辊弯曲宽翼缘构件残余应力的有限元模拟

弯曲宽翼缘钢构件常用于建筑和桥梁中,并在室温下通过辊弯机进行弯曲。辊弯过程改变了构件残余应力分布,可能影响拱构件的弹塑性屈曲性能。考虑材料非线性、几何非线性及接触,进行数值模拟,分析辊弯过程中弯曲宽翼缘构件的残余应力。将模拟结果与试验结果进行比较,结果表明:下翼缘吻合很好,上翼缘吻合较好,腹板吻合一般。结果证明有限元分析方法可用于研究辊弯曲宽翼缘构件的残余应力。     

Experimental investigation of residual stresses in roller bent wide flange steel sections

Residual stresses in straight hot rolled wide flange sections are well documented and have been investigated in the recent past. However, to the knowledge of the authors, residual stress measurements have not been published on roller bent wide flange sections. Straight sections are curved into roller bent ones at ambient temperatures by means of the roller bending process. Since roller bent sections underwent severe plastic deformation during the forming process, the well-known residual stress patterns from hot rolling may not be appropriate for the roller bent steel. Roller bent sections can be applied in halls, roofings and bridges, thereby acting as structural arches and it is important that a realistic residual stress pattern is implemented when assessing their load carrying capacity. An experimental program has been carried out to investigate the residual stresses in roller bent wide flange sections bent about the strong axis. Residual stresses were measured with the sectioning method. The experimental technique was investigated with respect to possible temperature influence and repeatability of the measurements. Experimental values revealed that the residual stress pattern and magnitude in roller bent sections is different when compared to their straight counterparts.     

Proposed residual stress model for roller bent steel wide flange sections

The manufacturing process of structural wide flange steel sections introduces residual stresses in the material. These stresses due to hot-rolling or welding influence the inelastic buckling response of structural steel members and need to be taken into account in the design. Based on experimental data standardized residual stress models have been proposed for inclusion in inelastic buckling analyses. By incorporating these residual stress models their effect on the resistance of beams and columns can be obtained. Residual stress models for roller bent steel sections are currently not available. Roller bent wide flange sections are manufactured by curving straight members at ambient temperature. This manufacturing technique, which is also known as roller bending, stresses the material beyond its yield stress, thereby overriding the initial residual stresses prior to bending and generating an entirely new pattern. This paper proposes a residual stress model for roller bent wide flange sections, based on earlier conducted numerical investigations which were validated by experimental research performed at Eindhoven University of Technology. The proposed residual stress model can serve as an initial state of a roller bent steel section in fully non-linear finite element analyses to accurately predict its influence on the inelastic buckling response.     

Mechanical properties of roller bent wide flange sections — Part 1: Experimental investigation

Arched roofs are built more and more with roller bent wide flange sections, serving as structural elements. Roller bent wide flange sections are manufactured from straight hot-rolled wide flange sections by a process called roller bending. The material is cold worked during forming, inducing a new distribution of mechanical properties across the section which is different compared to its original state. For the design of arches the use of original or nominal strength properties of the straight material neglects the influence of the roller bending process. This may lead to conservative or nonconservative designs. This paper presents the results of an extensive experimental investigation of the mechanical properties of roller bent wide flange sections. It comprises tensile tests and compression tests on coupons taken from roller bent sections and their straight counterparts. The results show that the roller bending process alters the mechanical properties of the material non-uniformly over the cross-section. In this paper the experimental results are presented. In a companion paper the experimental results are used to arrive at a set of equations that yields different stress-strain curves for specific zones across the roller bent steel section.     

