Nonlinear analysis of circular concrete-filled steel tubular short columns under axial loading

The confinement effect provided by the steel tube in a circular concrete-filled steel tubular (CFST) short column remarkably increases the strength and ductility of the concrete core. The reliable prediction using nonlinear analysis methods for circular CFST columns relies on the use of accurate models for confined concrete. In this paper, accurate constitutive models for normal and high strength concrete confined by either normal or high strength circular steel tubes are proposed. A generic fiber element model that incorporates the proposed constitutive models of confined concrete is created for simulating the nonlinear inelastic behavior of circular CFST short columns under axial loading. The generic fiber element model developed is verified by comparisons of computational results with existing experimental data. Extensive parametric studies are conducted to examine the accuracy of various confining pressure models and the effects of the tube diameter-to-thickness ratio, concrete compressive strengths and steel yield strengths on the fundamental behavior of circular CFST columns. A new design formula accounting for concrete confinement effects is also proposed for circular CFST columns. It is demonstrated that the generic fiber element model and design formula adequately predict the ultimate strength and behavior of axially loaded circular CFST columns and can be used in the design of normal and high strength circular CFST columns.     

Nonlinear analysis of circular concrete-filled steel tubular short columns under eccentric loading

This paper presents an effective theoretical model for the nonlinear inelastic analysis of circular concrete-filled steel tubular (CFST) short columns under eccentric loading. Accurate material constitutive relationships for normal and high strength concrete confined by either normal or high strength circular steel tubes are incorporated in the theoretical model to account for confinement effects that increase both the strength and ductility of concrete. The predicted ultimate bending strengths and complete moment-curvature responses of circular CFST columns under eccentric loading are compared with existing experimental results to examine the accuracy of the theoretical model developed. The fundamental behavior of circular CFST beam-columns with various diameter-to-thickness ratios, concrete compressive strengths, steel yield strengths, axial load levels and sectional shapes is studied using the verified theoretical model. Based on extensive numerical studies, a new design model for determining the ultimate pure bending strengths of circular CFST beam-columns is proposed. The theoretical model and formulas developed are shown to be effective simulation and design tools for the nonlinear inelastic behavior of circular CFST beam-columns under eccentric loading.     

Performance-based analysis of concrete-filled steel tubular beam-columns, Part I: Theory and algorithms

This paper presents a performance-based analysis (PBA) technique based on fiber element formulations for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects. Geometric imperfections, residual stresses and strain hardening of steel tubes and confined concrete models are considered in the PBA technique. Initial local buckling and effective strength/width formulas are incorporated in the PBA program to account for local buckling effects. The progressive local buckling of a thin-walled steel tube filled with concrete is simulated by gradually redistributing normal stresses within the steel tube walls. Performance indices are proposed to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam-columns under axial load and biaxial bending. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a thin-walled CFST beam-column section to satisfy equilibrium conditions. The analysis algorithms for thin-walled CFST beam-columns under axial load and uni- and biaxial bending are presented. The PBA program can efficiently generate axial load-strain curves, moment-curvature curves and axial load-moment strength interaction diagrams for thin-walled CFST beam-columns under biaxial loads. The proposed PBA technique allows the designer to analyze and design thin-walled CFST beam-columns made of compact or non-compact steel tubes with any strength grades and normal and high-strength concrete. The verification and applications of the PBA program are given in a companion paper.     

Strength and ductility of high strength concrete-filled steel tubular beam-columns

The ultimate strength and ductility of high strength thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects, are investigated in this paper, using a performance-based analysis (PBA) technique. The PBA technique accounts for the effects of geometric imperfections, residual stresses, strain hardening, local buckling and concrete confinement on the behavior of high strength thin-walled CFST beam-columns. The accuracy of the PBA technique is further examined by comparisons with experimental results. The PBA program is employed to study the effects of depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility of high strength thin-walled CFST beam-columns under combined axial load and biaxial bending. The results obtained indicate that increasing the depth-to-thickness ratio and axial load levels significantly reduces the stiffness, strength and ductility of CFST beam-columns. Increasing concrete compressive strengths increases the stiffness and strength, but reduces the axial ductility and section performance of CFST beam-columns. Moreover, the steel yield strength has a significant effect on the section and strength performance of CFST beam-columns but does not have a significant effect on their axial and curvature ductility.     

