Analysis of plate girders with perforated webs

A simple finite element formulation is proposed for studying the pattern of the membrane tension bands developed in the post-critical stages, when a plate girder with web openings is subjected to predominant shear loading. A modified version of Von Mises' criterion is used to simplify the computational process. These studies validate the equilibrium solutions proposed earlier by the authors. Comparisons of predicted ultimate loads by this theoretical treatment with the corresponding experimentally observed loads show that the predictions are marginally conservative and are therefore safe.     

Shear capacity of plate girders with trapezoidally corrugated webs

In this paper, the shear capacity of plate girders with trapezoidally corrugated webs is numerically studied using a non-linear finite element method. Effects of large deflections are taken into account and a perfectly elastic-plastic material model obeying a von Mises yield criterion is assumed. The following geometric parameters that influence the shear capacity of such girders are investigated: (1) the overall dimension of the web panel; (2) the web thickness; (3) the corrugation depth of the web; (4) the corrugation angle; and (5) the width of the plane sub-panel of the web. More specifically, the influence of these parameters both on the ultimate shear capacity and on the remaining shear capacity in the post-buckling range, as well as on the buckling modes, are reported. Based on the numerical results, empirical formulae that were proposed earlier for the prediction of the shear capacity are examined and suggestions for an optimal design of such girders in shear are given.     

Horizontally curved composite plate girders with trapezoidally corrugated webs

This paper is concerned with horizontally curved composite plate girders with trapezoidally corrugated webs. Finite element analysis using the computer package LUSAS is employed to investigate the behaviour and ultimate strength capacity of the girders. The presence of web openings of different proportions and their effects on the behaviour and ultimate strength of the girders are also investigated. Parameters that affect the behaviour of these girders are slenderness of the web d/t, web panel aspect ratio b/d, width to the depth of corrugation ratio b_h/h and size of openings. Influence of these parameters on the collapse behaviour is examined. Results are obtained in terms of ultimate strength, failure mechanism and load-deflection curves from the finite element analyses and, some typical results are presented herein. An approximate method to compute the shear capacity of these girders is presented. Comparison of the results with those predicted using the finite element method established the accuracy of the proposed method.     

波形钢腹板PC组合箱梁疲劳损伤对抗弯承载能力的影响研究

制作两根体外预应力波形钢腹板简支PC组合箱梁,其中第一根梁进行静力全过程试验,另一根梁先进行疲劳试验直至波形钢腹板出现疲劳破坏后进行静力加载全过程试验;得到两根组合箱梁在弹塑性阶段的基本力学性能、典型疲劳损伤特征和疲劳前后的抗弯承载力。根据混凝土材料的S-N曲线和疲劳荷载的实际应力比,推导混凝土材料疲劳损伤后的强度退化规律、总结混凝土割线模量、极限应变的退化规律,据此得到混凝土材料疲劳损伤前、后的本构关系;基于截面M-N-Φ关系编制体外预应力简支组合箱梁抗弯承载力的非线性全过程分析程序,对两根试验梁进行全过程加载的模拟分析,理论与试验结果吻合良好;两者均表明波形钢腹板的疲劳损伤对组合箱梁抗弯承载力影响不大,但会大大降低结构的延性。     

Ultimate load behaviour of webs in steel-concrete composite plate girders

The paper is concerned with the tension field action in webs of steel-concrete composite plate girders. A three-dimensional finite element model has been used to carry out nonlinear analyses on composite plate girders. The results obtained from the finite element analyses are compared with those from experiments. It is observed from the comparative study that the proposed nonlinear finite element model is capable of predicting the ultimate load behaviour of steel-concrete composite plate girders to an acceptable accuracy. Results are presented to explain the development of the tension field action in the webs and to illustrate a measure of the contribution by the concrete slab acting compositely with the girder to the changes in tension field compared to a plain steel girder.     

