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.     

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.     

Residual stress distributions in welded stainless steel sections

Residual stress magnitudes and distributions in structural stainless steel built-up sections have been comprehensively investigated in this study. A total of 18 test specimens were fabricated from hot-rolled stainless steel plates by means of shielded metal arc welding (SMAW). Two grades of stainless steel were considered, namely the austenitic grade EN 1.4301 and the duplex grade EN 1.4462. Using the sectioning method, the test specimens were divided into strips. The residual stresses were then computed by multiplying the strains relieved during sectioning by the measured Young׳s moduli determined from tensile and compressive coupon tests. Residual stress distributions were obtained for 10 I-sections, four square hollow sections (SHS) and four rectangular hollow sections (RHS). Peak tensile residual stresses reached around 80% and 60% of the material 0.2% proof stress for grades EN 1.4301 and EN 1.4462, respectively. Based upon the test data, simplified predictive models for residual stress distributions in stainless steel built-up I-sections and box sections were developed. Following comparisons with other available residual stress test data, the applicability of the proposed models was also extended to other stainless steel alloys. The proposed residual stress patterns are suitable for inclusion in future analytical models and numerical simulations of stainless steel built-up sections.     

冷成型双相不锈钢截面材料特性

给出了6个不同截面冷成型双相不锈钢的特性,其中2个为圆形中空截面,4个为矩形中空截面。试样为冷轧双相不锈钢带。确定方形和矩形中空截面高强度冷成型双相不锈钢的材料特性。对每种型材的薄弱和转角处进行拉伸试验,由此测量每种型材的弹性模量、0.2%弹性极限、1.0%弹性极限、抗张强度、断裂延伸率和Ramberg-Osgood参数(n)。通过短柱试验获得冷轧状态全截面的材料特性。测量6种型材的初始局部几何缺陷,绘制每种型材含初始几何缺陷的横截面图。采用断面法测量150×50×2.5截面的残余应力,测量并绘制截面上薄膜屈曲残余应力分布图。此外,给出适用于短柱的有限元模型,并与试验结果进行对比。将不锈钢短柱的试验强度与美国规范、澳大利亚/新西兰规范和欧洲规范的设计强度进行对比。总体看来,三种规范的计算结果都较为保守,其中欧洲规范的计算结果最为保守。     

Strength enhancements induced during cold forming of stainless steel sections

The material properties of stainless steel are sensitive to plastic deformation which causes an increase in yield strength by a process termed cold working. The different strain paths experienced around cold-formed cross sections during manufacture create unique material strength distributions for sections from different forming routes and also influence residual stress patterns. The research program presented herein has examined experimentally the material and residual stress distributions found in two types of cold-formed sections-cold-rolled box sections and press-braked angles. Predictive tools to harness the observed strength enhancements have been proposed and incorporated into models. Subsequent comparisons have shown that these strength enhancements, in particular those observed for cold-rolled box sections, should be employed in structural design to avoid considerable underestimation of member resistance.     

不锈钢构件截面的残余应力分析

对碳钢结构截面的残余应力的大小及分布的研究已经比较成熟,但是对不锈钢截面的残余应力研究却还很少见。不锈钢与碳钢有着不同的材料应力-应变特性和热性能,它们都影响着残余应力的形成。这意味着已确定的碳钢残余应力模型可能并不适合不锈钢。随着不锈钢的应用日益增多,对其残余应力的研究显得尤为重要。     

Numerical Modelling of Thin-Walled Stainless Steel Structural Elements in Case of Fire

In this paper, the structural response of stainless steel thin-walled elements submitted to fire is analysed numerically by means of the geometrically and materially non-linear Finite Element program SAFIR, including imperfections. In order to make these simulations, two main changes in the program were made: (i) the code was changed in order to deal with the stainless steel 2D material constitutive law to be used with shell elements and (ii) the possibility of the program to take into account residual stresses with shell finite elements was introduced. The stainless steel stress–strain relationship at high temperatures was based on the one presented in part 1.2 of Eurocode 3. To model the strain hardening exhibited by the stainless steels, using the shell element formulation, an approximation to the Eurocode 3 constitutive law was needed. Local and global geometrical imperfections were considered in the simulations. The paper shows the influence of the residual stresses on the ultimate load-carrying capacity of thin-walled stainless steel structural elements in case of fire.     

Class 4 stainless steel I beams subjected to fire

Structural elements composed of Class 4 sections are common in stainless steel buildings structures. These thin walled profiles are more susceptible to the occurrence of local buckling. Additionally, in beams the lateral-torsional buckling is also a common failure mode. These instability phenomena are intensified at high temperatures. This work has the main objective of presenting a numerical study on the fire behavior of beams with Class 4 stainless steel sections when subjected to pure bending and high temperatures. The influence of several parameters, as geometrical imperfections and residual stresses, on the ultimate load will be evaluated and comparisons between the numerical results and the Eurocode 3 rules will also be made.     

