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.     

薄壁钢管混凝土梁-柱的钢板局部屈曲分析

高强钢和混凝土的应用,使得薄钢板开始应用在填充混凝土的钢管梁柱中。然而,在组合梁柱中薄钢板的应用可能会增加局部屈曲,这将减弱这些构件的强度和延性性能。通过有限元分析方法,分析了在填充混凝土的薄壁钢管梁-柱中钢板的临界局部屈曲和局部屈曲后性能。运用几何和材料非线性分析来研究在压力和平面内弯曲作用下钢板中的临界局部和后张局部屈曲强度。非线性分析中考虑了钢板的初始几何缺陷和残余应力,材料屈服和应变硬化。基于非线性有限元分析结果,本文提出一组设计公式,以确定这种组合梁柱的临界局部屈曲和钢板的极限强度。此外,还提出在不均匀压力作用下,钢板极限强度设计中有效宽度的计算公式。这一组设计公式可以直接用于组合梁-柱的设计和考虑局部屈曲作用后的薄壁钢管混凝土梁-柱分析。     

Experimental behaviour of concrete-filled stiffened thin-walled steel tubular columns

An experimental study on the structural behaviour of concrete-filled stiffened thin-walled steel tubular columns is presented in this paper. The stiffening was achieved by welding longitudinal stiffeners on the inner surfaces of the steel tubes. Companion tests were also undertaken on 12 unstiffened concrete-filled steel tubular (CFST) columns, with or without steel fibres in the infill concrete. The test results showed that the local buckling of the tubes was effectively delayed by the stiffeners. The plate buckling initially occurred when the maximum load had almost reached for stiffened specimens, thus they had higher serviceability benefits compared to those of unstiffened ones. Some of the existing design codes were used to predict the load-carrying capacities of the tested composite columns.     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

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.     

Behavior of biaxially-loaded rectangular concrete-filled steel tubular slender beam-columns with preload effects

In composite construction, rectangular hollow steel tubular slender beam-columns are subjected to preloads arising from construction loads and permanent loads of the upper floors before infilling of the wet concrete. The behavior of biaxially loaded thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns with preloads on the steel tubes has not been studied experimentally and numerically. In this paper, a fiber element model developed for CFST slender beam-columns with preload effects is briefly described and verified by existing experimental results of uniaxially loaded CFST columns with preload effects. The fiber element model is used to investigate the behavior of biaxially loaded rectangular CFST slender beam-columns accounting for the effects of preloads and local buckling. Parameters examined include local buckling, preload ratio, loading angle, depth-to-thickness ratio, column slenderness, loading eccentricity and steel yield strength. The results obtained indicate that the preloads on the steel tubes significantly reduce the stiffness and strength of CFST slender beam-columns with a maximum strength reduction of more than 15.8%. Based on the parametric studies, a design model is proposed for axially loaded rectangular CFST columns with preload effects. The fiber element and design models proposed allow for the structural designer to efficiently analyze and design CFST slender beam-columns subjected to preloads from the upper floors of a high-rise composite building during construction.     

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.     

Local buckling of steel plates in rectangular CFT columns with binding bars

This paper presents a theoretical study on the elastic local buckling of steel plates in rectangular concrete-filled steel tubular (CFT) columns with binding bars under axial compression. It is assumed that the unloaded edges of the steel plate are elastically restrained against rotation, whereas the loaded edges are clamped. Based on the energy method, the formulas for elastic local buckling strength of the steel plate in rectangular CFT columns under axial compression are derived, which are calibrated with the experimental results. Then the formulas are employed to study the elastic local buckling of steel plates in rectangular CFT columns with binding bars under axial compression. It is shown that the binding bars can increase the local buckling coefficient, which results in improvement of the capacity of the steel plate to resist local buckling. Finally, appropriate spacing of binding bars, appropriate limitation for aspect ratio and corresponding appropriate limitation for width-thickness ratio are suggested for rectangular CFT columns with binding bars under axial compression.     

