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.     

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.     

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。     

Finite element simulation on mechanical and structural properties of cold-formed dimpled steel

The dimpling process is a novel cold-roll forming process that can enhance the steel material and structural performance by plastically deforming the material surface prior to the section forming operation [1]. Owing to the complex and interrelated nonlinear changes in contact, geometry and material properties that occur in the process and section forming, there have been no existing methods to simulate the process and resultant dimpled products and validate through physical measurements. This paper describes a numerical modelling approach and results into the mechanical properties and structural behaviour of cold-formed dimpled steel. A series of mechanical tests including tensile, plate bending and column compression tests on cold-formed plain and dimpled steel material were conducted for evaluation of numerical results. A finite element approach to practically simulate the dimpling process and experimental tests was presented. True stress–strain data obtained from tests were incorporated into nonlinear simulations of dimpled steel sheets and sections. The simulation of the dimpling process revealed that during the process, various levels of plastic strain are developed throughout the thickness of the steel sheet; this could correlate to the increase in the strength of the dimpled steel as observed in experimental tests and simulations. The simulation of the mechanical tests of dimpled specimens predicted similar results to the experiments, in terms of mechanical properties and structural behaviour. Since the finite element approach was able to successfully represent mechanical properties and structural behaviour of dimpled steel, it can be a powerful method in analysis and design of dimpled steel material and completed sections.     

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.     

Flange/web distortional buckling of cold-formed steel sections in bending

Recent experimental tests of cold-formed steel C- and Z-sections in bending have revealed unconservative results in the prediction of the bending moment resistance, using the current North American Design Standards. The failure mode of these tests was identified as flange/web distortional buckling. This mode of failure initially involves a rotation of the lip/flange component about the flange/web corner, which typically occurs for short half-wavelength distortional buckling. Near ultimate failure, an apparent lateral movement of the flange/web corner, which includes transverse bending of the web, is experienced. Various analytical methods that predict the moment resistance of sections which experience short half-wavelength distortional buckling were investigated and compared with the applicable test data. The modified Lau and Hancock 2 Model, with S136-94 Standard calculated effective section modulus, is recommended for use as the North American predictor model for the flange/web distortional buckling moment resistance of cold-formed steel sections in bending.     

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.     

Local buckling curves for the design of FRP profiles

Local buckling in FRP profiles is analyzed. Some experimental results in compression and bending, where local buckling of the flanges in compression occurred, are described and the critical stresses are summarized. A numerical model by the finite element method (FEM) is introduced and validated by comparison of the numerical results with the experimental ones. This finite element model is applied for a wide parametric analysis in order to individuate a buckling curve for the local buckling of the flange. An analytical expression of the buckling curve is developed, taking into consideration the orthotropy of the material, in which the restraint action of the web on the flange is explicitly introduced as a function of the geometrical and mechanical data of the section sub-components. The reliability of the proposed curve as a design tool is confirmed by comparison with the experimental results.     

Global instability of elliptical hollow section beam-columns under compression and biaxial bending

The global instability of elliptical hollow section members under combined compression plus biaxial bending is studied in this paper by means of laboratory testing and numerical simulations. A total of 9 beam-column tests were carried out under different combinations of compression and bending about both principal axes. The material properties of the tested sections were determined by means of tensile coupon tests. All tested elliptical hollow sections were EHS 150×75×5, and three nominal member lengths of 1 m, 2 m and 3 m were considered. Graphs of applied load versus mid-span bending moment, based on theoretical first and second order elastic considerations and the experimental second order inelastic response, are presented and described. Numerical models were initially validated against the experimental data using measured material and geometric properties, including imperfections. The models were subsequently employed in parametric studies to assess the influence of member slenderness and cross-sectional aspect ratio on the structural response. Finally, based on the experimental and numerical findings, design rules for hot-finished EHS beam-columns were assessed and statistically verified.     

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.     

Bending and torison of doubly symmetric core shear walls

A theoretical and experimental investigation of the flexural and torsional properties of doubly symmetric core shear walls, with lintel beams providing bracing across the openings at each storey level, is described. Such structures are used in tall buildings to support gravity loads and to resist horizontal forces induced by wind and earthquakes. The theoretical model developed is based on an equivalent closed section and is consistent with established open section and closed section behaviour at the two extremes of bracing. For intermediate bracing, the model incorporates the influences of bending and shear deformation of the bracing beams, out-of-plane bending of the side walls and continuousshear flow around the contour of the assumed equivalent closed section. The theoretical model is validated by a series of tests on perforated aluminium tubes, covering a wide range of lintel beam and effective side wall stiffnesses. The results indicate clearly that side wall distortion can reduce the torsional stiffness of such sections very significantly.     

