Hybrid steel plate girders subjected to patch loading, Part 2: Design proposal

The resistance of plate girders subjected to patch loading has been studied thoroughly for the case of homogenous girders. The particular case of hybrid girders has been generally treated identically than for homogenous specimens. In this paper, the current EN1993-1-5 formulation is evaluated and some peculiarities concerning the treatment of hybrid girders subjected to patch loading are pinpointed. It is numerically demonstrated that the moment capacity of the flanges does not play any role in the resistance of plate girders to patch loading as predicted in EN1993-1-5. Accordingly, a design proposal which corrects the current EN1993-1-5 formulation is presented at the end of the paper.     

Transversally stiffened plate girders subjected to patch loading. Part 1. Preliminary study

In this paper, an experimental programme of six steel plate girders subjected to patch loading as well as results of forty eight numerically-tested prototypes are presented. Results of ultimate load capacity as well as structural responses from these girders are provided. In addition, experimental and numerical values of ultimate load capacity are compared with those predicted by EN1993-1–5. With such results, the response of transversally stiffened steel plate girders is discussed throughout the paper. Particular emphasis is given to the influence of the transverse stiffening on the ultimate load capacity of the girders. It is observed that girders with largely spaced transverse stiffeners present a considerably different response from girders with closely spaced transverse stiffeners. The structural response for the former case has been thoroughly studied in the last decades whereas little attention has been paid for the latter. Further analysis of this particular topic is provided in a companion paper.     

Hybrid steel plate girders subjected to patch loading, Part 1: Numerical study

Extensive research focused on the structural behavior of hybrid steel plate girders is nowadays available in the literature. Furthermore, extensive research devoted to the resistance of homogeneous girders to patch loading has been performed in the last decades. Investigations dealing simultaneously with both fields are, however, rather scarce. The driving force behind developing the present research work has been the aim of completing the knowledge of the patch loading field for the particular structural alternative of hybrid steel plate girder. In the current paper, experimental results found in the literature as well as additional numerical simulations developed by the authors are summarized. The results presented can be used for assessing the resistance of hybrid steel plate girders subjected to patch loading. An in-depth exploit of such results is presented in a companion paper.     

Finite element investigation of shear failure of lean duplex stainless steel plate girders

The use of duplex stainless steel material has gained popularity in the last two decades thanks to its nature that combines well the advantages of both austenitics and carbon steel materials. The duplex grades offer a combination of higher strength than austenitics in addition to a great majority of carbon steels with similar or superior corrosion resistance. However, high nickel prices have more recently led to a demand for lean duplexes with low nickel content, such as grade EN 1.4162. Wide-ranging work is needed to include the lean duplex grade EN 1.4162, into design standards such as EN 1993-1-4. Accordingly, a finite element modelling for full-size lean duplex stainless steel plate girders of non-rigid end stiffeners of Grade EN 1.4162 is presented in this paper. The paper is principally concerned with shear failure mechanism characteristics of this type of plate girders, which is not yet investigated. The ABAQUS 6.6 programme, as a finite element package, is used in the current work. The lean duplex stainless steel material is simulated here based on an accepted stainless steel material model available in the literature. A number of transversely stiffened I-section plate girders having equal depth of 1000 mm in span of 4 m is considered and parametric studies regarding flange width-to-web depth ratio, flange-to-web thickness ratio and web plate slenderness are carried out. However, new conclusions on shear strength of lean duplex stainless steel plate girders are presented.     

Moment–shear interaction of stiffened plate girders—Tests and numerical model verification

Results of four full-scale tests on plate girders stiffened with transverse and longitudinal stiffeners subjected to interaction of high bending moment and shear force are presented and discussed. In longitudinal direction the web was stiffened with open or closed stiffeners positioned in the compression zone. Detailed information on initial geometric imperfection and residual stresses is given. The experimental results were used to verify numerical model. The resistance is compared against reduced stress method and effective width method given in EN 1993-1-5.     

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.     

剪切作用下锥形板梁的试验和数值研究

对剪切作用下的锥形钢板梁进行了试验和数值研究。试验包含4个缩尺锥形钢板梁试件,主要研究其临界剪切荷载和极限抗剪强度。此外,研究了锥形板的后屈曲特性。另外,对不同几何形状的锥形板进行了参数研究,以找到最有利的设计方案。分析的参数有:板的高宽比、翼缘的倾斜角、腹板和翼缘的长细比。由于性能的不同,对4种类型的锥形板梁分别进行建模和数值模拟。欧洲规范EN1993-1-5给出的锥形板的简化方法证实,在某些情况下,估计的极限剪切强度偏于不安全,需要进行修改。     

