduction due to yielding is performed through a smooth degradation, following a parabolic function. Effects of strain hardening, geometric imperfections and residual stresses are modeled in an efficient manner. In order to determine the full nonlinear equilibrium path and allow the correct determination of the collapse load, the solution strategies consider specialized “continuation” techniques such as the Arc-Length and the Generalized Displacement Control methods. Case studies are presented in order to demonstrate the accuracy, efficiency, and suitability of the implemented methods and techniques.     

随机节点位置安装偏差与杆件偏心对单层球面网壳承载力的影响研究

单层球面网壳属于缺陷敏感性结构,其稳定承载能力受各种缺陷影响。为量化节点位置安装偏差缺陷、杆件对节点的偏心缺陷及其二者耦合作用对网壳稳定承载力的影响程度,对1000个随机产生的K6型单层球面网壳展开深入研究。首先提出了能够考虑随机节点安装偏差、随机杆件偏心的力学模型,然后阐述了两种随机缺陷在数值计算中的实现方法,最后获得了不同大小的节点安装偏差、杆件偏心距对单层网壳稳定承载力的影响程度与规律。计算结果表明：节点安装偏差对网壳极限荷载的影响更为显著,杆件偏心对极限荷载的影响相对较小;当节点安装偏差较小时,杆件偏心对网壳极限荷载的影响更为显著;节点安装偏差相同时,杆件偏心越大,网壳极限荷载越小。当最大节点安装偏差R1=2cm、最大杆件偏心R2=10mm时,缺陷网壳的极限荷载较理想网壳平均下降了10.94%;当R1=4cm、R2=10mm时,极限荷载平均下降了16.43%。     

Analysis of hyperbolic cooling towers with local imperfections

Two methods to analyse hyperbolic cooling towers with local imperfections are presented. One method relies on the finite element technique. For this a specialized finite-element program, which can model any arbitrary imperfections while retaining the advantage offered by the basically axisymmetric nature of the shell, was developed. The other method is an approximate procedure, which may be implemented with a purely axisymmetric analysis capability. The two methods are compared through numerical studies. A cooling tower shell with a bulge-type imperfection is examined under dead load and wind load conditions. It is concluded that the finite-element model presented is effective for the analysis of such shells, while the equivalent-load method may be adequate for some cases. Also, it is shown that both meridional and circumferential stress resultants may be radically influenced by a small bulge imperfection.     

Influence of geometric imperfections on the load capacity of orthotropic stiffened and composite shells of revolution with arbitrary meridians and boundary conditions

A stiffness matrix for an element of a shell of revolution has been derived, considering arbitrary load distributions and initial geometric imperfections. This element-stiffness matrix is based on the transfer-matrix method and describes the whole section of a shell of revolution between two rings in modal coordinates (a so-called super-element). The modal coordinates here are circumferential Fourier members, thus reducing the partial differential equations to ordinary ones.

Several stability analyses investigating the sensitivity of composite shells to different geometric imperfection shapes were carried out. The influence of the load distribution and boundary conditions in combination with geometric imperfections was analysed by different modellings of a hypothetical Jupe Avant shell of the ARIANE 5 rocket.