轴力和双向受弯作用下短钢管混凝土梁柱的非线性分析

提出一种非线性纤维元分析法用于确定在轴力和双向受弯作用下短钢管混凝土梁柱的轴力-弯曲强度的交互图。针对被约束混凝土和结构钢的非线性本构模型对组合截面中性轴深度和方向采用有效正切算法进行迭代,以满足平衡条件。通过纤维单元分析结果与试验数据和现有解决方案的对比,验证了纤维元分析程序的有效性。采用该程序研究含钢量、混凝土抗压强度和钢屈服强度对于轴力-弯曲交互作用和钢管混凝土梁柱的影响。     

Nonlinear analysis of concrete-filled square stainless steel stub columns under axial compression

Concrete-filled stainless steel tubes (CFSST) can be considered as a new and innovative kind of composite construction technique, and have the potential to be used extensively in civil engineering. This paper employs a nonlinear analysis of square CFSST stub columns under axial compression. A three-dimensional nonlinear finite element (FE) model is developed using ABAQUS, where nonlinear material behaviour, enhanced strength corner properties of steel, and initial geometric imperfections are included. Close agreement is achieved between the test and FE results in terms of load-deformation response and ultimate strength. In light of the numerical results, the behaviour of stainless steel composite columns is compared with that of carbon steel composite columns. A simple model is proposed to calculate the ultimate strength of square CFSST stub columns.     

Investigation of FRP strengthened circular columns under biaxial bending

This paper presents the analysis and design of cylindrical reinforced concrete (RC) columns confined with fiber reinforced polymer (FRP) composites. The columns studied are under combined axial loads and biaxial bending moments. The fiber method modeling (FMM) together with finite element analysis (FEA) are adopted to investigate the behavior of such columns. The procedure finds the inclination and depth of the neutral axis that satisfy the equilibrium conditions. Moreover, the proposed analysis is capable of solving slender columns under biaxial bending through a developed computer program. The finite element derivation of a general stiffness matrix that accounts for the loss of symmetry of the cross-section due to material nonlinearity and biaxial moments is presented herein. The derivation starts from the principle of virtual work and develops an updated Lagrangian procedure for geometric nonlinear analysis. It should be noted that the stiffness for an elastic-plastic cross-section is a function of the current state and the past history of the strain of the column section as well as the stress-strain relations for each of concrete, steel and the fibers used. Therefore the cross-section is partitioned into a number of small elemental areas and a step-by-step application of the force-deformation equilibrium equation is applied. Interaction diagrams for columns under uniaxial bending are plotted and compared with experimental results conducted in the literature review. Moreover, contour lines for columns under biaxial bending are plotted. A parametric study was carried out to investigate the effect of various parameters on the strength of the column. The parameters include unconfined concrete strength, type of FRP used, thickness of FRP and the column height to the cross-sectional diameter (H/D) ratio. The developed diagrams provide the designer with an easy and reliable way to analyze and design such columns.     

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

Effective flexural stiffness of slender reinforced concrete columns under axial forces and biaxial bending

Most of the design codes (ACI-318-2008 and Euro Code-2-2004) propose the moment magnifier method in order to take into account the second order effect to design slender reinforced concrete columns. The accuracy of this method depends on the effective flexural stiffness of the column. This paper proposes a new equation to obtain the effective stiffness EI of slender reinforced concrete columns. The expression is valid for any shape of cross-section, subjected to combined axial loads and biaxial bending, both for short-time and sustained loads, normal and high strength concretes, but it is only suitable for columns with equal effective buckling lengths in the two principal bending planes. The new equation extends the proposed EI equation in the “Biaxial bending moment magnifier method” by Bonet et al. (2004) [6], which is valid only for rectangular sections. The method was compared with 613 experimental tests from the literature and a good degree of accuracy was obtained. It was also compared with the design codes ACI-318 (08) and EC-2 (2004) improving the precision. The method is capable to verify and design with sufficient accuracy slender reinforced concrete columns in practical engineering design applications.     