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.     

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.     

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.     

Flexural behaviour of stainless steel oval hollow sections

Structural hollow sections are predominantly square, rectangular or circular in profile. While square and circular hollow sections are often the most effective in resisting axial loads, rectangular hollow sections, with greater stiffness about one principal axis than the other, are generally more suitable in bending. Oval or elliptical hollow sections (EHS) combine the aesthetic external profile of circular hollow sections with the suitability for resisting flexure of rectangular sections, whilst also retaining the inherent torsional stiffness offered by all tubular sections. This paper examines the structural response of recently introduced stainless steel oval hollow sections (OHS) in bending and presents design recommendations. In-plane bending tests in the three-point configuration about both the major and minor axes were conducted. All tested specimens were cold-formed from Grade 1.4401 stainless steel and had an aspect ratio of approximately 1.5. The full moment-rotation responses of the specimens were recorded and have been presented herein. The tests were replicated numerically by means of non-linear finite element (FE) analysis and parametric studies were performed to investigate the influence of key parameters, such as the aspect ratio and the cross-section slenderness, on the flexural response. Based on both the experimental and numerical results, structural design recommendations for stainless steel OHS in bending in accordance with Eurocode 3: Part 1.4 have been made.     

GBT-based elastic–plastic post-buckling analysis of stainless steel thin-walled members

When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and materially non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress–strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner (Eng Struct 2009; 31(12): 3047–3058.). The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic–plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes - moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.     

A finite strip method for the elastic—plastic large dlisplacement analysis of thin-walled and cold-formed steel sections

A large deflection elastic—plastic analysis has been developed using the finite strip method of structural analysis to determine the non-linear local buckling behaviour of thin-walled and cold-formed sections in compression. The analysis accounts for plate geometric imperfections, the variation of yield stress around a section, the stress—strain characteristics of the material forming the section and complex patterns of residual stress produced by the cold-forming process.

The analysis is verified against reliable solutions for the non-linear buckling behaviour of plates and plate assemblies in axial compression and the non-linear overall buckling behaviour of a strut. The analysis is further compared with the results of plates with a rounded stress—strain curve typical of cold-formed steel and aluminium.     

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.     

Experimental and numerical investigation of high strength stainless steel structures

The paper summarises research on high strength stainless steel tubular structures conducted at the University of Hong Kong, and the Hong Kong University of Science and Technology. Square and rectangular hollow sections were investigated. The test specimens were cold-rolled from high strength austenitic and duplex stainless steel sheets. The material properties of the test specimens were determined by tensile coupon tests at normal room and elevated temperatures. The initial geometric imperfection and residual stress of the specimens were measured. The experimental and numerical investigation focused on the design and behaviour of cold-formed high strength stainless steel structural members. The results were compared with design strengths calculated using the American, Australian/New Zealand and European specifications for cold-formed stainless steel structures.     

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。     

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.     

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.     

Comparative experimental study of hot-rolled and cold-formed rectangular hollow sections

Square and rectangular hollow sections are generally produced either by hot-rolling or cold-forming. Cross-sections of nominally similar geometries, but from the two different production routes may vary significantly in terms of their general material properties, geometric imperfections, residual stresses, corner geometry and material response and general structural behaviour and load-carrying capacity. In this paper, an experimental programme comprising tensile coupon tests on flat and corner material, measurements of geometric imperfections and residual stresses, stub column tests and simple and continuous beam tests is described. The results of the tests have been combined with other available test data on square and rectangular hollow sections and analysed. Enhancements in yield and ultimate strengths, beyond those quoted in the respective mill certificates, were observed in the corner regions of the cold-formed sections—these are caused by cold-working of the material during production, and predictive models have been proposed. Initial geometric imperfections were generally low in both the hot-rolled and cold-formed sections, with larger imperfections emerging towards the ends of the cold-formed members—these were attributed largely to the release of through thickness residual stresses, which were themselves quantified. The results of the stub column and simple bending tests were used to assess the current slenderness limits given in Eurocode 3, including the possible dependency on production route, whilst the results of the continuous beam tests were evaluated with reference to the assumptions typically made in plastic analysis and design. Current slenderness limits, assessed on the basis of bending tests, appear appropriate, though the Class 3 slenderness limit, assessed on the basis of compression tests, seems optimistic. Of the features investigated, strain hardening characteristics of the material were identified as being primarily responsible for the differences in structural behaviour between hot-rolled and cold-formed sections.