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.     

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.     

Finite element simulations of residual stresses in roller bent wide flange sections

Curved structural wide flange steel sections are frequently used in buildings or bridges. These sections are usually curved at ambient temperatures with a roller bending machine. This process alters the residual stress distribution, which may affect the elasto-plastic buckling behavior of arches. This paper presents a numerical modeling technique to estimate residual stresses in curved wide flange sections manufactured by the pyramid roller bending process. The technique incorporates material non-linearity, geometrical non-linearity and contact modeling. Numerically obtained residual stresses are compared to experimental results and good agreement was found for the top flange. Only moderate agreement was observed for the web but very good coherence was realized for the bottom flange. It is concluded that a finite element analysis can be used to estimate residual stresses in roller bent wide flange 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.     

Design rules for out-of-plane stability of roller bent steel arches with FEM

This paper describes a numerical investigation into the out-of-plane buckling behavior of freestanding roller bent steel arches. As roller bent arches have structural imperfections which differ considerably from those of hot-rolled or welded sections, specific attention is paid to their inclusion in the numerical model. Sensitivity analyses are performed to assess the influence of the imperfections due to roller bending on the out-of-plane buckling response. The accuracy of the finite element model is checked by comparing the results with earlier performed experiments as presented in a related paper. The finite element model is able to replicate the structural behavior displayed by the experiments with good accuracy. A database is created with elastic–plastic buckling loads for a large number of freestanding roller bent arches. The numerical data is analyzed and presented in a so-called imperfection parameter diagram from which imperfection parameter curves are derived. The imperfection parameter curves are substituted into the European column curve formulation, leaving the original column curve formulation unaffected but extending its applicability to the out-of-plane buckling response of roller bent arches. The column curve with proposed imperfection parameter expressions can be used to check the out-of-plane buckling response of a roller bent steel arch with known non-dimensional slenderness.     

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。     

钢压弯构件弯扭屈曲的研究

本文简要介绍了近年来在西安冶金建筑学院完成的有关钢压弯构件弯扭屈曲研究的成果,包括以下几个方面;(1)确定钢压弯构件设计承载力的典型截面选择;(2)考虑钢材屈服非连续性或焊接残余应力影响时构件的非弹性弯扭屈曲;(3)单轴对称截面压弯构件的弯扭屈曲分析和试验研究;(4)双轴和单轴对称截面构件弯扭屈曲的实用相关公式;(5)绕截面弱轴弯曲的压弯构件的弯扭屈曲分析和试验;(6)冷弯薄壁型钢构件的非弹性弯扭屈曲的分析和试验。     

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.     

Lateral buckling strengths of cold-formed rectangular hollow sections

Code rules for designing steel beams against lateral buckling which are based on data for hot-rolled I-sections are unnecessarily conservative when used for cold formed rectangular hollow section beams.Cold-formed rectangular hollow section beams have different stress-strain curves, residual stresses, and crookedness and twist. The effects of residual stress on the inelastic buckling of I-section beams are not nearly as pronounced for hollow sections with two webs, while the strengthening effects of pre-buckling deflections are greater for hollow sections. Simplistic code rules for top flange loading are very conservative when applied to hollow sections.This paper reviews elastic lateral buckling behaviour and the strength rules used to design steel beams. It develops realistic models for cold-formed rectangular hollow beams which are analysed to predict the effects of moment distribution, load height and yield stress on their strengths. The results of the analyses are used to develop improved design rules which remove much of the conservatism of present design rules.     

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 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.     

焊接H型钢局部纵弯失稳下抗弯强度计算

对由厚度为6.0mm、名义屈服强度为315.0MPa的钢板制成的H型钢进行了一系列弯曲试验,研究焊接H型钢的抗弯强度。截面几何形状和侧向边界条件决定了薄壁受弯构件的屈曲形式(局部屈曲、侧向扭转屈曲或交互屈曲)。翼缘或腹板宽厚比较大的受弯构件最先出现局部屈曲,继而发生侧向扭转屈曲,在交互屈曲作用下材料最终破坏。侧向扭转屈曲下局部屈曲对抗弯强度有负面影响。计算薄壁抗弯构件名义屈服应力时应将该现象考虑在内。对翼缘和腹板宽厚比不同的焊接H型钢梁进行了试验。进行有限元分析时将局部和侧向扭转屈曲模态的初始缺陷及残余应力考虑在内。基于考虑焊接型材局部和侧向扭转屈曲相互作用的试验和有限元分析结果,给出直接强度法(DSM)计算抗弯强度的简化公式。计算强度曲线与AISC规范(2005),EC3(2003)及试验结果进行比较,验证了DSM方法所计算的强度曲线的准确性。通过试验得出薄壁焊接H型钢的抗弯强度和结构性能的有关结论。     

高温作用后高强Q690钢焊接截面残余应力试验研究

焊接中的不均匀受热和冷却使钢材内部产生残余应力,残余应力会降低钢构件的刚度、稳定承载力和疲劳性能。钢构件在高温下的强度退化、塑性和蠕变变形会引起截面残余应力改变,从而影响其火灾下及火灾后承载力。为此,采用高强Q690钢材制作了6个焊接构件,包括H形、箱形两种截面形式。利用切条法测量其在常温（20℃）下、600℃和800℃高温作用后的截面残余应力,得到不同温度作用后残余应力的大小与分布。结果表明：高温作用后,残余应力有不同程度的释放;经历600℃作用后,箱形与H形截面残余应力幅值均下降至常温下的约35%;经历800℃作用后,箱形与H形截面残余应力幅值均下降至常温下的15%以下。基于试验结果,提出Q690焊接截面残余应力分布模型及残余应力幅值随受火温度变化的折减系数。     

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.     

