直接分析设计法中的受压构件等效初始缺陷研究

在GB 50017—2017《钢结构设计标准》中，仅对考虑材料弹性阶段的直接分析设计法中的构件初始缺陷取值作出了规定，对考虑材料弹塑性发展的直接分析设计法中未给出构件初始缺陷取值的具体数值。为此，基于钢结构塑性稳定理论，利用轴心受压构件稳定系数反向推导其等效初始缺陷，包括初始几何缺陷和残余应力。根据不同的截面类型和钢材牌号，给出受压构件不同的等效初始缺陷，使直接分析设计方法能够真正地应用于实际工程中。利用直接分析设计软件NIDA，建立带有初始缺陷的弯曲单元，模拟受压构件的等效初始缺陷，得到构件的稳定承载力系数，并与轴压构件稳定系数φ进行对比分析，验证了构件等效初始缺陷取值的正确性。     

Sensitivity analysis of stability problems of steel plane frames

The objective of the paper is to analyse the influence of initial imperfections on the load-carrying capacity of a single storey steel plane frame comprised of two columns loaded in compression. The influence of the variance of initial imperfections on the variance of the load-carrying capacity was calculated by means of Sobol’ sensitivity analysis. Monte Carlo based procedures were used for computing full sets of first order and second order sensitivity indices of the model. The geometrical nonlinear finite element solution, which provides numerical results per run, was employed. The mutual dependence of sensitivity indices and column non-dimensional slenderness is analysed. The derivation of the statistical characteristics of system imperfections of the initial inclination of columns is described in the introduction of the present work. Material and geometrical characteristics of hot-rolled IPE members were considered to be random quantities with histograms obtained from experiments. The Sobol sensitivity analysis is used to identify the crucial input random imperfections and their higher order interaction effects.     

Sensitivity analysis of steel plane frames with initial imperfections

The article presents the sensitivity and statistical analyses of the load-carrying capacity of a steel portal frame. It elaborates a typical stability problem of a system comprising two single-storey columns loaded in compression. The elements of this system mutually influence each other, and this fact, in conjunction with the random imperfections, influences the load-carrying capacity variance. This mutual interaction is analysed using the Sobol’ sensitivity analysis. The Sobol’ sensitivity analysis is applied to identify the dominant input random imperfections and their higher order interaction effects on the load-carrying capacity. Majority of imperfections were considered according to the results of experimental research. Realizations of initial imperfections were simulated applying the Latin Hypercube Sampling method. The geometrical nonlinear solution providing numerical result per run was employed. The frame was meshed using beam elements. The columns of the plane frame are considered with two variants of boundary conditions. The dependence between mean and design load-carrying capacities and column non-dimensional slenderness is analysed.     

带初始缺陷的平面钢框架的敏感性分析

给出一个门式刚架承载力的敏感性和统计性分析。阐述了包括2个单层受压柱系统的典型稳定性问题,这个系统的要素相互影响,并且结合随机的不完善性,将影响承载力。采用Sobol敏感性分析法研究相互影响的因素。Sobol敏感性分析法应用于区别主要输入的随机缺陷和它们的高阶互动效应对承载力的影响。根据试验结果,考虑了大部分缺陷。采用拉丁超立方抽样方法,实现了对初始缺陷的模拟。几何非线性解决方案提供了数值解。采用梁单元对框架实现网格划分。平面钢框架的柱分别考虑采用2种边界条件。分析了承载力设计值与柱长度系数之间的关系。     

杆件初始缺陷对单层凯威特球面网壳地震响应影响研究

为研究杆件初始缺陷对单层凯威特球面网壳地震响应的影响,利用OpenSEES有限元程序,采用多段梁法模拟杆件初始缺陷,给出了OpenSEES模拟空间网格结构圆管杆件滞回的多段梁法建模参数合理取值,基于GB 50017—2003《钢结构设计规范》中压杆稳定系数拟合了圆管等效偏心率和正则化长细比的关系式。考虑杆件初弯曲方向随机分布,建立了不同参数单层凯威特球面网壳模型,对网壳增量动力分析的最大位移进行了比较。结果表明：当网壳处于弹性状态时,杆件缺陷对其地震响应的影响可以忽略;当网壳进入塑性状态后,杆件缺陷对其地震响应的影响不可忽略,不同杆件初弯曲方向的网壳地震响应离散程度随地震动强度提高基本呈增大趋势;地震动强度较大时,考虑杆件缺陷和结构整体缺陷的单层网壳地震响应和仅考虑整体缺陷的单层网壳地震响应差异较大,两者最大位移的相对大小并无规律性,其关键影响因素为地震作用下塑性杆件分布的离散程度。     

援巴布亚新几内亚国际会议中心玻璃采光顶整体稳定性和节点应力分析

援巴布亚新几内亚国际会议中心玻璃采光顶为圆形,跨度32m,结构为内外钢环与连系钢梁组成的空间结构。此结构受力特点类似扁壳,存在整体稳定性问题。文章利用有限元软件ABAQUS对其做了整体稳定性分析,对承受复杂应力的连接节点做了应力状态分析。分析结果表明:结构第二阶失稳模态为可能失稳模态其对应的线性屈曲特征值为8.67;全跨活荷布置下最大缺陷为跨度1/300的缺陷结构的失稳加载系数为4.0,其为线性特征值的46%。结构整体稳定承载力对初始缺陷不敏感。节点应力分析得到连接节点的材料处于弹性状态,节点是安全的。     

Imperfection sensitivity of plate girder webs subjected to patch loading

This paper is aimed at studying the influence of initial geometric imperfections on the postbuckling behavior of longitudinally stiffened plate girder webs subjected to patch loading. A sensitivity analysis is conducted herein using two approaches (deterministic and probabilistic) in order to investigate the effect of varying imperfection shape and amplitude on both, the postbuckling response and ultimate strength of plate girders under patch loading. This sensitivity analysis is performed by means of nonlinear finite element analysis. At first, the initial shape imperfections are modeled using the buckling mode shapes resulting from an eigenvalue buckling analysis. Thereafter, the amplitude of the buckling shapes for the various modes is varied, and then introduced in the nonlinear analysis. The results show the influence of these modes and amplitudes on the resistance to patch loading.     

