Numerical investigation of channel columns with complex stiffeners—part II: parametric study and design

A parametric study of cold-formed steel channel columns with complex stiffeners is performed using finite element analysis. An accurate and reliable finite element model is used for the parametric study in which different sizes of complex stiffeners are investigated. Column strengths predicted by the finite element analysis are compared with the unfactored design column strengths calculated using the American Specification and the Australian/New Zealand Standard for cold-formed steel structures. It is shown that the design strengths obtained from the specification and standard are generally conservative for fixed-ended cold-formed steel channel columns with complex stiffeners for the more slender sections having a plate thickness of 1 mm with the flat flange width to thickness ratio of 57, but unconservative for sections having a plate thickness of 2 mm with the flat flange width to thickness ratio of 27.     

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.     

Stub column tests of thin-walled complex section with intermediate stiffeners

A series of stub column tests on complex sections with intermediate stiffeners is presented in this paper. Initial geometric imperfections and material properties of the test specimens were measured. It is shown that the intermediate stiffeners could effectively enhance the local buckling stress of thin-walled sections. The test strengths are compared with the design strengths calculated using the direct strength method in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. It is shown that the direct strength method using finite strip method to obtain the buckling stresses is very conservative. Therefore, finite element method was used to predict the elastic buckling stresses. It is shown that the design strengths calculated using direct strength method based on the buckling stresses obtained from finite element analysis results generally agree with the test results well.     

Experimental and Numerical Study on Buckling Behavior of a Rigidly Stiffened Plate with Tee Ribs

In the bridge structures, stiffened plates are usually designed as rigidly stiffened when the orthotropic steel box girder is used as the main load-bearing structure. Therefore, the buckling mode of stiffened plates is plate buckling which occurs in subpanel supported by stiffeners. The orthotropic steel box girder is used as the main girder for Egongyan Rail Special Bridge, which is a self-anchored suspension bridge. Plates of the steel girder are rigidly stiffened with unequal spacing open ribs, and the most slender stiffened plate is the mid web stiffened with Tee ribs. In order to ensure the safety of the bridge, the buckling behavior of the web and orthotropic steel box girder under axial compression, including ultimate strength, post-buckling behavior and failure modes, should be clearly investigated by experimental and numerical methods. The design, loading and testing methods of the 1:4 scale model of the orthotropic steel box girder are introduced in detail firstly. The orthotropic steel box girder and the stiffened web finite element (FE) models are validated by the test results, and the effects of residual stress and the magnitude of geometric imperfections are discussed roughly. Based on the validated web FE model, a detailed parametric study is performed to systematically investigate the effects of residual stress and geometric imperfections on buckling behavior of the web. The effect of shapes of geometric imperfections discussed is highlighted. Through tracing stress states, the failure modes of stiffened plate are in agreement with the experimental phenomenon to some extent. Results show that shapes of geometric imperfections have significantly influenced post-buckling behavior and failure modes of the web, but slightly affected the ultimate strength. It is advised that residual stress and geometric imperfections should be controlled to make full use of excellent performance of steel materials.     

Ultimate strength of stiffened plates with a square opening under axial and out-of-plane loads

The high strength to weight ratio and high stiffness to weight ratio of stiffened plates find wide application in aircraft structures, ship structures, offshore oil platforms and lock gates. The strength and stability of stiffened plates is highly influenced by openings and initial imperfections. The main objective is to study the behaviour of stiffened steel plates with openings up to collapse and to trace the post-peak behaviour under axial and out-of-plane loads. Four stiffened steel plates with a square opening were fabricated for testing. Angle sections were used as stiffeners. Imperfections in the plate, stiffener and overall imperfection of the whole panel were measured. All fabricated panels were tested to failure. A finite element (FE) model was developed for the analysis of stiffened plates with initial imperfections and validated with the test results. Parametric studies were conducted using the developed FE model, and interaction curves and equations were developed for the design of stiffened plates with initial imperfections and openings. The interactive effect for stiffened panels with a square opening was found to be linear, with proportional reduction of the ultimate axial load carrying capacity due to the constant out-of-plane load.     