Flexural behavior of lean duplex stainless steel girders with slender unstiffened webs

The behavior of lean duplex stainless steel plate girders (LDIPGs) with slender unstiffened webs is studied in this paper. Firstly, shell finite element models are validated using experimental test results available in the literature. Secondly, these models are used to investigate the behavior of LDIPGs subjected to uniform bending. Parametric studies for the LDIPGs are carefully designed based on three parameters: the radius of gyration of the compression flange (r_T), the section modulus (S_x), and the unbraced length (L_b). The results showed that LDIPGs with higher r_T but similar S_x values can attain higher flexural strengths compared to their yield strengths because of the higher torsional rigidity of the flanges and stockier webs. On the other hand, by increasing the S_x value of the girder but keeping fixed the r_T values, the moment carried by the girder is found relatively to decrease with the simultaneous increase in the amount of steel. Finally, the numerical results are compared with predictions given by design standards. It is found that the EC3 provides conservative bending predictions. Accordingly, the imperfection factor associated to buckling curve (c) is recommended to be used in the scope of the design method provided by EN 1993-1-4.     

考虑腹板剪切变形的波形钢腹板组合箱梁剪力滞效应分析

在波形钢腹板组合箱梁中,剪力主要由波形钢腹板承担。由于波形钢腹板的抗剪刚度比混凝土腹板有较大程度的降低,波形钢腹板会产生较大的竖向剪切变形。为此,基于能量变分法建立了考虑腹板剪切变形的波形钢腹板组合箱梁剪力滞效应分析方法。通过试验对该理论分析方法进行验证,并基于该理论分析方法研究波形钢腹板剪切变形对剪力滞效应的影响。同时,基于该分析方法提出了采用影响线最不利加载方式进行相关规范中规定的汽车荷载作用下的波形钢腹板组合箱梁桥剪力滞效应分析。结果表明：考虑腹板剪切变形的分析方法与试验结果吻合度良好;波形钢腹板的剪切变形有利于减轻三跨连续梁正弯矩区的剪力滞效应,即考虑腹板剪切变形后翼缘有效宽度系数值更接近于1。     

Seismic analysis of steel structures considering damage cumulation

The research on the development of a reliable analytical model for seismic analysis of steel structures is presented. The non-linear damage cumulation hysteretic model incorporating the deterioration of stiffness, strength and strain hardening for structural steel is proposed and validated. The complete loading history, energy dissipation and the effect of the maximum plastic strain are taken into account in the model. The constants in the model are determined from regression analysis of experimental results of simple standard tensile and cyclic tests. Finite element formulations for beam and structural solid element considering the damage cumulation are derived. A computer program capable of calculating the hysteretic model of steel members, predicting the damage state and crack initiation, and carrying out non-linear time history seismic analysis of steel structures is developed. Solutions obtained from the model are in good agreement with experimental results. It was demonstrated that the damage cumulation effect is considerable and important in structural seismic analysis.     

波纹腹板H型钢梁变形性能

通过分析波纹腹板H型钢梁的弹性受力特点及剪切变形与弯曲变形的比例关系,提出对于此类型钢梁在计算变形时必须考虑剪切的影响,并通过试验和有限元模拟验证了上述结论。随后对各个构件的荷载-位移曲线分析得到了构件的延性系数,证明若设计合理,构件将具有较好的剪切强度和剪切延性,但是当构件为弯曲破坏控制时,构件延性一般。根据上述结论,提出了若干设计建议。     

波形钢腹板预应力混凝土组合箱梁扭转与畸变研究进展

有别于传统的混凝土箱梁,波形钢腹板预应力混凝土组合箱梁是一种较为新颖的桥梁上部结构形式,这种箱梁结构在偏心荷载作用下产生的扭转与畸变效应相对显著。为阐明这种箱梁的扭转与畸变特性及其研究现状,通过对大量文献的调研与实桥调查,系统介绍了箱梁扭转与畸变效应的计算理论（包括抗扭刚度）、扭转承载力、内力增大系数、横隔板的设置等方面的研究进展情况。研究表明,采用Umanski第二理论和弹性地基梁比拟法分别计算这种箱梁的扭转与畸变效应在理论上是可行的,但其工程适用性还需进行进一步检验。另外,我国在扭转承载力研究方面还较为欠缺,而在内力增大系数、横隔板的设置等方面尽管已经取得了一些成果,但还缺乏较为一致的结论。在充分考虑箱梁自身受力特性的基础上,加强波形钢腹板预应力混凝土组合箱梁扭转与畸变的研究,可为完善其设计方法奠定理论基础与提供更有力依据。     

