Ultimate capacity of battened columns composed of four equal slender angles

Cold-formed steel structural members play a great role in modern steel structures due to their high strength and light weight. The behavior and strength of battened column members composed of slender angle sections are mainly governed by local buckling of angle legs or torsional buckling of the angle between batten plates. Moreover, local buckling depends on the interaction between the width–thickness ratio of angle leg, overall slenderness ratio of angle between batten plates and overall slenderness of column. Theoretical study has been carried out by a nonlinear material and geometrical finite element model. Numerous cases of slender battened column sections having different width–thickness angle leg ratios, overall slenderness ratios between batten plates and overall slenderness ratios are chosen in this study. Complete ultimate strength curves are drawn and different failure modes are studied by taking different member lengths, which produce local or torsional buckling of single angles between batten plates or overall buckling of the member. Empirical equations for the effect of shear deformation factor and the ultimate axial load capacities of members formed of battened slender angle sections are proposed. Strengths of axially loaded battened members predicted using finite element as well as the proposed empirical equations is compared with the design strengths obtained using North American and European codes. It is concluded that the design strengths predicted by North American and European codes are generally conservative, and these design rules have been shown to be reliable using reliability analysis.     

Q460高强钢焊接箱形截面轴压构件整体稳定性能研究

为研究高强度钢材轴心受压钢柱的整体稳定性能,对5个国产Q460钢材焊接箱形截面柱进行了轴心受压试验研究。试验对试件的几何初弯曲、荷载初偏心以及截面的纵向残余应力分布均进行了测量。基于试验结果,分析了该类钢柱的失稳破坏形态和整体稳定承载力,建立了有限元分析模型并对试验结果进行模拟计算。研究结果表明：试件破坏模态均为整体弯曲失稳形态,大部分试件稳定承载力高于规范设计值;有限元分析模型能够准确地考虑几何初始缺陷和残余应力的影响,计算结果与试验结果吻合良好;通过与国内外钢结构设计规范的对比,提出了国产Q460高强钢焊接箱形截面轴压构件整体稳定设计的建议方法,即可以统一采用我国或欧洲规范的b类曲线进行设计,而不需要按板件宽厚比大小进行分类。     

Q460高强钢焊接工字形截面简支梁整体稳定性能与设计方法研究

为研究Q460高强钢焊接工字形截面简支梁的整体稳定性能,对跨中无侧向支撑的3个双轴对称和6个单轴对称焊接工字形截面简支梁进行了整体弯扭屈曲试验。实测了试件的截面残余应力和初始几何缺陷,并分析其整体弯扭屈曲变形特征和稳定承载力。建立考虑残余应力和初始几何缺陷的有限元模型对简支梁受力进行了模拟,模拟结果与试验结果吻合良好,基于试验验证的有限元模型计算了大量不同截面尺寸和跨度的Q460高强钢焊接工字形截面简支梁的整体稳定承载力。将试验和有限元参数分析结果与GB 50017—2017《钢结构设计标准》、JGJ/T 483—2020《高强钢结构设计标准》、欧洲规范EN 1993-2005和美国规范ANSI/AISC 360-2016的简支梁整体稳定系数公式的计算结果进行比较,结果表明GB 50017—2017和ANSI/AISC 360-2016的计算结果偏于不安全,EN 1993-2005的计算结果过于保守,JGJ/T 483—2020的计算结果偏于安全且最为接近。最后,在JGJ/T 483—2020的简支梁整体稳定系数计算公式基础上引入增大系数,并根据截面高宽比的不同,取用不同的长细比指数对该公式予以修正,修正后的公式更适用于Q460高强钢焊接工字形截面简支梁的设计计算。     

Ultimate compressive strength of plate elements in aluminium: Correlation of finite element analyses and tests

A study with the objective of assessing the reliability of non-linear finite element analyses in predictions of the ultimate strength of aluminium plates subjected to in-plane compression is presented. Outstand elements of alloy AA6082 in tempers T4 and T6 and internal elements of alloys 5083 M and 6082 TF were analysed for a range of b/t-ratios. For the latter class both non-welded and welded plates were studied, the non-welded plates having two levels of geometric imperfections. The accuracy of the predictions was evaluated by comparison with existing experimental results. It was found that the overall correlation between the experimental and predicted ultimate compressive strengths was good. The finite element analyses reproduced the main effects of slenderness, stress-strain curve (i.e. alloy and temper), geometric imperfections and welding (i.e. residual stresses and heat-affected zones) that were observed in the experiments     

