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.     

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.     

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 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.     

基于试验和规范预测冷弯Z型钢组合柱的整体抗压性能

对冷弯型钢组合构件进行压缩试验,以确定比利时工程实践中的常用构件———双Z型钢柱的整体抗压性能。对8组4.45m的长柱进行全尺试验,并记录每个样本6个点处的平面外位移和应变。根据柱高中点处的线应变评估初始缺陷的影响。采用欧洲钢结构规范将所得到的极限性能和预测方法相结合。对预测分析中的假定以及规范中的差异进行了解释与探讨。由于范围受限,构件中的某些性能无法使用欧洲规范进行预测。还可使用北美规范进行冷弯型钢构件设计,其所提供的设计方法略有优势。提出了EN1993-1-3∶2006修正方法,以及基于直接强度法的设计方法。     

冷弯厚壁型钢残余应力影响分析

结合现有关于冷弯型钢残余应力的研究成果,用有限元软件模拟分析了在初始缺陷影响下,冷弯厚壁双槽钢柱焊接组合截面构件,在冷弯残余应力单独作用以及焊接残余应力和冷弯残余应力共同作用下的整体稳定性。分析发现:在焊接残余应力和冷弯残余应力共同作用下,厚壁轴心受压构件的整体稳定性能普遍比现有规范的结果低,最大误差达15%。因此在确定该构件稳定承载力时,应考虑焊接残余应力和冷弯残余应力的共同作用。     

Computational modeling of cold-formed steel

The objective of this paper is to provide an overview of computational modeling, both elastic buckling and nonlinear collapse analysis, for cold-formed steel members. Recent research and experiences with computational modeling of cold-formed steel members conducted within the first author's research group at Johns Hopkins University are the focus of the presented work. This admittedly biased view of computational modeling focuses primarily on the use of the semi-analytical finite strip method and collapse modeling using shell finite elements. Issues addressed include how to fully compare finite strip and finite element solutions, and the importance of imperfections, residual stresses, material modeling, boundary conditions, element choice, element discretization, and solution controls in collapse modeling of cold-formed steel. Examples are provided to demonstrate the expected range of sensitivity in cold-formed steel collapse modeling. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.     

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。     

焊接热切高强H型钢的残余应力

构件中所存在的残余应力会大大影响钢结构组件的刚度和疲劳寿命。虽然对于低碳钢的结构部件有较多的研究,但由于在常温和高温下应力-应变关系和材料属性的不同,造成了残余应力分布在高强钢构件中与低碳钢焊接而成的构件中的差异。因此,有必要研究由高强钢焊接而成的结构部件中残余应力的分布。对3个屈服强度460MPa的焊接热切高强型钢柱的残余应力进行研究,对不同横截面大小也进行了分析。使用切片法和钻孔法测量,并对两种方法所获得的残余应力进行比较。所测量的残余应力的大小和分布与碳钢中的一致,然而却有相对更小的残余应力比。最后,根据所测量的值,提出一个简化的由热切H型钢焊接而成的460MPa高强钢构件的残余应力分布。     

Strength and ductility of corner materials in cold-formed stainless steel sections

The cold work from the manufacturing process of cold-formed steel members can enhance the strength but reduce the ductility of materials. Due to a high cost of stainless steels, it is desirable to utilize this enhanced strength and avoid the early fracture in cold-formed stainless steel members. The paper is concerned with the prediction of the enhanced stress–strain behaviour and reduced ductility of corner materials in cold-formed stainless steel sections. The enhanced strength of corner materials has been traditionally determined using empirical models. However, most of these empirical models are only able to predict the enhanced 0.2% proof strength, but are neither capable of predicting the enhanced ultimate strength nor able to determine the reduced ductility. This paper first presents a modified weighted-average method for predicting the post-ultimate stress–strain behaviour and the fracture strain for stainless steels. An advanced numerical approach is next presented for predicting the full-range stress–strain behaviour of corner materials in cold-formed stainless steel sections, in which the modified weighted-average method is incorporated. The accuracy of this approach is demonstrated by comparing its predictions with test results. The proposed approach is generally applicable to cold-worked materials for predicting their enhanced strength, reduced ductility and full-range stress–strain behaviour. The proposed method and numerical results can explain why and how the ultimate strength of cold-formed steels can be increased and how the post-ultimate stress–strain behaviour can be utilized through cold working.     

Residual stress influence on material properties and column behaviour of stainless steel SHS

The paper describes the influence of forming-induced residual stresses in stainless steel SHS (Square Hollow Sections) on both the material itself and the behaviour of compressed members. The residual stress contribution to the stress–strain diagram concerning the initial modulus of elasticity and non-linearity is shown by the comparison of as-delivered and stress-relieved material. An analytical model covering the influence of residual stresses on material behaviour was developed and verified numerically. The FE study using the Abaqus software determines the influence of residual stresses in compressed members both on local and global buckling. Finally, the study on behaviour of member includes the influence of a varying degree of material non-linearity as an independent parameter representing the behaviour of various steels in long and stub columns with residual stresses.     