Behavior of stiffened liquid-filled conical tanks

Unreinforced steel conical-shaped containment vessels are frequently used in water tower applications. The failure of one of these structures in Fredericton, New Brunswick, Canada, several years ago, raises the question of whether there are adequate safety provisions for existing conical tanks. The aim of this investigation is to study the effect of welding rectangular-shaped longitudinal stiffeners to enhance the buckling capacity of existing conical tanks and to improve the design of new structures. The investigation is carried out numerically using an in-house developed shell element model that includes the effects of geometric and material non-linearities and accounts for geometric imperfections. The study focuses on two cases of tanks reinforced by longitudinal stiffeners in the lower region: the case of stiffeners free at their bottom edge, which would correspond to the retrofit of existing tanks; and the second having stiffeners anchored to the bottom slab of the tank, which can duplicate the situation of a new design. An extensive parametric study is conducted to assess the typical behavior of the two cases and to determine the critical imperfection shape that leads to the minimum buckling capacity of such type of stiffened shell structures. Finally, a comparison between the buckling capacity of unstiffened and longitudinally stiffened conical tanks that have the same volume of steel is conducted, revealing a major benefit of including stiffeners.     

Research on cold-formed steel columns

The paper summarises research on cold-formed steel columns performed by the author. Cold-formed steel members are either cold-rolled or brake-pressed into structural shapes. As a result, cold-formed steel open sections are usually singly-point- or non-symmetric. The most common types of singly-symmetric sections are channel and angle. The research focused on cold-formed steel open sections, such as plain and lipped channels, channels with simple and complex edge stiffeners as well as plain and lipped angles, and unequal angles. In addition, cold-formed steel built-up closed sections with intermediate stiffeners were investigated. Both experimental and numerical investigations into the strength and behaviour of cold-formed steel columns were conducted. The column strengths obtained from these investigations were compared with the design strengths obtained using various international standards for cold-formed steel structures. Furthermore, the behaviour and design of cold-formed steel lipped channel columns at elevated temperatures were also investigated. The paper also summarises the design recommendations for cold-formed steel columns.     

Numerical investigation of channel columns with complex stiffeners—part I: test verification

A numerical investigation on fixed-ended cold-formed steel channel columns with complex stiffeners subjected to axial load is described in this paper. The complex stiffeners of the channel sections consist of simple lips with return lips. The specimens were brake-pressed from high strength zinc-coated structural steel sheets having a nominal yield stress of 450 MPa. A non-linear finite element model is developed and verified against experimental results of fixed-ended channel columns with complex stiffeners. Initial geometric imperfections and material non-linearity are included in the model. The calibrated model is shown to provide accurate predictions of the experimental ultimate loads and failure modes of the tested columns.     

Strength of slender concrete filled high strength steel box columns

The use of thin walled steel sections coupled with concrete infill has been used on various building projects with great advantage. The currently available international standards for composite structures are limited to the design of concrete filled steel columns with compact sections. However, there is limited research work in the literature available which is concerned with slender concrete filled thin-walled steel columns. This paper presents a comprehensive experimental study of thin walled steel sections utilising high strength steel of a thin walled nature and filled with normal strength concrete. A numerical model is developed herein in order to study the behaviour of slender concrete filled high strength steel columns incorporating material and geometric non-linearities. For this analysis, the equilibrium of the member is investigated in the deformed state, using the idealised stress–strain relationships for both the steel and concrete materials, considering the elastic and plastic ranges. This paper presents both an experimental and theoretical treatment of coupled local and global buckling of concrete filled high strength steel columns sometimes termed interaction buckling. The experimental results of columns with high strength steel casings conducted herein by the authors are used for comparison. The effect of the confined concrete core is also addressed and the method shows good agreement with the experimental results of concrete filled steel columns with compact sections. The behaviour of concrete filled steel slender columns affected by elastic or inelastic local buckling is also investigated and compared with relevant experimental results. The paper then concludes with a design recommendation for the strength evaluation of slender composite columns using high strength steel plates with thin-walled steel sections, paying particular attention to existing codes of practice so as not to deviate from current design methodologies.     

带加劲肋的复杂截面薄壁柱的试验研究

进行了带加劲肋的复杂截面管柱的一系列试验研究。测量了试件的初始几何缺陷和材料特性。加劲肋能有效增强薄壁构件的局部稳定性。将试验强度与采用北美、澳大利亚、新西兰规范中针对冷弯型钢结构的直接强度法计算的设计强度进行对比,结果表明,采用有线条法确定屈曲荷载的直接强度法非常保守。因此,采用有限元法确定弹性屈曲荷载,结果表明,采用此直接强度法计算的设计强度与试验结果吻合较好。     

Analytical investigation of access holes in load-bearing diaphragms of steel box girders

This paper presents a series of parametric studies on the effect of access holes on the strength of the load-bearing diaphragms in steel box girder bridges. These parameters include the number of bearings, initial imperfections, the size and location of access holes, and the size of stiffeners around the openings. The load-bearing diaphragms were modeled using three-dimensional finite element analyses for material and geometric nonlinearities. It was found that the opening can be made large enough for practical purposes in order to provide convenient access to the inside of the box girder with no significant reduction in the ultimate strength of the load-bearing diaphragm. The location of the access hole has no detrimental effect on the diaphragm strength.     