Design of cold-formed steel unequal angle compression members

Cold-formed steel unequal angles are non-symmetric sections. The design procedure of non-symmetric sections subjected to axial compression load could be quite difficult. The unequal angle columns may fail by different buckling modes, such as local, flexural and flexural–torsional buckling as well as interaction of these buckling modes. The purpose of this study is to investigate the behaviour and design of cold-formed steel unequal angle columns. A nonlinear finite element analysis was conducted to investigate the strength and behaviour of unequal angle columns. The measured initial local and overall geometric imperfections as well as the material properties of the angle specimens were included in the finite element model. The finite element analysis was performed on fixed-ended columns for different lengths ranged from stub to long columns. It is demonstrated that the finite element model closely predicted the experimental ultimate loads and the behaviour of cold-formed steel unequal angle columns. Hence, the model was used for an extensive parametric study of cross-section geometries. The column strengths obtained from the parametric study were compared with the design strengths calculated using the North American Specification for cold-formed steel structural members. It is shown that the current design rules are generally unconservative for short and intermediate column lengths for the unequal angles. Therefore, design rules of cold-formed steel unequal angle columns are proposed.     

Investigation of concrete encased steel composite columns at elevated temperatures

This paper presents a nonlinear 3-D finite element model investigating the behaviour of concrete encased steel composite columns at elevated temperatures. The composite columns were pin-ended axially loaded columns having different cross-sectional dimensions, different structural steel sections, different coarse aggregates and different load ratios during fire. The nonlinear material properties of steel, concrete, longitudinal and transverse reinforcement bars as well as the effect of concrete confinement at ambient and elevated temperatures were considered in the finite element models. The interface between the steel section and concrete, the longitudinal and transverse reinforcement bars, and the reinforcement bars and concrete were also considered allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the column. The initial overall (out-of-straightness) geometric imperfection was carefully included in the model. The finite element model has been validated against published tests conducted at elevated temperatures. The time–temperature relationships, deformed shapes at failure, time–axial displacement relationships, failure modes and fire resistances of the columns were evaluated by the finite element model. It has been shown that the finite element model can accurately predict the behaviour of the columns at elevated temperatures. Furthermore, the variables that influence the fire resistance and behaviour of the composite columns comprising different load ratios during fire, different coarse aggregates and different slenderness ratios were investigated in parametric studies. It is shown that the fire resistance of the columns generally increases with the decrease in the column slenderness ratio as well as the increase in the structural steel ratio. It is also shown that the time–axial displacement relationship is considerably affected by the coarse aggregate. The fire resistances of the composite columns obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite columns at elevated temperatures. It is shown that the EC4 is conservative for all the concrete encased steel composite columns, except for the columns having a load ratio of 0.5 as well as the columns having a slenderness ratio of 0.69 and a load ratio of 0.4.     

Structural performance of cold-formed high strength stainless steel columns

This paper describes an accurate finite element model for the structural performance of cold-formed high strength stainless steel columns. The finite element analysis was conducted on duplex stainless steel columns having square and rectangular hollow sections. The columns were compressed between fixed ends at different column lengths. The effects of initial local and overall geometric imperfections have been taken into consideration in the finite element model. The material nonlinearity of the flat and corner portions of the high strength stainless steel sections were carefully incorporated in the model. The column strengths and failure modes as well as the load-shortening curves of the columns were obtained using the finite element model. Furthermore, the effect of residual stresses in the columns was studied. The nonlinear finite element model was verified against experimental results. An extensive parametric study was carried out using the verified finite element model to study the effects of cross-section geometries on the strength and behaviour of cold-formed high strength stainless steel columns. The column strengths predicted from the parametric study were compared with the design strengths calculated using the American Specification, Australian/New Zealand Standard and European Code for cold-formed stainless steel structures. The results of the parametric study showed that the design rules specified in the American, Australian/New Zealand and European specifications are generally conservative for cold-formed high strength stainless steel square and rectangular hollow section columns, but unconservative for some of the short columns.     

