An investigation into non-linear interaction between buckling modes

This paper is a contribution to the understanding of the interaction between overall lateral-torsional buckling and local buckling of a beam under transverse loading. It concentrates on the case where the critical load for local buckling is smallest. Three approaches have been used: numerical analysis using the asymptotic theory; a qualitative analysis using an a priori simple discrete model; and experiments. The study suggests that just three modes in the asymptotic analysis are adequate to describe the interactive behaviour. The resulting reduced potential energy expression is quite similar to that of the a priori simple discrete model and provides insight into the destabilizing phenomenon. The experiments confirm these results.     

Global buckling and the interaction of initial imperfections of columns subjected to conservative loading

This paper deals with the problem of global instability of slender systems with imperfections. The inaccuracies in the systems are modelled assuming an initial curvature and the introduction of the eccentricity of an external load. Systems loaded by Euler’s load or by a force directed towards the positive pole are considered. The problem is formulated on the basis of an energetic method. Analysis of the global imperfections is carried out. The results of analytical, numerical and experimental research concerning the mutual relations between the introduced imperfections and their influence on the system behaviour are presented.     

Recommendations on imperfections in the design of plated structural elements of bridges

High-yield strength steel-plated structures represent competitive solutions when used in steel and steel–concrete composite bridges. Nevertheless, further modifications may still be introduced at the design stage in the case of slender sections, in order to minimize the number of their stiffeners and thereby economize on manufacturing costs. Eurocode 3 “Design of steel structures” specifies design methodologies for slender plates subjected to compression and for stiffeners. Moreover, the use of Finite Element Method (FEM) software is fast becoming an alternative analytical method for the design of complete structures or structural elements, as it offers a more realistic approach. This paper makes recommendations for FEM assessments of plated sections in bridges that take the initial imperfections, geometric imperfections and residual stresses of the sections into account, in order to arrive at realistic results.     

Regarding the buckling of pipelines subject to axial loading

The buckling of submarine pipelines subject to axial loading has received attention in the form of linearised study. Both vertical and lateral deflection modes have been analysed. This paper concentrates on two crucial factors which must be considered further before any formal non-linear predictive analyses can be meaningfully undertaken.     

The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures

Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability.     

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.     

Interaction of buckling modes in castellated steel beams

This paper investigates the behaviour of normal and high strength castellated steel beams under combined lateral torsional and distortional buckling modes. An efficient nonlinear 3D finite element model has been developed for the analysis of the beams. The initial geometric imperfection and material nonlinearities were carefully considered in the analysis. The nonlinear finite element model was verified against tests on castellated beams having different lengths and different cross-sections. Failure loads and interaction of buckling modes as well as load-lateral deflection curves of castellated steel beams were investigated in this study. An extensive parametric study was carried out using the finite element model to study the effects of the change in cross-section geometries, beam length and steel strength on the strength and buckling behaviour of castellated steel beams. The parametric study has shown that the presence of web distortional buckling causes a considerable decrease in the failure load of slender castellated steel beams. It is also shown that the use of high strength steel offers a considerable increase in the failure loads of less slender castellated steel beams. The failure loads predicted from the finite element model were compared with that predicted from Australian Standards for steel beams under lateral torsional buckling. It is shown that the Specification predictions are generally conservative for normal strength castellated steel beams failing by lateral torsional buckling, unconservative for castellated steel beams failing by web distortional buckling and quite conservative for high strength castellated steel beams failing by lateral torsional buckling.     

工程结构在多灾害耦合作用下的研究进展

我国地处亚欧板块、太平洋板块和印度洋板块之间,且疆域辽阔、海岸线绵长,这就自然形成了我国地震、强风和降雨等自然灾害频发。工程结构,包括高层建筑、村镇低矮房屋建筑群、输电塔线体系等生命线工程,在其全寿命周期内会遭受地震、强风和降雨等多种灾害的单独或同时作用。传统设计方法基于最不利荷载对结构进行设计,忽略了多种灾害耦合作用对结构全寿命周期抗灾性能的影响。文章总结了该课题组近年来在多灾害研究领域所取得的主要成果,包括：①根据中国强震台网中心和中国气象局数据中心提供的地震、风和降水数据,开展了极端事件单独作用和耦合作用的危险性分析;同时,提出了基于Copula函数的联合概率模型分析方法;②提出工程结构在多种灾害耦合作用下的性能评估和荷载修正系数计算方法;③开展了高层建筑在地震和强风单独作用以及同时作用下的风险分析及荷载修正系数计算;进行了村镇低矮房屋在地震和洪水耦合作用下的风险分析;对风雨耦合作用下的输电塔线体系进行了易损性分析。结果表明：①在考虑灾害发生概率时,不同灾害(例如,地震、强风和降雨)同时作用对结构性能评估具有显著影响;②由本文方法计算的荷载组合系数均不小于规范值,建议对现行规范中地震和风荷载的设计强度进行适当修正。因此,在对工程结构进行抗多灾耦合作用的性能分析和设计方法研究时,应综合考虑多种灾害的耦合效应。     