波形钢腹板PC组合箱梁抗扭性能试验

通过试验的方法,研究波形钢腹板PC组合箱梁在偏心荷载作用下,挠度、横向位移、刚性扭转角、箱梁截面的翘曲应变、翘曲应力及波形钢腹板的附加剪应力的分布规律,以了解悬臂波形钢腹板PC组合箱梁在扭转作用下的力学性能。研究表明:波形钢腹板翘曲应变很小,可忽略不计;翘曲应力在底板上呈现明显的直线分布规律,且最大值出现在底板的角点处;波形钢腹板上的剪应力分布较均匀,附加剪应力在腹板上的分布也有类似的规律。     

Stress distribution in the flanges of girders with corrugated webs

The corrugated steel plate is a widely used structural element in many fields of application because of its numerous favorable properties. Due to the web corrugation the normal and shear stress distribution in the flange and web plates are different from the stress distribution of the conventional I-girders under in-plane bending and shear. The focus of this paper is the analysis of the stress distribution in the flanges of the girders with corrugated webs. Due to the corrugated web an additional transverse bending moment arises in the flange, which results in an additional normal stress distribution what has an effect on the bending moment resistance. The additional transverse bending moment comes from the shear force in the corrugated web and its value depends on the geometry of the corrugation profile. The effect and the tendency of this transverse bending moment are analyzed in the current paper. Based on experimental background a numerical model is developed to analyze the stress distribution in the flanges. Tendency of the additional normal stresses are determined and based on the numerical results an enhanced design method is proposed to determine the transverse bending moment and the additional normal stresses.     

Refined analysis for cold bending steel plate girders

Cold bending is a simple, economical fabrication method for curving steel elements primarily used in building applications. In this method, appropriate loads are applied to obtain the desired curvature. The authors recently developed approximate analytical solutions for curving unstiffened, symmetrical or non-symmetrical girders. These solutions relating loads to residual deformation were used to establish limits on geometry, maximum load and curvature so that Bauschinger effects did not have to be considered. This paper refines and extends the earlier solution by incorporating previously neglected factors relating to loading, support condition and girder geometry that resulted in under-estimation of the stiffness of the system. Revised equations are presented and their application described by an illustrative example.     

Postbuckling and ultimate state of stresses in steel plate girders

In [1], nonlinear large deflection finite element analysis was implemented to depict the characteristics of the shear failure mechanism of steel plate girders. That paper aimed at clarifying how–when–why and where plastic hinges form in flanges. The present paper extends those results to the state of stresses in web plates. It is shown that although the principal compressive stresses in the center of the web plates remain constant after an elastic buckling, they do increase considerably in other regions. In addition, the angles at which tension fields form; and the ultimate strength of plate girders is discussed and compared to those obtained by different theoretical and experimental hypotheses.     

Patch loading resistance of girders with corrugated webs

The corrugated steel plate is a widely used structural element in many fields of application because of its favourable properties and has been applied since the 1920s. For the last 20 years it has been increasingly used in the web of steel and composite bridges. When such a bridge is incrementally launched, buckling of the thin steel web may occur. In this paper, a numerical model is developed on the basis of previous experiments. Numerical investigations are made for the determination of the patch loading resistance, and the geometric parameters which influence the patch loading resistance and the structural behaviour are determined and analysed. Existing design formulas from the literature are summarised from the point of view of bridges, and enhanced according to the numerical results and the existing and additional experiments.     