Mechanical properties of roller bent wide flange sections — Part 2: Prediction model

This paper provides a series of simple equations that allow the structural engineer to predict the mechanical properties across the section of roller bent wide flange steel members: proportional limit, yield stress, ultimate tensile stress, strain at ultimate tensile stress and strain at rupture. The equations are based on experimental results from tensile tests performed on coupons taken from roller bent wide flange sections which are presented in a companion paper. The newly obtained mechanical properties yield seven different full stress-strain curves for nine specific locations on the steel cross-section. The stress-strain models for the material of the flanges are defined by non-linear curves. The stress-strain characteristics in the web allow the material to be represented by bi-linear stress-strain curves. Comparison between predicted adjustments in mechanical properties due to roller bending and measured properties gives good agreement. The obtained stress-strain curves are suitable for implementation in finite element models for the analysis of arch structures employing beam, shell or solid elements.     

Influence of cold bending on the resistance of wide flange members

Cold rolling is used for bending straight members with hot rolled wide-flange sections to create arches. Extensive studies have shown that the influence of residual stresses due to hot rolling on the resistance of wide-flange steel sections is nonnegligible. On the contrary, the residual stress pattern due to roller bending has been only recently identified. Its effects on the elasto-plastic behavior of curved members have not been studied sufficiently. In this paper, an in-depth study of the influence of such residual stresses is performed. Considering the residual stress pattern due to cold bending, interaction diagrams and buckling curves for cold bent steel arches are developed. The results are quantified and compared with those for hot-rolled and stress free members. This allows designers to appreciate the available margins of safety when using standard interaction equations and buckling curves for cold bent members. Furthermore, the results suggest the necessity for the development of buckling curves for cold bent members including initial imperfections.     

单轴对称工字钢梁的弹塑性稳定系数

工字钢梁在工业厂房中应用非常广泛,而平面外弯扭失稳是薄壁构件的主要失稳模式,比单独的扭转失稳和弯曲失稳要复杂的多。以往钢梁稳定研究主要集中在双轴对称截面,单轴对称截面的整体稳定性研究较少。为此,对承受跨中集中荷载和关于跨中对称的两点荷载的单轴对称工字钢梁进行了弹塑性弯扭屈曲分析,考虑初始变形和两种残余应力分布。通过算例分析得到不同截面尺寸和荷载作用点高度的稳定系数变化规律,以修正的ECCS公式为基础拟合得到了适用于单轴对称截面横向荷载作用下的弯扭屈曲稳定系数公式,该公式适用于的荷载作用点高度为剪心到上翼缘以上120mm,和截面宽高比为0.42~0.76范围内的单轴对称工字钢梁。与有限元计算结果对比表明,公式计算结果与有限元分析结果符合良好,且公式与有限元计算结果相比较为保守。     

Experimental study on residual stresses in welded monosymmetric I-section

为了研究单轴对称焊接工字形截面残余应力分布规律,采用盲孔法对15个单轴对称工字形截面试件进行了试验研究,得到了不同试件全截面纵向残余应力分布,研究了腹板高厚比、翼缘宽厚比、翼缘宽度、施焊顺序等对残余应力的影响。试验结果表明：残余压应力数值与截面尺寸直接相关,残余拉应力数值受截面尺寸影响较小;腹板中靠近宽翼缘一侧的残余压应力峰值大于靠近窄翼缘一侧的压应力峰值;翼缘宽度增大时,分布于所在翼缘和腹板的残余压应力减小;施焊顺序对翼缘上的残余应力及腹板上的残余拉应力峰值有一定影响,而腹板上的残余压应力没有明显变化。基于试验结果,提出了适用于单轴对称焊接工字形截面的残余应力分布模型,该模型能够较准确反映各种因素的影响。     

Local Flange Bending and Continuity Plate Requirements in Double-Web H-Shaped Columns

In steel moment frames, columns are subjected to unbalance moment that is transmitted into the joint through a couple of concentrated forces at the centroid of the beam’s flanges. If the flexural capacity of the column flange is less than produced moment by these tensile or compressive forces, use of continuity plates in the panel zone is necessary. Since in box-shaped column, welding the forth edge of a continuity plate to the column flange may not be easily done and is usually accompanied by remarkable difficulties, double-web H-shaped columns as an appropriate alternative, which often do not require continuity plates, can be used. Numerous studies are carried out on local flange bending in H–shaped columns and are referred in the valid guidelines. The behavior of double-web column’s flange is between box shaped and H-shaped column’s flange. This paper presents analytical and numerical modeling of double web column to estimate local flange bending. The numerical modeling is derived from the results of finite element analyses. Based on these two approaches, some equations are presented to estimate local flange bending of double web columns, and are shown their efficiency and accuracy.     