U型加劲肋加固的高强钢面板体系的面内极限抗压强度

通过非线性有限元分析(FEA)研究使用U型加固件纵向加劲的面板的极限抗压强度。对112个由各种细长参数的面板和柱以及加固件组成的模型进行分析。模型包括了普通钢材和高强钢的弹塑性应变硬化本构关系。有限元分析中也包括了初始几何缺陷和残余应力。将有限元分析得出的结果与欧洲规范3EN1993-1-5、FHWA-TS-80–205和其他可用公式计算出的强度进行比较。基于分析结果,可得出一个针对使用普通钢材或高强钢(HPS)加劲板系统的新的强度预测公式。结果表明:当柱的长细比较大时,使用欧盟规范3EN1993-1-5和FHWA-TS-80–205可能导致设计过于保守;而采用所提出简化形式的公式可更精确地预测强度,从而得出更经济的设计。     

波浪腹板工形梁局部承压承载力设计方法研究

波浪腹板工形梁的局部承压性能目前国内外研究较少。在总结前人对平腹板和梯形波折腹板梁局部承压极限承载力研究工作的基础上,对波浪腹板工形梁的局部承压性能及设计方法进行研究。通过有限元数值分析,揭示波浪腹板工形梁在局部压力作用下的破坏形式以及腹板几何初始缺陷对局部承压性能的影响,在几何参数分析的基础上建立局部承压极限承载力的简化计算公式。最后针对同时承受局部荷载和弯矩的波浪腹板工形梁,建立截面弯矩与局部压力之间的M-P承载力相关计算公式,并通过有限元数值计算进行验证。     

Behavior of beam web panel under opposite patch loading

Elastic buckling is studied for a panel with various boundary conditions including simple supports, fixed supports and elastic restraints. The panel is subjected to opposite patch loading. Following a review of existing work on the effects of localized compression, also known as patch loading, a study is conducted to take into account the restraints provided by the flanges of the I beam in a realistic manner. This study is based on a finite element model implemented in the CAST3M software. A new equation is proposed to calculate the buckling critical coefficient for a beam web panel considering the rotational stiffness provided by the flanges. The model is then applied to longitudinally stiffened web panels which are subjected to opposite patch loading.A parametric analysis is performed to determine the transition from a global buckling mode to a local buckling mode where the sub-panels on each side of the stiffener behave separately. The numerical results show that the flexural rigidity of the stiffener is the appropriate parameter that governs the buckling mode. From these results, a formula is proposed to calculate the buckling critical coefficient of stiffened web panels.     

Design of composite hybrid plate girder bridges based on reliability and optimization

A practical and efficient reliability-based optimization approach to the design of both unstiffened and stiffened composite hybrid plate girders for highway bridges is presented. The steel weight of the built up plate girder is adopted as the objective to be minimized and all constraints specified in the AASHTO bridge code are considered in the optimization process. The solution is obtained by coupling an optimization program with a reliability analysis program. Numerical examples illustrate the application of the approach to reliability-based optimum design of unstiffened and stiffened composite plate girders. Sensitivity analyses are also performed for finding the rates of change of the optimum solution with respect to changes in problem preassigned parameters.     

Structural Health Monitoring in Incrementally Launched Steel Bridges: Patch Loading Phenomena Modeling

In this paper, a realistic nonlinear 3D simulation of an incrementally launched steel bridge girder is presented. The numerical simulation accounts for three sources of nonlinearity: geometry, material and boundary conditions. For the sake of depicting the capabilities of the presented numerical model in structural verifications, the study is focused on the patch loading field, a structurally complex phenomenon. Patch loading (or concentrated loading) is one of the most typically encountered structural verifications on incrementally launched steel I-girders. The presented realistic simulation is based upon an experimentally calibrated numerical model and may provide relevant information at both design and construction stages. For the former, the predictive capabilities of the model for inferring the potential failure due to patch loading are depicted. For the latter, the results obtained are displayed in a way that may be useful for planning a Structural Health Monitoring (SHM) deployment aimed at controlling the patch loading-related phenomena in incrementally launched steel plate girders.     

Strength of I-girders with Delta stiffeners subjected to eccentric patch loading

In this paper the effects of Delta stiffeners on strength and behavior of I-girders subjected to eccentric patch loading has been investigated. To achieve the objectives extensive computer work has been carried out using the finite element method. The beams considered here had different geometry and stiffeners arrangement. The reliability of the numerical models and results are confirmed by comparison with experimental results which show good agreement. Furthermore, the results indicate that numerical models can be used to analysis different I-girders with different stiffeners. The results also show that Delta stiffeners are more efficient than other stiffeners, especially in the case of eccentric patch loading; also the capacity of critical patch loading of I-girders increases by about 95 percent compared to the other stiffened girder.     