Local buckling of steel plates in concrete-filled thin-walled steel tubular beam-columns

The availability of high strength steels and concrete leads to the use of thin steel plates in concrete-filled steel tubular beam-columns. However, the use of thin steel plates in composite beam-columns gives a rise to local buckling that would appreciably reduce the strength and ductility performance of the members. This paper studies the critical local and post-local buckling behavior of steel plates in concrete-filled thin-walled steel tubular beam-columns by using the finite element analysis method. Geometric and material nonlinear analyses are performed to investigate the critical local and post-local buckling strengths of steel plates under compression and in-plane bending. Initial geometric imperfections and residual stresses presented in steel plates, material yielding and strain hardening are taken into account in the nonlinear analysis. Based on the results obtained from the nonlinear finite element analyses, a set of design formulas are proposed for determining the critical local buckling and ultimate strengths of steel plates in concrete-filled steel tubular beam-columns. In addition, effective width formulas are developed for the ultimate strength design of clamped steel plates under non-uniform compression. The accuracy of the proposed design formulas is established by comparisons with available solutions. The proposed design formulas can be used directly in the design of composite beam-columns and adopted in the advanced analysis of concrete-filled thin-walled steel tubular beam-columns to account for local buckling effects.     

多边形空心钢管混凝土轴压短柱非线性分析

在轴压试验结果的基础上,选择合理的材料本构关系模型,应用大型通用ANSYS有限元软件对四边形和八边形空心钢管混凝土短柱进行了有限元模拟,着重讨论了有限元模型的建立方法,并通过模拟结果与试验结果的对比,验证了有限元模型的合理性。     

Seismic behaviour of square CFT beam-columns under biaxial bending moment

This paper investigates the behaviour of square concrete-filled steel tubular (CFT) beam-columns subjected to biaxial moment. Nine tests on beam-columns are reported here under a combined loading of constant axial load and cyclic lateral load applied at varying angles to the axis of the cross-section, referred to as ‘diagonal’ loading. The specimens were prepared in order to evaluate the influence of different parameters on the overall structural response, their ductility and their energy dissipation ability; the parameters included the effects of axial load ratio, width-to-thickness ratio, concrete compressive strength, slenderness ratio and load angle on the moment strength. The experimental results indicate that the ductility and energy dissipation ability of biaxially loaded square CFT columns decrease with increasing the axial load ratio. Their ductility and energy dissipation ability was also observed to decrease as the concrete compressive strength increased while the ductility was barely affected by the load angle. An increase in the load angle of biaxially bent square CFT beam-columns led to a slight decrease of the moment strength. Both EC4 and AIJ code provisions were shown to predict with reasonable accuracy the moment strength capacity observed in the tests, while the ACI-predicted moment strength gave to slightly conservative values. On the other hand, the LRFD code provisions greatly underestimated their moment strength.     

Ultimate capacity of rectangular concrete-filled steel tubular columns under unequal load eccentricities

The paper describes 36 experimental tests conducted on rectangular and square tubular columns filled with normal and high strength concrete and subjected to a non-constant bending moment distribution with respect to the weak axis. The test parameters were the nominal strength of concrete (30 and 90 MPa), the cross-section aspect ratio (square or rectangular), the thickness (4 or 5 mm) and the ratio of the top and bottom first order eccentricities e_top/e_bottom (1, 0.5, 0 and − 0.5). The ultimate load of each test was compared with the design loads from Eurocode 4, presenting unsafe results inside a 10% safety margin. The tests show that the use of high strength concrete is more useful for the cases of non-constant bending moment, whereas if the aim is to obtain a more ductile behavior the use of concrete-filled columns is more appealing in the cases of normal strength concrete with non-constant bending moments because, although they resist less axial force than the members with HSC, they obtain a softened post-peak behavior.     

钢管混凝土短柱在轴向冲击荷载下的动力分析

通过有限元计算软件,分析了在冲击荷载作用下钢材强度、混凝土强度以及含钢率对钢管混凝土短柱承载力强度的影响,对沿试件长度方向试件的径向位移进行了分析,并对试件进行了变质量分析,得出钢管混凝土试件在材料、尺寸确定的情况下承受轴向荷载时,位移主要由冲击能量决定。     

Behaviour of short and slender concrete-filled stainless steel tubular columns

In this paper, a series of tests were carried out on short and slender concrete-filled stainless steel tubular columns to explore their performance under axial compression or combined actions of axial force and bending moment. Empty short steel hollow sections were also tested for comparison. The test results showed that the performance of the composite columns was quite good and have the potential to be used extensively as structural members. Comparisons of the test results were also made with several existing design methods for conventional concrete-filled carbon steel tubular columns as presented in Australian standard AS 5100 (2004), American code AISC (2005), Chinese code DBJ/T 13-51-2010 (2010), and Eurocode 4 (2004), which indicates that all the codes are somewhat conservative in predicting the load-carrying capacities of both short and slender columns.     