Creep buckling of thin-walled polymeric pipe linings subject to external groundwater pressure

Repair of deteriorated sewer pipes is now often undertaken by installing a tight fitting thin-walled polymeric lining inside the cracked/deformed host pipe. It is demonstrated that structural design of these systems is most appropriately focused on proving a suitable factor of safety against long term creep buckling of the lining subject to external groundwater pressure within the confines of the host pipe. A programme of research identifying the appropriate performance criteria is then described. Firstly a suitable means of defining the required long term constitutive behaviour is considered. Secondly a series of laboratory tests which enable system behaviour to be defined is described. Finally a finite element model is developed, capable of predicting the required time dependent, highly nonlinear, long term system behaviour, and which therefore provides a suitable basis for the development of appropriate design guidelines.     

Stresses and pressures in thin-walled structures with damage and imperfections

This paper is a sequel to a recent book of the author, in which stress concentrations and redistributions due to structural imperfections in thin-walled structures were reviewed. Here the emphasis is on other complementary aspects. Only shape damage and imperfections are considered in the paper, while intrinsic imperfections are out of the scope discussed. The mechanics of generation of damage is studied for several cases, including a relative in-plane displacement that induces an out-of-plane distortion; impact of an object on the structure; impact of the structure on a rigid surface; damage due to local buckling; and removal of part of the structure. Possible mechanisms that lead to the generation of imperfections include errors in construction; influence of misfits and misalignments; welding; and design-imperfections. Practical cases in which imperfections are measured and data banks of such information is also briefly reviewed. The field of mechanics of stress redistributions, and the modeling of distortional damage using numerical tools, are discussed with reference to previous publications by the author. New problems of changes in the pressures due to modifications in the shape are highlighted, with reference to the discharge of silos. Finally, several areas are identified in which future developments are expected for the next five to ten years.     

Finite element analysis and design of sandwich panels subject to local buckling effects

Past research into the local buckling behaviour of fully profiled sandwich panels has been based on polyurethane foams and thicker lower grade steels. The Australian sandwich panels use polystyrene foam and thinner and high strength steels, which are bonded together using separate adhesives. Therefore a research project on Australian sandwich panels was undertaken using experimental and finite element analyses. The experimental study on 50 foam-supported steel plate elements and associated finite element analyses produced a large database for sandwich panels subject to local buckling effects, but revealed the inadequacy of conventional effective width formulae for panels with slender plates. It confirmed that these design rules could not be extended to slender plates in their present form. In this research, experimental and numerical results were used to improve the design rules. This paper presents the details of experimental and finite element analyses, their results and the improved design rules.     

Design rules for lateral torsional buckling of channel sections subject to web loading

Bemessungsregeln für das Biegedrillknicken von U‐Querschnitten unter Belastung in Stegebene. In der Praxis kommen häufig U‐Querschnitte zum Einsatz. Eurocode 3 enthält jedoch keine Bemessungsregeln für exzentrisch, d.h. nicht im Schubmittelpunkt, belastete Träger mit U‐Querschnitt. In diesem Beitrag werden fünf Bemessungsvorschläge vorgestellt, erläutert und ihre Anwendbarkeit mit Hilfe von Finite‐Element‐Berechnungen überprüft. Die berechneten Tragfähigkeiten der Bemessungsmodelle werden mit Traglasten verglichen, die auf Grundlage von geometrisch und materiell nichtlinearen Berechnungen an Trägern mit Imperfektionen (GMNIA) ermittelt wurden. In der numerischen Parameterstudie werden die Querschnittsabmessungen, das Verhältnis von Spannweite zur Trägerhöhe, der Lasttyp und der Lastangriffspunkt variiert. Die Belastung wirkt jedoch lediglich in Stegebene. Basierend auf einem der bisherigen Bemessungsvorschläge wird im Rahmen dieser Untersuchung ein neuer Bemessungsvorschlag formuliert, der die Regelungen des Eurocode 3 widerspruchsfrei ergänzt.     