Nonlinear behaviour of eccentrically loaded FR concrete-filled stainless steel tubular columns

This paper investigates the nonlinear behaviour of eccentrically loaded fibre reinforced (FR) concrete-filled stainless steel tubular composite columns. A nonlinear 3-D finite element model for the axially loaded composite columns, recently reported by the author, was extended to study the structural performance of the eccentrically loaded composite columns. The columns were pin-ended subjected to an eccentric load acting along one axis. The model accounted for the inelastic behaviour of the composite column components, effect of FR concrete confinement and interface between the stainless steel section and concrete. The measured initial local and overall geometric imperfections were carefully incorporated in the model. The finite element model has been validated against tests previously reported by the author. Furthermore, the variables that influence the eccentrically loaded composite column behaviour and strength comprising different eccentricities, different column slenderness and different concrete strengths were investigated in an extensive parametric study comprising 72 columns. The composite column strengths and moment resistances predicted from the finite element analysis were compared with the design composite column strengths and moment resistances calculated using the Eurocode 4. The study has shown that finite element modelling could effectively assess the accuracy of the design rules in current codes of practice.     

Numerical simulation of concrete encased steel composite columns

This paper investigates the behaviour of pin-ended axially loaded concrete encased steel composite columns. A nonlinear 3-D finite element model was developed to analyse the inelastic behaviour of steel, concrete, longitudinal and transverse reinforcement bars as well as the effect of concrete confinement of the concrete encased steel composite columns. The interface between the steel section and concrete, the longitudinal and transverse reinforcement bars, and the reinforcement bars and concrete were also considered that allowed the bond behaviour to be modeled and the different components to retain their profile during the deformation of the column. Furthermore, the initial overall (out-of-straightness) geometric imperfection was carefully incorporated in the model. The finite element model has been validated against published experimental results. The main objective of the study was to understand the structural response and modes of failure of the columns and to assess the composite column strengths against current design codes. The study covered slender, non-slender, stub and long concrete encased steel composite columns. The concrete strengths varied from normal to high strength (20-110 MPa). The steel section yield stresses also varied from normal to high strength (275-690 MPa). Furthermore, the variables that influence the composite column behaviour and strength comprising different slenderness ratios, concrete strength and steel yield stress were investigated in a parametric study. It is shown that the increase in structural steel strength has a small effect on the composite column strength for the columns having higher relative slenderness ratios due to the flexural buckling failure mode. The composite column strengths obtained from the finite element analysis were compared with the design strengths calculated using the American Institute for Steel Construction AISC and Eurocode 4 for composite columns. Generally, it is shown that the EC 4 accurately predicted the design strength for the concrete encased steel composite columns having a concrete cylinder strength of 30 MPa and structural steel yield stresses of 275 and 460 MPa, which are in the limits of the code, which otherwise, was generally conservative. The AISC predictions were quite conservative for all the concrete encased steel composite columns.     

Experimental investigation of load carrying capacity of the slender reinforced concrete columns wrapped with FRP

Axial compression test was conducted on 6 elliptical modified rectangular slender reinforced concrete columns wrapped with FRP, with a slenderness ratio L/b ranging between 4.5 and 17.5. The test result showed that the effect of the slenderness ratio on the load carrying capacity of FRP-wrapped concrete columns is more significant than that of ordinary reinforced concrete columns. The strengthening effect decreases with increase of the slenderness ratio. When the slenderness ratio is less than 17.5, the load carrying capacity of FRP-wrapped columns is still 20% higher than that of ordinary reinforced concrete column. The columns were then successfully analyzed with the commercial finite element software ANSYS, taking into account of the constitutive relationship of concrete reinforced with FRP, the failure criterion and the initial geometrical imperfections. The effect of the cross-sections, steel ratio and the confinement ratio is investigated and a simplified formula for the stability coefficient to facilitate design of FRP-wrapped columns is derived.     