Shear resistance in stainless steel plate girders with transverse and longitudinal stiffening

This paper summarizes and presents main results of the investigation conducted in the Department of Construction Engineering of the UPC dealing with shear behaviour of stainless steel plate girders. Initial shear buckling stress together with ultimate shear capacity of these structural elements have been evaluated with special attention paid to the effect of including stiffeners, both transverse and longitudinal. The studies conducted, both numerical and experimental tests, have permitted the development of new and simple design expressions to determine more accurately the initial shear buckling stress in stainless steel web panels and the ultimate capacity of plate girders considering the presence of a rigid or non-rigid end post.     

Flexural strength of hollow tubular flange plate girders with slender stiffened webs under mid-span concentrated loads

A three-dimensional elastic finite element (FE) model, considering merely the geometric nonlinearity, is used in the first part of this paper to study the overall buckling resistance of hollow tubular flange plate girders (HTFPGs). Modeling is conducted using the general-purpose FE software package ABAQUS under mid-span concentrated loads. The developed model consists of the type and number of elements that allows capturing the different possible buckling mode patterns including local, interactive and lateral-torsional buckling. Finite element results revealed that, unlike the case of conventional beams with solid webs, the moment-gradient factor $C_b$ is significantly influenced by the girder geometry and slenderness. Hence, an equation representing the $C_b$ factor for the case of HTFPGs with slender stiffened webs is proposed. The paper extends to investigate the nonlinear flexural strengths of such girders. The results are compared to the AISC predictions. The original AISC predictions are found to be highly conservative using the code recommended $C_b$ value as well as the current proposed value. However, the suggested AISC strength (found in Hassanein et al., 2013 [1]) using $C_b=1.35$ is found to be the best among other values but it suffers from the discontinuity in the flexural strength-unbraced length relationship. Accordingly, a line representing the middle part of this relationship is currently assumed. Comparisons with FE results indicate that the currently proposed AISC method can fairly predict the flexural strength of the HTFPGs with slender stiffened webs.     

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.     

不锈钢薄腹梁受剪性能试验研究

通过对7根不锈钢薄腹梁进行受剪性能试验研究,分析了梁腹板的剪切屈曲和屈曲后强度。结果表明：所有梁均发生剪切屈曲破坏,薄腹板中形成拉力带,上翼缘和横向加劲肋中出现塑性铰;根据腹板表面应变和侧向鼓曲变形测得的剪切屈曲应力均低于理论计算的弹性剪切屈曲应力;梁的受剪承载力显著高于腹板剪切屈曲时的荷载,具有较高的屈曲后强度;梁端设置封头肋板可以提高梁的受剪承载力。基于得出的试验结果及现有其他试验数据,对两种考虑腹板屈曲后强度的受剪承载力计算方法进行评估,我国GB 50017—2017《钢结构设计标准》中的公式仅考虑了腹板的受剪承载力,其计算结果总体偏于保守,但是对腹板高厚比较小(λs<1.5)的不锈钢薄腹梁,受剪承载力计算偏于不安全,且计算结果离散性较大;EN 1993-1-4中的计算公式中同时考虑了腹板和翼缘的受剪承载力,其计算结果偏于保守且离散性较小。     

Longitudinally stiffened hybrid steel plate girders subjected to patch loading

Hybrid girders subjected to patch loading have been analyzed in a detailed fashion for the case in which the plates that assemble the girders are transversally stiffened. Scant work, however, is available for the case in which the girders are hybrid and, simultaneously, longitudinally stiffened. The driving force for developing the present research work is to complete the knowledge of the patch loading field for the particular structural alternative of a hybrid steel plate girder assembled with a longitudinal stiffener. In the current paper, a numerical database of 255 simulations on longitudinally stiffened steel girders subjected to patch loading developed by the authors is presented. The results obtained are used for assessing the resistance of longitudinally stiffened hybrid steel plate girders subjected to patch loading. Some discrepancies between the numerical and EN1993-1-5 results are pinpointed. A design proposal which enhances the current EN1993-1-5 formulation is given at the end of the paper.