Experimental and Numerical Study on Buckling Behavior of a Rigidly Stiffened Plate with Tee Ribs

In the bridge structures, stiffened plates are usually designed as rigidly stiffened when the orthotropic steel box girder is used as the main load-bearing structure. Therefore, the buckling mode of stiffened plates is plate buckling which occurs in subpanel supported by stiffeners. The orthotropic steel box girder is used as the main girder for Egongyan Rail Special Bridge, which is a self-anchored suspension bridge. Plates of the steel girder are rigidly stiffened with unequal spacing open ribs, and the most slender stiffened plate is the mid web stiffened with Tee ribs. In order to ensure the safety of the bridge, the buckling behavior of the web and orthotropic steel box girder under axial compression, including ultimate strength, post-buckling behavior and failure modes, should be clearly investigated by experimental and numerical methods. The design, loading and testing methods of the 1:4 scale model of the orthotropic steel box girder are introduced in detail firstly. The orthotropic steel box girder and the stiffened web finite element (FE) models are validated by the test results, and the effects of residual stress and the magnitude of geometric imperfections are discussed roughly. Based on the validated web FE model, a detailed parametric study is performed to systematically investigate the effects of residual stress and geometric imperfections on buckling behavior of the web. The effect of shapes of geometric imperfections discussed is highlighted. Through tracing stress states, the failure modes of stiffened plate are in agreement with the experimental phenomenon to some extent. Results show that shapes of geometric imperfections have significantly influenced post-buckling behavior and failure modes of the web, but slightly affected the ultimate strength. It is advised that residual stress and geometric imperfections should be controlled to make full use of excellent performance of steel materials.     

关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.     

Iterative Fourier decomposition of imperfection measurements at non-uniformly distributed sampling points

Buckling of cylindrical shells subject to axial compression is acutely sensitive to the form and amplitude of geometric imperfections present in the structure. As a result, many attempts have been made to measure geometric imperfections in cylindrical shells both in laboratory specimens and less frequently in full-scale structures. The imperfections are generally interpreted using the well-known method of Fourier decomposition, so that the different components of imperfections can be more easily related to structural features such as positions of welds and their effects on buckling strength better understood. A common situation in imperfection measurements on full-scale shell structures is that some parts of the structure are not accessible, due to the presence of accessories such as service ladders and pipes. As a result, a measurement grid with non-uniform intervals is generally employed in imperfection surveys on full-scale structures. This paper first shows that when results from such surveys are interpreted using the traditional Fourier decomposition method, the resulting Fourier series cannot provide an accurate representation of the discrete measurement data due to the non-uniform distribution of sampling points. The paper then presents an iterative Fourier decomposition method which overcomes this problem. The theoretical background of the proposed method is detailed, followed by a numerical demonstration of the effectiveness of the method.     

On the modelling of different types of imperfections in silo shells

The assessment of imperfections is most important for determining the load-bearing capacity of a thin-walled shell structure. Different ways of modelling imperfections are discussed in this paper and steel silo shells are used as an application. Buckling tests were performed on different types of model shell - standard quality and high quality with reduced heat input during welding. For the numerical studies two different approaches were used as well: an axisymmetric approach with substitute geometric imperfections and an FEM approach, where the nodal coordinates were derived from surveying the specimen. It was found that there is considerable gain in the buckling strength due to the presence of the granular solid. The larger the initial imperfections in the shell the greater the gain in strength compared to the empty cylinder. The modelling of the uneveness of the edges with uneven dead loading is also discussed.     

Flexural strength of tubular flange girders

A tubular flange girder is an I-shaped steel girder with either rectangular or round tubes as flanges. A tubular flange girder has a much larger torsional stiffness than a conventional I-shaped plate girder of similar weight, which results in a much larger lateral-torsional buckling strength. Finite element (FE) models of tubular flange girders with hollow tubes (HTFGs) are developed in this paper, considering material inelasticity, instability, initial geometric imperfections, and residual stresses. A parametric study is performed using the FE models to study the effects of stiffeners, geometric imperfections, residual stresses, cross section dimensions, and bending moment distribution on the lateral-torsional buckling flexural strength of HTFGs. These analytical results are used to evaluate formulas for determining the flexural strength of HTFGs.     

Numerical modelling of steel plate girders at normal and elevated temperatures

The main goal of this study is to increase the knowledge on the behaviour of steel plate girders subjected to shear buckling at both normal and elevated temperatures. Hence, numerical models were duly validated with experimental tests from the literature. Experimental tests on steel plate girders with different configurations were numerically reproduced, showing a good agreement between numerical and experimental results. Afterwards, applying the validated numerical models, sensitivity analyses on the influence of initial imperfections were performed. Different values for the maximum amplitude of geometric imperfections were considered and residual stresses were also taken into account. Finally, the effect of the end supports configuration was also studied aiming to understand the strength enhancement given by the rigid end support at normal temperature and evaluating if that strength enhancement is maintained in case of fire.     

Degradation of the compression strength of square plates due to initial deflection

The influence of initial deflections on collapse strength of thin square plates in uniaxial in-plane compression is studied emphasising an integral energy measure of the imperfections. In calculations of the plate strength, measured data on distortions of stiffened plating in ships as well as buckling modes, compound and localised shapes are considered. The strength values are compared normalising the initial deflections by the energy measure or by the commonly employed amplitude to thickness ratio. The paper extends the previous study on strength of rectangular plates [Sadovský Z, Teixeira AP, Guedes Soares C. Degradation of the compression strength of rectangular plates due to initial deflection. Thin-Walled Structures 2005;43:65-82].     

The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.     

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam-column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.     