Life-cycle performance of structures subject to multiple deterioration mechanisms

This paper studies structural deterioration as a result of the combined action of progressive degradation (e.g., corrosion, fatigue) and sudden events (e.g., earthquakes). The structural condition at a given time is measured in terms of the system’s remaining life, which is defined in practice by an appropriate structural performance indicator (e.g., inter-story drift). Structural reliability is evaluated against prescribed design and operation thresholds that can be used to establish limit states or intervention policies. It is assumed that sudden events conform to a compound point process with shock sizes and interarrival times that are independent and identically distributed random variables. Progressive deterioration is initially modeled as a deterministic function. Randomness is later included also as a shock process with times between random deterioration jumps described by a suitable deterministic function. Structural performance with time is modeled as a regenerative process and an expression for the limiting average performance is obtained. The model is illustrated with some examples and compared with similar models showing the importance of including the damage history when studying the life-cycle performance of infrastructure systems.     

屈曲约束支撑与黏滞阻尼器的减震效果对比研究

以某钢筋混凝土框架结构工程实例为研究对象,选取与场地条件相匹配的地震动作为激励,在SAP2000程序中计算了该结构在多遇和罕遇地震作用下的非线性动力反应,并在框架结构模型中分别设置屈曲约束支撑和黏滞阻尼器。通过试算确定消能减震装置的参数,使得两种消能减震结构在多遇地震作用下的位移减震率均为40%。在此条件下,对比分析了结构的层间位移角、楼层加速度、基底剪力、柱轴力、塑性铰分布和各层阻尼器的工作状态。分析表明：在多遇地震作用下,屈曲约束支撑增大了结构的加速度响应,而黏滞阻尼器能够减小结构的加速度响应;在罕遇地震作用下,二者均能有效控制楼层的加速度响应,而屈曲约束支撑的位移减震效果更好,但黏滞阻尼器对框架柱内力的减少效果更为显著。     

Stochastic fatigue crack growth in steel structures subject to random loading

Uncertainty in fatigue crack growth under service load conditions arises from the statistical characteristics of crack growth under constant amplitude loading and from random variable amplitude loading. This study generalizes previous stochastic fatigue crack growth models by incorporating a time-dependent noise term described by arbitrary marginal distributions and autocorrelations to model the uncertainty in the crack growth under constant amplitude loading. A computationally efficient approach for handling wide-band random loadings based on the rainflow method of stress cycle identification also is developed. The method is illustrated with a fatigue reliability analysis of a steel miter gate at a lock and dam facility operated by the US Army Corps of Engineers.     

Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints

Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed inplane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behaviour with respect to fiber orientation changes significantly, in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behaviour has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally, determining the fiber orientations. The finite element method, coupled with an optimisation routine, is employed in analysing and optimising the laminates. Numerical results are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads.     

Survivability of steel frame structures subject to blast and fire

The lesson learned from the terrorist attacks on buildings is the need to assure structures’ ability to sustain local damage without total collapse. Some of the terrorist attacks take the form of blast followed by fire which may cause catastrophic failure of the structure. This paper presents a numerical model for analyzing steel frame structures subject to localized damage caused by blast load and subsequently investigating their survivability under fire attack. The proposed numerical method adopts a mixed-element approach for modeling large-scale framework and it is proven to be sufficiently accurate for capturing the detailed behaviour of member and frame instability associated with the effects of high-strain rate and fire temperature. Design implications related to the use of various numerical models for separate assessment of blast and fire resistance of steel structures and their components are discussed. Fire–blast interaction diagrams are generated to determine the fire resistance of columns considering the initial damage caused by the blast loads. A multi-storey steel building frame is analyzed so that the complex interaction effects of blast and fire can be understood and quantified. The frame is found to be vulnerable, as it possesses little fire resistance due to the deformation of key structural elements caused by the high blast load.     

Permanent deformations of rigid-plastic structures subject to random dynamic loads

The probabilistic analysis of the inelastic displacement response for simple rigid-plastic structures subject to dynamic loads is considered.The paper presents a method able to approximate the probability density function of the residual displacement at any time $\text{t}$. The procedure is based on the filtered Poisson process theory. This model aims to idealize the input stochastic process (i.e. the loading function) and to describe the output process (i.e. the residual displacement). The extension to elastic-perfectly plastic structures is immediate. Finally a numerical example is developed in order to show the computational aspects of the method.