Semi-empirical design of complex metal beams by buckling analysis

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry–Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams.     

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.     

竖向荷载作用下柱列支撑体系受力性能试验研究及有限元分析

为研究柱列支撑体系的受力性能和验证有限元方法分析该问题的可靠性,对带有不同初始几何缺陷分布的单层和双层柱列支撑体系进行静力模型试验研究。研究结果表明:由于试验模型中柱和水平撑杆的初始几何缺陷的随机分布,水平撑杆受压力或拉力也是随机的;双层柱列支撑体系的极限承载力高于单层柱列支撑体系的极限承载力,且双层柱列支撑体系中的水平撑杆减小柱的计算长度超过柱高的一半;柱列支撑体系的失稳破坏是由于单柱失稳破坏引发的。采用有限元模型对试验进行了模拟验证,计算结果与试验结果吻合良好。     

初始几何缺陷对大跨度钢桁架吊装稳定性影响

利用大型通用有限元软件ANSYS对大跨度钢桁架吊装过程建立了有限元模型,研究了初始几何缺陷对大跨度钢桁架吊装的稳定性影响。结果表明,在两吊点方案中容易发生屈曲的位置为跨中上弦杆部分,而四吊点方案在吊装过程中跨中下弦杆部分较易发生平面外失稳。     

考虑结构缺陷敏感性影响的单层空间网格结构形态优化研究

自由曲面单层空间网格结构以总应变能为优化目标时,优化后的结构以轴向应变能为主而弯曲应变能极小,结构承载能力较高;但在考虑初始几何缺陷影响后,其承载力会大幅下降,结构对初始几何缺陷异常敏感,经过形态优化后的结构实际承载力并不高。为此,提出以结构弯曲应变能比例作为约束条件的单层网格结构形态优化方法。该方法通过控制优化终止时结构内部弯曲应变能比例,调节结构弯曲应变能和总应变能比例关系,降低优化后结构对初始几何缺陷的敏感性,可得到考虑初始几何缺陷后仍具有较高承载力的结构形态。自由曲面单层空间网格结构数值算例表明,优化后结构在考虑初始几何缺陷后,其承载力相比传统优化方法有较大提高,证明了所提方法的可行性。     

Assessment of the ultimate strength of narrow stiffened panel test specimens

The ultimate strength of five narrow stiffened panels tested with two stiffeners under axial compression until collapse and beyond is determined by finite element analysis, and is compared with experimental results. Models with two half bays plus one full bays in the longitudinal direction are used in the finite element analysis. The material properties used in the finite element analysis have been evaluated by tensile tests. The initial geometrical imperfections also affect significantly the collapse behavior of the stiffened panels. Hence, the initial imperfections of the stiffened plates were measured before the experiment. The results of the FE analysis with measured and with equivalent initial imperfections are compared and conclusions are derived about the possible bias of the results when the initial imperfections are not measured.     

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.     

随机缺陷场对网壳结构性能影响的研究

施工误差、杆件的初偏差等不可控制因素必然导致网壳结构具有一定的初始缺陷.初始缺陷及其随机性是影响结构稳定和承载力的重要因素.基于标准正交基的随机场展开法为理论基础,通过对随机初始缺陷相关结构的分解将其投影在结构屈曲模态正交基上.算例表明,本方法可以用较少的随机变量描述原随机缺陷场,从而全面高效地寻求初始缺陷的最不利分布形式,保证缺陷敏感性结构具有较高的安全可靠性,适用于大型工程结构的随机缺陷分析.     

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.     

锈蚀箱梁极限强度试验中板变形量的分析

根据垂直弯曲荷载下3个锈蚀箱梁板的压应力试验结果,分析初始和倒塌后的板变形量。研究初始缺陷和腐蚀对倒塌后最终变形的影响,得出不同的荷载响应、初始缺陷和板高厚比之间的关系。分析初始缺陷、板高厚比和倒塌后最终变形,建立高厚比准则以计算倒塌后变形。     

Analysis of plate deflections during ultimate strength experiments of corroded box girders

The objective of this work is to analyze the initial and post-collapse plate deflections based on measurement records of the experiments of three corroded box girders subjected to pure vertical bending loading inducing a compressive stress on deck. The effect of initial imperfections and corrosion degradation on the final post-collapse deformation shape has been investigated and a relationship between different loading responses, shape of initial imperfections and plate slenderness has been derived. Analyzing initial imperfections, plate slenderness and final post-collapse deformations, a slenderness criterion has been established to predict the post-collapse deformation shape.     

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.     

火灾下凯威特单层球面网壳非线性分析

以凯威特K6型单层球面网壳为分析对象,采用火灾动力模拟软件FDS模拟大空间火灾温度场,利用有限元软件ANSYS进行火灾下结构的非线性分析,研究网壳结构在火灾高温下的极限荷载、结构的缺陷敏感性及失稳模态的影响因素和变化规律。结果表明,火灾中的网壳结构在升温初期以热膨胀为主,极限荷载增大,而后随着温度的升高,材料软化,极限荷载迅速降低;矢跨比、火源位置、支承条件及初始缺陷对火灾下网壳结构极限荷载的影响有较好的规律性;升温对网壳结构缺陷敏感性的影响与温度场分布有关;失稳模态在火灾迅速升温阶段会发生根本性的变化。