Experimental investigation of the overall buckling behaviour of 960 MPa high strength steel columns

Investigations of the mechanical performance of high strength steel structures have become a research hotspot in civil and structural engineering, and existing experimental studies of their overall buckling behaviour have hitherto focused mainly on columns fabricated from either 460 MPa or 690 MPa steels. The present study describes an experimental programme including six pin-ended 960 MPa steel columns under axial compression. Both welded I- and box-section specimens are considered. The initial geometric imperfections and cross-sectional residual stresses are reported, with the axial loading, deformation and the strain distributions at the mid-length section being monitored during the testing. The buckling mode is clarified, and the buckling capacity is compared with design results according to current national design codes. Based on the experimental results, a finite element model is described and validated, and then used to perform a large number of parametric studies, considering different cross-sectional dimensions and column slendernesses. It is found that all specimens failed by overall flexural buckling, and the corresponding column curves in current design codes underestimate the dimensionless buckling strength of 960 MPa steel columns. Higher and more adequate column curves are suggested for such columns, and new column curves are proposed based on a non-linear fitting of the parametric results.     

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.     

Experimental investigation of built-up cold-formed steel section battened columns

This paper presents an experimental investigation on behaviour and design of built-up cold-formed steel section battened columns. The built-up columns were pin-ended and consisted of two cold-formed steel channels placed back-to-back at varied spacing of intersection. The two channels were connected using batten plates, with varying longitudinal spacing. The cold-formed steel channel sections were manufactured by brake-pressing flat strips having a plate thickness of 2 mm. The built-up cold-formed steel section battened columns had different slenderness and geometries but had the same nominal length of 2200 mm. The column strengths, load–axial shortening, load–lateral displacement and load–axial strain relationships were measured in the tests. In addition, the failure modes and deformed shapes at failure were observed in the tests and reported in this paper. Overall, the built-up column tests provided valuable experimental data regarding the column behaviour that compensated the lack of information on this form of construction as well as used to develop nonlinear 3-D finite element models. The column strengths measured experimentally were compared against design strengths calculated using the North American Specification, Australian/New Zealand Standard and European Code for cold-formed steel columns. Generally, it is shown that the specifications were unconservative for the built-up cold-formed steel section battened columns failing mainly by local buckling, while the specifications were conservative for the built-up columns failing mainly by elastic flexural buckling.     

高强度钢材轴心受压钢柱整体稳定性能的缺陷影响研究

为研究高强度钢材轴心受压构件的整体稳定受力性能,了解构件的几何初始缺陷和截面残余应力对其屈曲强度和失稳变形的影响,以及与普通强度钢材轴压杆相比高强度钢材柱的整体稳定性能对缺陷敏感性的变化,采用有限元方法进行数值模拟计算,通过变换几何初始缺陷系数、残余应力数值大小和钢材强度等参数,对计算结果进行对比分析。研究结果表明,随着钢材强度的提高,高强度钢材轴压杆的整体屈曲强度对初始缺陷的敏感性明显降低,特别是对残余应力分布的敏感性;此外,初始缺陷的影响还与构件的长细比有直接关系。研究工作进一步揭示了高强度钢材轴压柱整体稳定性能的特点和优势。     

单伸臂梁和双跨连续梁的整体稳定性能分析

利用ANSYS有限元程序对单轴对称工字形单伸臂梁和双跨连续梁整体稳定试验进行了有限元模拟。分析中考虑了材料非线性、初始几何缺陷及残余应力的影响,提出了合理的有限元分析模型与网格划分密度,分析结果与试验结果吻合较好。研究表明,截面类型、荷载作用位置、加荷比例以及梁段的跨度比对构件的稳定承载力影响显著,焊接残余应力对构件的整体稳定承载力影响不可忽视。采用有限元模型能够有效地模拟构件的实际受力状态,可以用来进行大量的参数分析,从而取代复杂的物理试验。     

Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners

This paper presents an experimental investigation and a finite element analysis on cold-formed channels with inclined simple edge stiffeners compressed between pinned ends. Compression tests of pin-ended channel columns with inclined simple edge stiffeners have not been performed till now. A total of 36 channel specimens including three different cross sections with different edge stiffener inclined angles and column lengths were tested. Detailed measurements of initial geometric imperfections and material properties of the specimens were also conducted before the above tests. Failure modes include local buckling, distortional buckling, flexural buckling and interaction among these buckling modes were observed in tests. The results indicate that inclined angle and loading position significantly affect the ultimate load-carrying capacity and failure mode of specimens. Moreover, a non-linear finite element model was developed and verified against tests. Geometric and material non-linearities were included in the model. Results from the finite element analysis agree well with experimentally ultimate loads and failure modes. However, it should be improved on prediction for certain displacement.     