复合材料腰梁受弯性能的试验研究

为在基坑支护中采用玻璃纤维复合材料(GFRP)腰梁取代传统材料腰梁,进行了材料性能试验和工字形、双背槽形两种截面形式梁的受弯试验,对GFRP梁的受力性能和破坏形态进行了研究.试验结果表明,材料性能、构件的稳定性以及腹板和翼缘连接处的局部受压应是GFRP构件设计分析的主要内容.复合材料腰梁截面形式的优化选取既要考虑满足稳...     

Bifurcation of locally buckled point symmetric columns—Experimental investigations

The bifurcation equations for locally buckled point symmetric sections are derived in a companion paper [Rasmussen KJR. Bifurcation of locally buckled point symmetric columns—analytical developments. Thin-walled Struct, submitted for publication]. In the present paper, two series of experiments are reported, one on narrow flange Z-sections and one on wide flange Z-sections. The main objective of the tests was to validate the bifurcation load predictions derived in [Rasmussen KJR. Bifurcation of locally buckled point symmetric columns—analytical developments. Thin-walled Struct, submitted for publication] against experimental values. A further objective of the tests on narrow flange sections was to investigate the change in the direction of overall buckling, as predicted by the theory, from principal axis directions to non-principal directions. A further objective of the tests on wide flange sections was to investigate the possible change of the critical overall buckling mode from a flexural mode to a torsional mode as a result of local buckling. Agreement is generally found between analytical and experimental results.     

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.     

Bending capacity of composite girders with Class 3 section

In this research, the flexural behaviour of composite girders under non-monotonic service loads and the bending capacity of composite girders with Class 3 section were studied through experimental work. Three specimens were fabricated and, through the 4-point flexural test, the stiffness and strength of the composite girder under hogging moments were observed. Test specimens were overhanging simple support beams, in total 6 m long. From the test results, the deflection, stiffness, moment-curvature relationship, and strain distribution of the composite girder section under service and ultimate loading were analyzed. The flexural behaviour under reloading-unloading cycles and tension stiffening effects on the mechanical behaviour of composite girders were discussed. The ultimate strength of composite girders with different Class flange sections and a same Class web section were also studied. Test results were analyzed by design equations in Eurocode 3 and 4 for flexural stiffness and sectional resistances. Also, a new simple design equation for the bending capacity of composite girders with Class 3 sections was suggested.     

自然老化作用下GFRP管材耐久性研究

通过试验测定GFRP管材建成的临时预应力网壳结构材料的纵向和横向剩余力学指标,并与管材的初始力学参数作比较,研究长期预应力以及老化作用对材料力学性质的影响,对材料的耐久性做出评价。研究结果表明,GFRP管材有较好的耐久性,纵向和横向弯曲弹性模量在长期低水平预应力(最高约30%极限承载力)和自然环境老化的作用下并没有显著的下降,但长期预应力的存在引起管材横向力学性能的退化和不稳定性,从而使截面椭圆化引起的纵向弯曲破坏更容易发生,引起材料纵向弯曲性能,尤其是纵向弯曲强度的退化和不稳定性。     

Column tests of cold-formed steel non-symmetric lipped angle sections

The geometry of angle sections is simple, but the behaviour and design calculations of angle sections can be quite complicated. Furthermore, lipped angle sections with unequal flange widths form a non-symmetric section and the behaviour of the section is even more complicated than a singly-symmetric angle section with equal flange widths. A test program on cold-formed steel non-symmetric lipped angle columns is presented. The non-symmetric angle sections were brake-pressed from high strength structural steel sheets having nominal yield stresses of 450 and 550 MPa with plate thicknesses of 1.0, 1.5 and 1.9 mm. The material properties of the column specimens were obtained by tensile coupon tests. The behaviour and strengths of cold-formed steel non-symmetric lipped angle columns were investigated. The test strengths are compared with the design strengths calculated using the North American Specification for the design of cold-formed steel structural members. In addition, the current design rules in the North American Specification for cold-formed steel non-symmetric lipped angle columns are assessed using reliability analysis. It is shown that the design strengths are generally quite conservative.     

Behavior of thin-walled circular hollow section tubes subjected to bending

Thin-walled steel circular hollow sections (CHSs) are widely used in wind turbine towers. The tower tubes are mainly subjected to bending. There have been a few experimental studies on the bending behavior of thin-walled CHS steel tubes. This paper describes a series of bending tests to examine the influence of section slenderness on the inelastic and elastic bending properties of thin-walled CHS. In addition, the influence of stiffeners welded in the steel tube is considered. Sixteen bending tests were performed up to failure on different sizes of CHS with diameter-to-thickness ratio (D/t) varying from 75 to 300. The experimental results showed that the specimens with small diameter-to-thickness ratios failed by extensive plastification on the central part of the tube. With the increase of diameter-to-thickness ratio, the local buckling phenomena became more pronounced. The stiffeners in the steel tubes increased the load carrying capacity and improved the ductility of the specimens. The experimental results were compared with current design guidelines on thin-walled steel members in AISC-LRFD, AS4100 and European Specification. It was found that the test results agreed well with the results based on AS4100 design code.