Prediction of the flexural strengths of welded H-sections with local buckling

This paper describes the flexural strength of welded sections based on a series of flexural tests performed on H-sections fabricated from steel plates of thickness 6.0 mm with nominal yield stress of 315.0 MPa. Thin-walled flexural members undergo local, lateral-torsional or their interactive buckling according to the section geometries and lateral boundary conditions. Flexural members with the flanges or the web of large width-to-thickness ratios may undergo local buckling before lateral-torsional buckling and their interaction before the final collapse of the section. The local buckling has a negative effect on the flexural strength based on the lateral-torsional buckling. This phenomenon should be considered in the estimation of the nominal flexural strength of thin-walled flexural members. Welded H-section beams composed of the flanges and the web with various width-to-thickness ratios were tested to failure. The initial imperfections in local and lateral buckling mode, and residual stresses were included in the FE analyses. Simple design flexural strength formulas for the direct strength method (DSM) were proposed based on the test and FE results of welded sections to account for interaction between local and lateral-torsional buckling. The design strength curves were compared with the AISC specifications (2005), Eurocode3 (2003) and test results. The adequacy of the strength curve for the DSM was confirmed. A set of conclusions on the flexural strength and structural behavior of thin-walled welded H-sections was drawn from the experimental studies.     

Column curves for elliptical hollow section members

A thermo-mechanical finite element analysis model is developed to predict residual stress patterns in hot-rolled sections. The model is first verified against experimental measurements for residual stresses reported for I-sections reported in the literature. The method is then used to predict residual stresses in elliptical hollow sections. A sensitivity analysis is then conducted to assess the influence of various input parameters of the model on the predicted residual stress patterns. The effects of cross-section geometric parameters on the residual stress distribution are then investigated.A series of column curves is generated providing the compressive capacity of a column as a function of slenderness. The column curves are generated based on a) elasto-plastic geometrically nonlinear analyses, b) including the effect of residual stresses as predicted from thermo-mechanical analyses and c) incorporating initial geometric out-of straightness according to the fundamental buckling mode as predicted from an elastic buckling eigen value analysis. Generated column curves are then compared to those in current design codes. A best fit for the numeric results obtained is conducted to cast them in a format similar to that in the current codes.     

Ermüdungsprobleme dünnwandiger kaltgeformter Bauteile

Fatigue behaviour of thin‐walled coldformed steel profiles. Current design concepts for thin‐walled structural members take local buckling into account in determining the ultimate capacity. Local buckling may be accompanied by large deformations, which entail secondary bending stresses. Such secondary stresses can be neglected in usual design, but there are no information available regarding their influence on fatigue design. For the investigation of that problem fatigue tests were carried out with thin‐walled cold‐formed U‐channels exposed to pure bending. Following the systematically numerical investigations it will be proposed to limit the cyclic load by 60% of the ultimate load in order to avoid fatigue damage of thin‐walled cold‐formed profiles.     

Plastic mechanisms database for thin-walled cold-formed steel members in compression and bending

Short members of thin-walled cold-formed (TWCF) steel sections, in compression and bending, fail by forming local plastic mechanisms. Taking into account the localised buckling pattern, the collapse of slender members, due to the interaction between local and overall buckling modes, is always characterised by local plastic mechanism failure mode. Based on these two observations, the ultimate strength in interactive buckling of these members can be regarded as an interaction between localised plastic mode and overall elastic one.The yield line mechanism method has been widely used to predict the sectional strength (e.g. local) of thin-walled cold-formed steel members that involve failure mode characterized by local collapse mechanisms. This method can be also used to study post-collapse behaviour and to evaluate the load-carrying capacity, ductility and energy absorption.This paper is based on previous studies and some latest investigations of authors, as well as the literature collected data. It represents an attempt to make an inventory, classify and range geometrical and analytical models for the local-plastic mechanisms aiming to characterize the ultimate capacity of some of the most used cold-formed steel sections in structural applications.     

工形截面钢拱考虑腹板局部屈曲的承载力设计方法研究

把工形截面钢拱的腹板做高做薄是提高其承载力的有效方法之一。该文采用大挠度弹塑性壳单元模型,研究焊接工形截面两铰圆弧钢拱在允许腹板局部屈曲条件下的平面内稳定承载力及其设计方法,其中考虑钢拱几何初始缺陷和残余应力的影响。首先,对钢拱在均匀轴压力作用下的承载力和破坏机理进行有限元数值分析和参数研究,考察拱截面腹板高厚比、钢拱几何长细比、截面翼缘腹板板厚比和翼缘宽厚比对钢拱稳定系数的影响。在设定的钢拱翼缘宽厚比范围内,基于大量的钢拱承载力数值分析结果,提炼出腹板高厚比和翼缘腹板板厚比组合效应的等效正则化腹板高厚比,进而获得钢拱稳定系数与等效正则化腹板高厚比以及钢拱正则化长细比之间关系的计算公式。其次,研究压弯组合作用下钢拱腹板高厚比变化对钢拱整体稳定承载力的影响,揭示钢拱压弯组合作用下的破坏机理及稳定承载力。最后通过对大量钢拱算例进行不同压弯组合工况下的极限承载力分析,提出了钢拱在一般荷载或组合荷载作用下承载力设计的计算公式。     

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.