竖向加劲钢板剪力墙门槛刚度研究

为研究设置竖向加劲肋的钢板剪力墙的弹性屈曲性能,采用有限元法对竖向加劲钢板剪力墙弹性屈曲性能进行研究,分析加劲肋的刚度、加劲数量和钢板高宽比等因素的影响。研究表明:设置竖向加劲能有效提高钢板墙剪切临界应力,钢板高宽比、加劲肋数目和加劲肋抗弯刚度均对钢板剪力墙屈曲系数有较大影响。提出加劲肋门槛刚度的判定标准和计算公式,该判定标准考虑了加劲肋扭转刚度的影响。与有限元结果的比较表明,具有较好的精度,且明显优于文献结果。     

Shear buckling resistance of steel and aluminium plate girders

During the development of Eurocode 9 for aluminium alloy structures a number of design methods for the shear buckling resistance of plate girders were appraised, by comparison with experimental data. Among studied methods the so-called rotated stress field method [Höglund, T., Design of thin plate I girders in shear and bending with special reference to web buckling. Royal Institute of Technology, Department of Building Statics & Structural Engineering, Stockholm, 1972], with some modifications, was found to give the best agreement with 366 tests on steel plate girders as well as 93 tests on aluminium alloy plate girders in shear. The method is simple to use and is applicable to unstiffened, transversally and longitudinally stiffened and trapezoidally corrugated webs. This paper presents the rotated stress field method and summarizes the result of the comparisons, including the design methods in Eurocode 3, Part 1.1, version April 1992, for steel plate girders. The rotated stress field method is also adopted in Eurocode 3, Part 1.5: plated structures, draft July 1996.     

小片荷载偏心作用下具有三角加劲肋的Ⅰ型梁的强度分析

分析了三角加劲肋对小片荷载偏心作用下Ⅰ型梁强度和性能的影响作用。运用有限元分析方法对具有多种几何尺寸以及不同的加劲肋分布位置的梁进行了大量计算。经与试验结果进行对比,确认了数值模型及其计算结果的有限性。此外,结果显示:该数值模型可用于分析具有不同加劲肋的各种Ⅰ型梁;三角加劲肋比其他类型的加劲肋更为有效,尤其在小片荷载偏心作用下;同时相比于其他加劲肋,采用三角加劲肋的梁的临界小片荷载承载力上升了近95%。     

Parametric analysis of the lateral–torsional buckling resistance of steel beams in case of fire

Numerical modelling of the lateral–torsional buckling of steel beams at elevated temperature has shown that the beam design curve from EN 1993-1-2 is over-conservative in the case of non-uniform bending. Based on the newly proposed methodology for cold design from the EN 1993-1-1, an improved proposal for the lateral–torsional buckling of unrestrained steel beams subjected to fire is presented in this paper that addresses the issue of the influence of the loading type, the steel grade, the pattern of the residual stresses (hot-rolled or welded sections) and the ratio h/b, between the depth h and the width b of the cross-section on the resistance of the beam, achieving better agreement with the numerical behaviour while maintaining safety. The proposal is found to be safe and accurate through an extensive comparison with the results of FEM numerical simulations of more than 5000 beams. A statistical study of the results is performed, showing the accuracy of the improved proposal presented in this paper.     

Interactive Optimization of Multispan Plate Girders

An efficient and robust optimization algorithm is presented for minimum weight disign of continous multispan steel plate girders using the general geometric programming technique. The loading on the girder can consist of any number of concentrated and uniformly distributed loads. The nonlinear programming problem is formulated on the basis of the last edition of the American Institue of Steel Construction (AISC) specification. The desing variables are the flange width and thickness, teh web depth and thickness, and the dimensions and spacings of the transverse stiffeners for stiffened plate girders. In the optimization algorithm, the nonlinear primal problem is transformed to and via double condesation. The algorithm is quite general and can be applied to stiffened of unstiffened, homogeneous or hybird plate girders. The girder may be fully restrained agained lateral torsional buckling or may haae lateral supports only at selected locations along the length ofthe girder. The algorithm id implemented in FORTRAN 77 in an interactive computing environment with graphic capabilities. The grogram can display the plate girder elevtion, various cross sections, and loading on the girder. Three examples are presented, a two-span homogeneous, a three-span hybird, and a five-span homogeneous plate girder.     

Investigation on the Collapse Behavior of Diagonal Stiffened Composite Plate Girders Subjected to Shear Loading

In this study, a new analytical method is presented to estimate the shear capacity of diagonally stiffened steel–concrete composite plate girders. This method is formulated based on tension field action in steel girder web and failure mechanism of concrete slab deck. To validate the accuracy of the proposed method, the obtained results are compared with three-dimensional finite element analysis of composite plate girders with different configuration of stiffeners. The results of analytical and numerical investigations indicate that the proposed method can accurately estimate the ultimate shear capacity of composite plate girders. In addition, it is shown that the diagonal stiffeners on one hand can reduce the buckling effects of shear panel of girders and on the other hand can increase the strength of elastic shear buckling and ultimate shear capacity of girders well in comparison with the unstiffened thin steel plate girders.