Numerical investigation of longitudinally stiffened web channels predominantly in shear

In practice, there is a wide variety of commercially available channel sections with complex shapes where the web is stiffened by adding longitudinal intermediate stiffeners. These stiffeners may improve the shear capacity of the channels. Recently, the Direct Strength Method (DSM) of design of cold-formed sections has been extended in the North American Specification for Cold-Formed Steel Structural Members (NAS S100:2012) to include shear based on research by the authors. The prequalified sections include flat webs and webs with small intermediate longitudinal stiffeners. To extend the range to larger intermediate stiffeners as occurs in practice, a series of predominantly shear tests of lipped channel sections with one web stiffener of different shapes and various sizes has been performed at the University of Sydney. Six different types of stiffened web channel sections were tested along with an additional reference plain section. All tests were conducted with straps screwed on the top flanges adjacent to the loading points. These straps provide torsion/distortion restraints which may enhance the shear capacities of the sections. The test failures were observed mainly in the combined bending and shear modes. Numerical simulations based on the Finite Element Method (FEM) using the software package ABAQUS/Standard are also performed to compare with and calibrate against the tests. The accurate results from the FEM models allow extension of the test data. Based on the reliable FEM models, a series of FEM modelling of predominantly shear tests for stiffened web channels has been performed without straps attached to the top flanges adjacent to loading points. The test and FEM results are subsequently plotted against the DSM interaction curves between bending and shear where the interaction is found to be significant. An extended range of DSM prequalified sections with longitudinally stiffened web channels in shear is proposed in this paper.     

Effect of reinforcement stiffeners on square concrete-filled steel tubular columns subjected to axial compressive load

Eight stiffened square concrete-filled steel tubular (CFST) stub columns with slender sections of encasing steel and two non-stiffened counterparts were tested subjected to axial compressive load. Four types of reinforcement stiffeners and steel tensile strips were introduced to postpone local buckling of steel tubes, in which the tensile strip was first used as stiffener in CFSTs. The stiffening mechanism, failure modes of concrete and steel tubes, strength and ductility of stiffened square CFSTs were also studied during the experimental research. A numerical modeling program was developed and verified against the experimental data. The program incorporates the effect of the stiffeners on postponing local buckling of the tube and the tube confinement on concrete core. Extensive parametric analysis was also conducted to examine the influencing parameters on mechanical properties of stiffened square CFSTs.     

New launching method for steel bridges based on a self-supporting deck system: FEM and DOE analyses

This paper studies a new launching method for steel bridges based on a self-supporting deck system. This new and patent-protected procedure is able to launch bridges of a span length up to 150 m, in an economical and sustainable way. The use of the last span segments to reinforce the critical sections during launching replaces other conventional temporary means applied nowadays. The main objective of this research paper is to numerically analyse the best double deck configuration as well as to define an approach to stiffener distribution in order to avoid the patch loading phenomenon in the slender webs. With this in mind, the pre-design of a triangular cell along the low flange of each web is presented. A three dimensional finite element model (FEM) is built and the design of experiments technique (DOE) is applied to obtain the best bridge configuration. This new construction method can be used together with a continuous launching system in order to increase the velocity of the whole operation and to improve safety during launching. Very good results have been obtained, in terms of deflection, patch loading resistance and vertical load on the pushing device. The comparison with other different construction systems and the application to a real case allows us to ensure the viability of the method described.     

带加劲肋方钢管混凝土柱的静力特性

方钢管内填混凝土柱(CFSTs)在现代建筑中的使用越来越广泛,与钢柱和混凝土柱相比,其材料性能和功效均有所提高。然而,尽管方钢管混凝土柱的屈曲特性优于中空钢管,由于局部屈曲,其外包钢管截面的高厚比仍受到限制。针对外包钢管带加劲肋的方钢管混凝土柱,提出了一些新的加劲肋形式。为评估这些加劲肋对方钢管混凝土柱力学性能的影响,并与传统加劲肋进行比较,该文对4个带不同加劲肋的方钢管混凝土柱和1个无加劲肋方钢管混凝土柱进行了试验。试验研究了材料的抗力、延性和失效模式等力学性能,为了对试样的综合性能进行预测和总结,也从理论上对这些力学性能进行了研究。为了解各参数对力学性能的影响,该文进行了数值模拟和大量的参数研究,相关学者的试验数据验证了数值分析结果的准确性。基于试验结果和以往的研究,提出了截面强度的设计建议。     

