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.     

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.     

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。     

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.     

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.     

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。     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Numerical investigation of inelastic buckling of steel–concrete composite beams prestressed with external tendons

The ultimate resistance of a continuous composite beam is governed by either distortional lateral buckling or local buckling, or an interactive mode of the two which is sharply different from the torsional buckling mode in a bare steel beam. A finite element model is developed and based on the proposed FE model, inelastic finite element analysis of composite beams in negative bending is investigated, considering the initial geometric imperfection and the residual stress patterns and the FE results are found agree well with the test results. Parametrical analysis is carried out on the prestressed composite beams with external tendons in negative bending. Factors that influence load carrying performance and buckling moment resistance of prestressed composite beams are analyzed, such as initial geometric imperfection, residual stress in steel beams, force ratio, which is defined as the extent of prestressing force and negative reinforcement in the beams, as well as the slenderness ratios of web, flange, and beams. By varying cross-section parameters, 25 groups of composite beams under negative uniform bending with initial geometric imperfection, residual stress as well as different force ratios, 200 beams in total are studied by means of the FE method. The computed buckling moment ratios are drawn against the modified slenderness proposed by the authors and compared with the Chinese Codified steel column design curve. It is demonstrated that the tentative design method based on the Chinese Codified design curve can be used in assessment of buckling strength of composite beams in a term of the modified slenderness defined.     

Inelastic restrained distortional buckling of continuous composite T-beams

This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress-strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element.     

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。     

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.     

残余应力分布对焊接不锈钢工字形截面梁整体稳定性能的影响

焊接残余应力导致不锈钢梁截面纤维过早达到屈服,并严重降低不锈钢梁的抗弯刚度。为了研究残余应力对焊接工字形不锈钢梁侧扭屈曲的影响,根据目前被广泛采纳的不锈钢工字形截面残余应力分布模型,采用有限元方法,对残余应力分布模型的主要因素进行参数化分析,研究这些因素对不锈钢梁侧扭屈曲的影响,使对焊接工字形不锈钢梁的整体稳定性能的研究更加完善。结果表明:翼缘残余压应力峰值对不锈钢梁侧扭屈曲的影响最为显著。