Konsistente geometrische Ersatzimperfektionen für den numerisch gestützten Beulsicherheitsnachweis axial gedrückter Schalen

Consistent equivalent geometric imperfections for the numerical buckling strength verification of axially compressed shells. A geometrically and materially nonlinear analysis with imperfections included (GMNIA) is the most sophisticated and perspective the most accurate method of a numerical buckling strength verification of steel shell structures. By this way, equivalent geometric imperfections, which have to cover the influence of all deviations from the nominal dates of the resistance parameters, are fundamental. The problems resulting from this aim are discussed in the paper. The Eurocode gives hints regarding the application of equivalent imperfections and makes statements about their amplitudes, which are to be adopted. It is shown, that the current regulation doesn't cover all relevant parameters with respect to the load bearing capacity. This way, inconsistencies between numerically and experimentally determined buckling resistances arise for several geometries. Modifications are suggested for the basic buckling case of the axially compressed shell to succeed in consistent equivalent geometric imperfections.     

FEM‐Untersuchung zur Beurteilung des Einflusses von geometrischen Imperfektionen auf die Lebensdauer von Schraubenverbindungen bei Windkraftanlagen

FEM‐Investigation to evaluate the influence of geometric imperfections on fatigue of preloaded bolt connections of Wind Energy Converters. There is a strong influence on fatigue of preloaded bolted ring flange connections with geometric imperfections, as they are used for tubular steel towers of wind turbines. This can result in fatigue failure of the connections because the bolts could not take the high dynamic loads sufficiently. This paper is dealing with the results of [1] in which the influence on fatigue of variing geometric imperfections at L‐flanges was investigated numerically. The results of this thesis paper lead to a gener criteria, which can be very useful in order to rate geometric imperfections, as they appear in production line. It should be used to sensitize manufactorers and quality responsible staff in reason of allowable tolerances in the assembly process of windturbine towers.     

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.     

Nonlinear analysis of concrete-filled square stainless steel stub columns under axial compression

Concrete-filled stainless steel tubes (CFSST) can be considered as a new and innovative kind of composite construction technique, and have the potential to be used extensively in civil engineering. This paper employs a nonlinear analysis of square CFSST stub columns under axial compression. A three-dimensional nonlinear finite element (FE) model is developed using ABAQUS, where nonlinear material behaviour, enhanced strength corner properties of steel, and initial geometric imperfections are included. Close agreement is achieved between the test and FE results in terms of load-deformation response and ultimate strength. In light of the numerical results, the behaviour of stainless steel composite columns is compared with that of carbon steel composite columns. A simple model is proposed to calculate the ultimate strength of square CFSST stub columns.     

Q460高强度钢材焊接H形截面弱轴压弯柱承载力试验研究

为了研究高强度钢材中厚板焊接H形截面压弯柱的承载力,采用国产Q460高强度钢材11 mm、21 mm中厚板制作了6个焊接H形截面压弯柱,试件截面自由外伸翼缘板宽厚比分别为7、5、3,长细比分别为40、55、80。通过对Q460低合金高强度钢材的材性测试、3种焊接截面残余应力测试、各试件初始几何缺陷测量及承载力试验,进行了H形截面弱轴压弯构件整体失稳承载力的试验研究,并与采用GB 50017-2003《钢结构设计规范》进行计算的承载力对比;同时以理想弹塑性模型,综合考虑试件初始缺陷建立有限元模型,分析计算其承载力。试验及分析结果表明：Q460低合金高强度钢材具有强度高、塑性性能较好等特点;由实测截面残余应力值得到其分布形式与普通钢材焊接H形截面残余应力分布基本相同;高强度钢材焊接H形截面压弯构件承载力试验值明显高于GB 50017-2003设计公式计算值;文中采用的有限元分析方法可以较准确地计算试件的承载力。研究成果为高强度钢材在实际工程中的应用提供试验参考。     

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。     

初始几何缺陷对钢框架柱性能的影响(Ⅱ):参数分析

在钢框架二阶弹性分析中,结构整体初始几何缺陷和构件的初始几何缺陷是实际存在的,其影响不可忽略。通过平面子结构理论模型进行参数分析,结果证明,对于弱支撑钢框架柱,结构的整体几何缺陷和构件几何缺陷对弯矩的影响均可以等效为作用于楼层处的假想水平力,假想水平力是作用于该楼层的竖向荷载的函数。     

Shear strength of trapezoidal corrugated steel webs

Shear strength of trapezoidal corrugated steel webs is an important issue for the design of box girder bridges with trapezoidal corrugated steel webs. Eight H-shape steel girders with trapezoidal corrugated webs are firstly tested to investigate the shear behavior of webs. An extensive parametric study based on the linear elastic buckling analysis is then conducted to derive the simplified formula for calculating the elastic shear buckling strength of trapezoidal corrugated steel webs considering three different shear buckling modes. The proposed formula can give more satisfactory results for predicting the elastic shear buckling strength than some available formulae provided in the literature when compared with the numerical results. Furthermore, the nonlinear buckling analysis is conducted to intensively investigate the shear strength associated with initial geometric imperfections, and the formulae of the shear strength are proposed. Good agreements can be observed between the results calculated using the proposed prediction formula in this paper and the experimental results, and a design formula is also recommended for the routine shear design of trapezoidal corrugated steel webs.     

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.     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

初始几何缺陷对钢框架柱性能的影响(Ⅰ):理论模型

在钢框架二阶弹性分析中,结构整体初始几何缺陷和构件的初始几何缺陷是实际存在的,其影响不可忽略。因此在由单根柱和梁组成的平面子结构二阶弹性理论模型中,引入以上两种几何缺陷,得出了位移与内力的计算公式。利用该理论模型,可以考虑各参数对框架柱二阶效应的影响,并能系统分析框架结构整体几何缺陷与构件几何缺陷对二阶弹性弯矩的影响。