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.     

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.     

Numerical study of built-up double-Z members in bending and compression

The use of the finite element method (FEM) for the design of composed, thin-walled, structural steel members is considered. The bolted double-Z frame member is an interesting and economical engineering solution, already used in practice [1]. However, the European recommendations for the design of steel structures do not consider built-up members from cold-formed steel profiles. Finite element analysis is used to capture the various buckling effects that shape the response of slender thin-walled members. From the finite element model, the importance of initial imperfections and stiffness of connections is identified. The experimentally validated model predictions show that a non-linear finite element analysis can predict the member behaviour, in terms of failure mode and ultimate load, yield line pattern, overall stiffness and local strain in the cold-formed profiles. To obtain a good prediction, overall and localised initial imperfections should be considered and included in the analysis.     

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.     

厚壁冷弯方矩管和热轧H型钢轴压极限承载力的对比研究

运用ANSYS有限元软件,在综合考虑初始几何缺陷、残余应力、冷弯效应等因素的基础上,分析了厚壁冷弯方、矩钢管和热轧H型钢轴心压杆的极限承载力,并将它们的极限承载力计算结果进行对比,得出相关结论,为轻钢结构框架柱构件截面选型提供了参考.     

Experimental investigation of post-fire mechanical properties of cold-formed steels

Cold-formed steel members are widely used in residential, industrial and commercial buildings as primary load-bearing elements. During fire events, they will be exposed to elevated temperatures. If the general appearance of the structure is satisfactory after a fire event then the question that has to be answered is how the load bearing capacity of cold-formed steel members in these buildings has been affected. Hence after such fire events there is a need to evaluate the residual strength of these members. However, the post-fire behaviour of cold-formed steel members has not been investigated in the past. This means conservative decisions are likely to be made in relation to fire exposed cold-formed steel buildings. Therefore an experimental study was undertaken to investigate the post-fire mechanical properties of cold-formed steels. Tensile coupons taken from cold-formed steel sheets of three different steel grades and thicknesses were exposed to different elevated temperatures up to 800 °C, and were then allowed to cool down to ambient temperature before they were tested to failure. Tensile coupon tests were conducted to obtain their post-fire stress–strain curves and associated mechanical properties (yield stress, Young׳s modulus, ultimate strength and ductility). It was found that the post-fire mechanical properties of cold-formed steels are reduced below the original ambient temperature mechanical properties if they had been exposed to temperatures exceeding 300 °C. Hence a new set of equations is proposed to predict the post-fire mechanical properties of cold-formed steels. Such post-fire mechanical property assessments allow structural and fire engineers to make an accurate prediction of the safety of fire exposed cold-formed steel buildings. This paper presents the details of this experimental study and the results of post-fire mechanical properties of cold-formed steels. It also includes the results of a post-fire evaluation of cold-formed steel walls.     

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.     

偏心受压冷弯薄壁槽钢的卷边角度优化设计

为了使得钢结构的性能与用钢量比达到最优,前人对槽型钢的截面尺寸优化进行了较为充分的研究。但是,涉及卷边角度的优化特别是偏心受压工况下的优化分析却很缺乏。以Yao-Teng偏心受压计算公式,结合遗传算法,以冷弯卷边槽钢柱偏心受压为例,将槽钢卷边角度与偏心距作为设计变量,寻找在不同偏心距受压情况下,达到最大畸变屈曲临界应力的卷边角度。基于有限条分析程序,对两端简支与两端固支情况下不同截面尺寸构件的畸变屈曲临界应力进行了计算分析,最终得出不同偏心距受压下统一的最优卷边角度。为了方便工程设计人员设计时参考,建议卷边角度统一取为100°。     

A finite element analysis model for the behaviour of cold-formed steel members

A finite element analysis model for the post-local buckling behaviour of cold-formed steel (CFS) members subjected to axial compression has been developed. The finite element model consists of a Total Lagrangian nonlinear 9-node “assumed strain” shell finite element, and experimental-based material properties models to represent the body of the CFS sections. Experimentally derived residual stress variations, and initial geometric imperfections have also been incorporated. A special loading technique and a displacement solution algorithm were employed to obtain a uniform displacement condition at the loading edges. Details of a test program involving 20 non-perforated, and perforated cold-formed stub-column steel sections have been presented in the second part of the paper. The comparison between the test results, and the finite element results was performed for axial and lateral displacement behaviour, buckling loads, ultimate loads, and axial stress distribution. The comparison forms the basis for the evaluation of the efficiency, and the accuracy of the finite element model, and it indicated that the finite element analysis model constructed herein gives accurate and consistent results for the behaviour of the cold-formed steel members subjected to axial compression.