A novel steel section for concrete-filled tubular columns

In modern structural constructions, concrete-filled steel tubular (CFT) columns have gradually become a central element in structural systems like tall buildings, bridges and so forth. The effective parameters on load carrying capacity of CFT columns are the bond between the steel and internal concrete, local buckling strength of steel tube, creep of concrete and loading conditions of column at connections. Considering these effective parameters, a novel section is suggested which can be used for columns of tall buildings and bridges with large spans. The main characteristic of the suggested steel section is internal longitudinal symmetric stiffeners. In the present study, a comparative investigation into the behavior of this novel section (with circular and octagonal shapes) and the most common used sections of CFT columns has been carried out under axial and cyclic loading. Having verified the finite element modeling, several different analyses have been undertaken. The results of the analyses clearly exhibit the increase in strength and ductility of the suggested novel section under axial and cyclic loading and therefore, its application is recommended in construction practice.     

配有圆钢管的钢骨混凝土轴压短柱的极限承载力计算（Ⅱ）

针对钢管混凝土核心短柱轴压状态,采用汉基塑性全量理论对钢管进行极限承载力分析,得到屈服时钢管竖向应力对承载力的贡献,同时对核心混凝土采用Drucker-Prager屈服准则进行钢管约束下的承载力的计算分析.考虑配箍率对极限承载力的影响,提出了不同配箍率下的钢管混凝土核心短柱的极限承载力计算公式,并与现有试验数据进行对比,结果吻合良好,为钢管混凝土轴压短柱极限承载力的计算提供一种新的方法.     

配有圆钢管的钢骨混凝土轴压短柱的极限承载力计算（Ⅰ）

针对钢管混凝土核心短柱轴压状态,采用汉基塑性全量理论对钢管进行极限承载力分析,得到屈服时钢管竖向应力对承载力的贡献,同时对核心混凝土采用Drucker-Prager屈服准则进行钢管约束下的承载力的计算分析.考虑配箍率对极限承载力的影响,提出了不同配箍率下的钢管混凝土核心短柱的极限承载力计算公式,并与现有试验数据进行对比,结果吻合良好,为钢管混凝土轴压短柱极限承载力的计算提供一种新的方法.     

High strength circular concrete-filled steel tubular slender beam-columns, Part I: Numerical analysis

High strength circular concrete-filled steel tubular (CFST) slender beam-columns are frequently used in high-rise composite buildings because they possess higher strength and stiffness than normal strength ones. Most nonlinear inelastic methods of analysis for circular CFST slender beam-columns have not considered the effects of high strength materials and concrete confinement that significantly increases the strength and ductility of the concrete core. As a result, these methods produce computational solutions that deviate considerably from experimental results. This paper presents a new numerical model for predicting the nonlinear inelastic behavior of high strength circular CFST slender beam-columns under axial load and bending. The numerical model developed not only accounts for confinement effects on the concrete core and circular steel tubes but also incorporates initial geometric imperfections of beam-columns. Axial load-moment-curvature relationships obtained from the fiber element analysis of column cross-sections are utilized to determine the equilibrium states in the inelastic stability analysis of slender beam-columns. Computational algorithms are developed for determining the axial load-deflection and axial load-moment interaction curves for slender beam-columns. The numerical model is implemented in a computer program, which is shown to be an efficient and accurate simulation tool that can be used to investigate the fundamental behavior of high strength circular CFST slender beam-columns. The verification and applications of the numerical model are given in a companion paper.     

Behaviour of reinforced and concrete-encased composite columns subjected to biaxial bending and axial load

An experimental investigation of the behaviour of reinforced concrete columns and a theoretical procedure for analysis of both short and slender reinforced and composite columns of arbitrarily shaped cross section subjected to biaxial bending and axial load are presented. In the proposed procedure, nonlinear stress–strain relations are assumed for concrete, reinforcing steel and structural steel materials. The compression zone of the concrete section and the entire section of the structural steel are divided into adequate number of segments in order to use various stress–strain models for the analysis. The slenderness effect of the member is taken into account by using the Moment Magnification Method. The proposed procedure was compared with test results of 12 square and three L-shaped reinforced concrete columns subjected to short-term axial load and biaxial bending, and also some experimental results available in the literature for composite columns compared with the theoretical results obtained by the proposed procedure and a good degree of accuracy was obtained.