Residual stress of 460 MPa high strength steel welded i section: Experimental investigation and modeling

A reliable estimation of residual stress within steel sections is important in steel structural design and construction, especially for high strength steel which has been increasingly used in recent years. An experimental investigation was conducted in this paper to quantify the residual stresses in 460 MPa steel welded I sections using sectioning method. The magnitude and distribution of both compressive and tensile residual stresses were obtained based on 1972 sets of original data measured from eight different sections. The effects of width-thickness ratios of the flange and web, steel plate thickness, weld type and interaction of the flange and web were investigated. It was found that the compressive residual stress magnitude was largely related to the sectional dimension, while no direct correlation was found with the weld type and size for tensile ones. No residual stress interaction between the flange and web was identified because of the stress equilibrium within each individual part. In addition, a distribution model was proposed in this paper and well described the experimental results, which can be used to investigate and design the buckling behavior of 460 MPa high strength steel members.     

Residual stresses in press-braked stainless steel sections,II: Press-braking operations

The manufacturing process of cold-formed thin-walled steel members induces cold work which can be characterized by the co-existent residual stresses and equivalent plastic strains and has a significant effect on their structural behaviour and strength. The present paper and the companion paper are concerned with the prediction of residual stresses and co-existent equivalent plastic strains in stainless steel sections formed by the press-braking method. This manufacturing process consists of the following two distinct stages: (i) coiling and uncoiling of the sheets, and (ii) press-braking operations. This paper first presents an analytical solution for the residual stresses and the co-existent equivalent plastic strains that arise from the second stage while a corresponding analytical solution for the first stage is presented in the companion paper. In both solutions, plane strain pure bending is assumed and the effect of material anisotropy is taken into account. On the basis of these two analytical solutions, an analytical model is presented to predict residual stresses and equivalent plastic strains in press-braked stainless sections. The predictions of the analytical model are shown to be in close agreement with results from a finite element-based method, demonstrating the validity and accuracy of the analytical model. The analytical model provides a much simpler method for the accurate prediction of residual stresses and equivalent plastic strains in different parts of a press-braked stainless steel section than a finite element-based method.     

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.     

Residual stresses in cold-rolled stainless steel hollow sections

Stainless steel exhibits a pronounced response to cold-work and heat input. As a result, the behaviour of structural stainless steel sections, as influenced by strength, ductility and residual stress presence, is sensitive to the precise means by which the sections are produced. This paper explores the presence and influence of residual stresses in cold-rolled stainless steel box sections using experimental and numerical techniques. In previous studies, residual stress magnitudes have been inferred from surface strain measurements and an assumed through-thickness stress distribution. In the present study, through-thickness residual stresses in cold-rolled stainless steel box sections have been measured directly by means of X-ray diffraction and their effect on structural behaviour has been carefully assessed through detailed non-linear numerical modelling. Geometric imperfections, flat and corner material properties and the average compressive response of stainless steel box sections were also examined experimentally and the results have been fully reported. From the X-ray diffraction measurements, it was concluded that the influence of through-thickness (bending) residual stresses in cold-rolled stainless steel box sections could be effectively represented by a rectangular stress block distribution. The developed ABAQUS numerical models included features such as non-linear material stress-strain characteristics, initial geometric imperfections, residual stresses (membrane and bending) and enhanced strength corner properties. The residual stresses, together with the corresponding plastic strains, were included in the FE models by means of the SIGINI and HARDINI Fortran subroutines. Of the two residual stress components, the bending residual stresses were found to be larger in magnitude and of greater (often positive) influence on the structural behaviour of thin-walled cold-formed stainless steel sections.     