高强度Q690钢柱受火后受力性能试验研究

为了获得高强度Q690钢柱受火后的受力性能,采用电炉将2根高强度Q690钢焊接H形截面柱升温至800℃后自然冷却至常温,对受火后钢柱进行受压试验,得到钢柱的承载力和破坏模式。为考察受火对钢柱承载力的影响,对2根同尺寸不受火钢柱也进行受压试验。使用ABAQUS软件建立了试验钢柱有限元模型,考虑钢材受火后力学性能的退化和截面残余应力的影响,模拟试验构件的结构响应,并与试验结果进行对比。研究表明:钢柱均发生了绕弱轴的整体失稳破坏;经800℃受火作用后的钢柱承载力与不受火相比降低30%左右;有限元分析结果与试验结果吻合良好。进而采用有限元模型分析受火温度、冷却方式、长细比等参数对受火后Q690钢柱整体稳定系数的影响,有限元分析发现:受火后Q690钢柱稳定系数随受火温度升高呈先增大后减小的趋势,转折点为800℃左右;受火温度较低时冷却方式对Q690钢柱稳定系数影响较小,受火温度高于800℃后影响显著;受火后Q690钢柱稳定系数随长细比增大而降低,长细比小于80时,降低幅度较大,长细比超过80时,降低幅度减小。     

焊接T形截面轴心压杆的弯扭屈曲

《钢结构设计规范》(GB50017-2003)提出采用换算长细比法对单轴对称截面绕对称轴失稳按弯扭屈曲计算,该方法是否合理,各文献看法不一。借助有限元分析软件对焊接T形截面压杆的弯扭屈曲进行了几何非线性与物理非线性分析,考虑残余应力和几何缺陷的影响,并与“规范”(GB50017-2003)计算结果相比较。结果表明:规范值和文中计算结果吻合较好,规范是合理的、安全的、经济的。     

An approach for evaluating fire resistance of high strength Q460 steel columns

To develop a methodology for evaluating fire resistance of high strength Q460 steel columns, the load bearing capacity of high strength Q460 steel columns is investigated. The current approach of evaluating load bearing capacity of mild steel columns at room temperature is extended to high strength Q460 steel columns with due consideration to high temperature properties of high strength Q460 steel. The critical temperature of high strength Q460 steel column is presented and compared with mild steel columns. The proposed approach was validated by comparing the predicted load capacity with that evaluated through finite element analysis and test results. In addition, parametric studies were carried out by employing the proposed approach to study the effect of residual stress and geometrical imperfections. Results from parametric studies show that, only for a long column (slenderness higher than 75), the magnitude and distribution mode of residual stress have little influence on ultimate load bearing capacity of high strength Q460 steel columns, but the geometrical imperfections have significant influence on any columns. At a certain slenderness ratio, the stability factor first decreases and then increases with temperature rise.     

钢管混凝土平缀管格构柱换算长细比计算方法

分析了现有钢管混凝土平缀管格构柱换算长细比计算方法的假定条件和计算式,并将各方法计算的极限承载力与试验结果进行对比;以格构柱剪切柔度理论为基础,对钢管混凝土平缀管格构柱各变形项与总剪切变形量的比值进行分析,指出现有换算长细比计算方法的不合理之处。借鉴钢管混凝土（斜缀条）格构柱换算长细比乘法算法的计算思路,在剪切系数计算式中采用考虑节点构造参数影响的剪切柔度简化计算式,拟合得到放大系数与剪切系数的关系式。结果表明:采用所提出的换算长细比计算方法及GB 50923—2013中稳定系数计算方法得到的计算结果与试验结果吻合良好,证明该方法简单、实用且具有足够的精度。