Static behaviors of reinforcement-stiffened square concrete-filled steel tubular columns

Square concrete-filled steel tubes (CFSTs) are gaining increasing usage in modern construction practice, offering improved mechanical properties and increased material efficiency compared with the individual steel and core concrete components. However, the cross-section slenderness of the encasing steel is, although more inflexible than a comparable hollow steel tube, restrained due to local buckling. A number of innovative kinds of reinforcement stiffeners have been put forward particularly for the square CFSTs with slender sections of encasing steel. To investigate the mechanical effect of the reinforcement stiffeners and compare them with traditional ones in practice, four square CFSTs welded with various reinforcement stiffeners and one reference CFST have been tested, and are presented in this paper. The mechanical behaviors such as the resistance, ductility and failure modes investigated during the test were also studied in the theoretical research, which was carried out to predict and further summarize the comprehensive properties of the specimens. A numerical analysis program was written and verified with related scholars’ experimental data, and extensive parametric analysis was conducted to investigate the influencing parameters on mechanical properties. Design recommendation for the cross-section strength has been put forward based on the test results and previous research.     

Local buckling of steel equal angle members with normal and high strengths

Steel angle sections have been widely accepted with the development of steel structures, and such members made by high strength steel (HSS) sections are also increasingly used in buildings and bridges, and especially in transmission towers and long span trusses. Compared to normal strength steels, HSS exhibits different mechanical properties, which can cause different local buckling behavior. A finite element analysis (FEA) was performed in this paper to investigate the local buckling of steel equal angle members with different strengths under axial compression, where the residual stresses and the initial geometric imperfections of specimens were accurately described. Through this work, the relationship of the ultimate local buckling stress of steel equal angle members under axial compression as a function of steel strength and width-to-thickness ratio was established. By comparing the FEA results with the international design specifications (ANSI/AISC 360-10 and Eurocode 3), a modified design formula was developed and corresponding design suggestions were proposed, to take into account the effects of steel strength.     

对火灾中的铝结构进行局部屈曲分析:有限元模型

对温度升高时压力作用下的细长铝合金截面进行试验研究的结果已经表述在相关论文中。本文对这些试验进行了有限元模拟分析,为此构建了一个新的本构模型,用以计算火灾下的铝合金结构。从有限元模型中获得的临界温度与试验中得到的数据非常吻合(平均温差为1°C,标准偏差为7°C)。构建的有限元模型用于确定板的最大宽厚比,此时在板屈曲前已发生了完全的塑性变形。     

Inelastic behaviour and design of cold-formed channel sections in bending

The aim of this paper is to investigate the inelastic bending capacity of cold-formed channel sections, and provide design rules to account for such behaviour. An extensive experimental and analytical analysis of 42 cold-formed channel sections in three different geometric categories is conducted, including simple channel sections, channel sections with simple edge stiffeners and channel sections with complex edge stiffeners. The sections were cold-formed from G450 steel with nominal thickness of 1.6 mm, and varying theoretical buckling stresses ranging between elastic to seven times the yield stress. The results of the pure bending experimental investigations show that current international cold-formed steel specifications are conservative, for channel sections with low slenderness values. The experimental results are used to propose revisions to current international cold-formed steel specifications.     

Biaxially loaded high-strength concrete-filled steel tubular slender beam-columns,Part I: Multiscale simulation

The steel tube walls of a biaxially loaded thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-column may be subjected to compressive stress gradients. Local buckling of the steel tube walls under stress gradients, which significantly reduces the stiffness and strength of a CFST beam-column, needs to be considered in the inelastic analysis of the slender beam-column. Existing numerical models that do not consider local buckling effects may overestimate the ultimate strengths of thin-walled CFST slender beam-columns under biaxial loads. This paper presents a new multiscale numerical model for simulating the structural performance of biaxially loaded high-strength rectangular CFST slender beam-columns accounting for progressive local buckling, initial geometric imperfections, high strength materials and second order effects. The inelastic behavior of column cross-sections is modeled at the mesoscale level using the accurate fiber element method. Macroscale models are developed to simulate the load-deflection responses and strength envelopes of thin-walled CFST slender beam-columns. New computational algorithms based on the Müller's method are developed to iteratively adjust the depth and orientation of the neutral axis and the curvature at the column's ends to obtain nonlinear solutions. Steel and concrete contribution ratios and strength reduction factor are proposed for evaluating the performance of CFST slender beam-columns. Computational algorithms developed are shown to be an accurate and efficient computer simulation and design tool for biaxially loaded high-strength thin-walled CFST slender beam-columns. The verification of the multiscale numerical model and parametric study are presented in a companion paper.