Inelastic local buckling of curved plates with or without thickness-tapered sections using finite strip method

This paper addresses the inelastic local buckling of the curved plates using finite strip method in which buckling modes and displacements of the curved plate are calculated using sinusoidal shape functions in the longitudinal direction and polynomial functions in the transverse direction. A virtual work formulation is employed to establish the stiffness and stability matrices of the curved plate whilst the governing equations are then solved using a matrix eigenvalue problem. The accuracy and efficiency of the proposed finite strip model is verified with finite element model using ABAQUS as well as the results reported elsewhere while a good agreement is achieved. In order to illustrate the proposed model, a comprehensive parametric study is performed on the steel and aluminium curved plates in which the effects of curvature, the length of the curved plate as well as circumferential boundary conditions on the critical buckling stress are investigated. The developed finite strip method is also used to determine the buckling loads of the curved plates with thickness-tapered sections as well as critical stresses of the aluminium cylindrical sectors that are subjected to uniform longitudinal stresses.     

Investigation of ductility in hybrid and high strength steel beams

Compactness and lateral support configuration provisions for design of steel beams are formulated so as to ensure that the resulting beam exhibits adequate ductility. It appears from the current research that slenderness limitations are not valid for beams made of the high strength steel grades. In this paper an attempt is made to study on influence of flange and web slenderness as well as lateral support spacing of homogenous and hybrid welded I-sections made of high strength steel on member ductility. For this purpose an experimentally verified nonlinear numerical analysis of the local and overall stability was performed. These beams are subjected to constant moment loading a new theoretical method is proposed to calculate the rotation capacity for this loading type. A comparative study was carried out between this method and numerical study results to ensure the accuracy of proposed method. In this research realistic material behavior and residual stresses were adopted in finite element models. Results have shown that using the high strength steel in cross sections subjected to bending has a significant effect on flexural behavior of these members. Meanwhile, in present study, interaction between the flange and web slenderness ratios was evaluated in accordance to AISC criteria for compact sections.     

冷成型钢截面残余应力的有限元分析

冷成型钢截面上的残余应力可能是决定其性能和强度的一个重要因素。通过破坏性的试验方法对残余应力进行测量不仅费时,精度也很有限。本文提出了一个预测压弯成形薄壁截面上残余应力的有限元方法,该方法克服了实验室测量的缺点,提供了一个有力的工具来考察不同的成形参数对残余应力的大小和分布的影响,并因此可以对这些成形参数进行优化。在该方法中,通过解析的方法考虑了成卷和开卷的影响,并将得到的残余应力作为随后的冷弯过程有限元模拟的初始应力。经比较,本文方法的数值结果和实验室实测值吻合很好,证明了该方法的可行性和精度。本文方法给出了整个截面残余应力的分布和沿壁厚的变化,并解释了两个相同截面中残余应力可能会存在很大差别的原因。     

Section moment capacity tests of LiteSteel beams

The LiteSteel beam (LSB) is a new cold-formed hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. In addition to this unique geometry, the LSB sections also have unique characteristics relating to their stress–strain curves, residual stresses, initial geometric imperfections and hollow flanges that are not encountered in conventional hot-rolled and cold-formed steel channel sections. An experimental study including 20 section moment capacity tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. The presence of inelastic reserve bending capacity in these beams was investigated in detail although the current design rules generally limit the section moment capacities of cold-formed steel members to their first yield moments. The ultimate moment capacities from the tests were compared with the section moment capacities predicted by the current cold-formed and hot-rolled steel design standards. It was found that compact and non-compact LSB sections have greater moment capacities than their first yield moments. The current cold-formed steel design standards were found to be conservative in predicting the section moment capacities of compact and non-compact LSB sections, while the hot-rolled steel design standards were able to better predict them. This paper has shown that suitable modifications are needed to the current design rules to allow the inclusion of available inelastic bending capacities of LSBs in design.     

Stiffened steel plates under uniaxial compression

The stability of steel plates stiffened with tee-shape sections under uniaxial compression and combined uniaxial compression and bending was investigated using a finite element model. The emphasis of the work presented in this paper was to find the parameters that uniquely describe the strength and behaviour of stiffened steel plates. A finite element model, validated using the results of tests on full-size stiffened plate panels, was used to investigate the scale effect for five dimensionless parameters. The parameters investigated were: the transverse slenderness of the plate, the slenderness of the web and flange of the stiffener, the ratio of torsional slenderness of the stiffener to the transverse slenderness of the plate, and the stiffener-to-plate area ratio. Average magnitude residual stresses and initial imperfections were assumed for this study.A parametric study covering a wide range of dimensionless parameters indicated that stiffened steel plates do not fail by stiffener tripping unless a bending moment is applied to create flexural compressive stresses in the stiffener. Although plate buckling and overall buckling were found to lead to a very stable post-buckling behaviour, the interaction between these two buckling modes was found to give rise to a sudden loss of capacity following initial plate buckling. The plate transverse slenderness, the stiffener slenderness-to-plate slenderness ratio, and the stiffener-to-plate area ratio were found to have a significant effect on this behaviour.A comparison of the numerical analysis results with API and DnV design guidelines indicates that the guidelines predict stiffened steel plate capacity with various degrees of success, depending on the governing mode of failure. Neither guidelines address the potential interaction-buckling phenomenon.     

Residual stresses in press-braked stainless steel sections,I: Coiling and uncoiling of sheets

The manufacturing process of cold-formed thin-walled steel members induces cold work which can be characterized by the co-existent residual stresses and equivalent plastic strains and has a significant effect on their structural behaviour and strength. The present paper and the companion paper are concerned with the prediction of residual stresses and co-existent equivalent plastic strains in stainless steel sections formed by the press-braking method. This manufacturing process consists of the following two distinct stages: (i) coiling and uncoiling of the sheets, and (ii) press-braking operations. This paper presents an analytical solution for the residual stresses and co-existent equivalent plastic strains that arise from the first stage. In the analytical solution, the coiling–uncoiling stage is modelled as an inelastic plane strain pure bending problem; the stainless steel sheets are assumed to obey Hill’s anisotropic yield criterion with isotropic hardening to account for the effects of material anisotropy and nonlinear stress–strain behaviour. The accuracy of the solution is demonstrated by comparing its predictions with those obtained from a finite element analysis. The present analytical solution and the corresponding analytical solution for press-braking operations presented in the companion paper form an integrated analytical model for predicting residual stresses and equivalent plastic strains in press-braked stainless steel sections.     

Residual stress analysis of structural stainless steel sections

The magnitude and distribution of residual stresses in structural carbon steel sections have been thoroughly investigated. However, few residual stress measurements have been made on structural stainless steel sections. Stainless steel has differing material stress-strain characteristics and thermal properties to carbon steel, both of which influence the formation of residual stresses. This suggests that established carbon steel residual stress models may not be appropriate for stainless steel. With increased use of stainless steel in load bearing applications, it is important to establish the residual stresses that exist within structural members. An experimental program to quantify the residual stresses in stainless steel sections from three different production routes has therefore been carried out. Comprehensive residual stress distributions have been obtained for three hot rolled angles, eight press braked angles and seven cold rolled box sections, with a total of over 800 readings taken. This paper presents the experimental techniques implemented and the residual stress distributions obtained as well as discussing the assumptions commonly made regarding through thickness residual stress variations. In the hot rolled and press braked sections, residual stresses were typically found to be below 20% of the material 0.2% proof stress, though for the cold rolled box sections, whilst membrane residual stresses were relatively low, bending residual stresses were found to be between 40% and 70% of the material 0.2% proof stress.