Nonlinear analysis of short concrete-filled steel tubular beam-columns under axial load and biaxial bending

This paper presents a nonlinear fiber element analysis method for determining the axial load-moment strength interaction diagrams for short concrete-filled steel tubular (CFST) beam-columns under axial load and biaxial bending. Nonlinear constitutive models for confined concrete and structural steel are considered in the fiber element analysis. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a composite section to satisfy equilibrium conditions. The accuracy of the fiber element analysis program is verified by comparisons of fiber analysis results with experimental data and existing solutions. The fiber element analysis program developed is employed to study the effects of steel ratios, concrete compressive strengths and steel yield strengths on axial load-moment interaction diagrams and the C-ratio of CFST beam-columns. The proposed fiber element analysis technique is shown to be efficient and accurate and can be used directly in the design of CFST beam-columns and implemented in advanced analysis programs for the nonlinear analysis of composite columns and frames.     

Local buckling of structural steel shapes

The objectives of this paper are to (1) provide analytical expressions for the elastic cross-section local buckling stresses, including element interaction, of hot-rolled steel structural shapes, and (2) compare these local buckling results to the assumptions inherent in the local slenderness limits of the US AISC structural steel specification. The cross-section local buckling stress is determined by finite strip analysis (FSA). Local stability of each cross-section in the AISC shapes database (excluding pipes) is considered in axial compression, as well as positive and negative bending about the major and minor geometric axes. Local buckling stresses are converted into plate buckling coefficients (k’s) and simplified expressions are provided for all observed k’s. The new k’s explicitly include elastic web-flange interaction amongst the elements comprising the cross-section. The k values from the FSA are compared to those inherently assumed in the AISC Specification, significant differences are observed.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.     

带肋冷弯薄壁方钢管混凝土柱滞回性能研究

对3根带肋冷弯薄壁方钢管混凝土柱进行滞回试验,主要参数为轴压比。试验结果表明：纵向加劲肋有效延缓了钢管壁局部屈曲的发生;其滞回曲线饱满,具有良好的耗能能力;随着轴压比的增大,柱承载力略有增大,而延性、耗能能力则明显减小;当横向位移大于6倍的屈服位移时,大轴压比的刚度退化速度最快。建立了该类试件的有限元模型,对比可得有限元模拟结果与试验结果吻合较好。基于有限元模型对该类构件开展机理分析和参数分析。结果表明：在带肋冷弯薄壁方钢管的约束下,核心混凝土的强度得到了较大提高;钢管局部屈曲发生在峰值荷载后,局部屈曲只发生在纵向加劲肋和钢管角部间;材料强度、轴压比、钢管宽厚比和长细比等参数对该类构件的承载力有较大影响;混凝土强度、轴压比和长细比对荷载-位移骨架曲线形状有较大影响。基于参数分析建议了该类构件的简化滞回模型,简化计算结果和有限元计算结果吻合较好。     

Finite element analysis and design of sandwich panels subject to local buckling effects

Past research into the local buckling behaviour of fully profiled sandwich panels has been based on polyurethane foams and thicker lower grade steels. The Australian sandwich panels use polystyrene foam and thinner and high strength steels, which are bonded together using separate adhesives. Therefore a research project on Australian sandwich panels was undertaken using experimental and finite element analyses. The experimental study on 50 foam-supported steel plate elements and associated finite element analyses produced a large database for sandwich panels subject to local buckling effects, but revealed the inadequacy of conventional effective width formulae for panels with slender plates. It confirmed that these design rules could not be extended to slender plates in their present form. In this research, experimental and numerical results were used to improve the design rules. This paper presents the details of experimental and finite element analyses, their results and the improved design rules.     

Monotonic and cyclic behavior of concrete-filled steel-tube beam-columns considering local buckling effect

A mathematical model is developed to evaluate the monotonic and cyclic behavior of concrete-filled steel tube (CFST) beam-columns with rectangular cross section. The model includes the reduction in the steel compressive strength due the local buckling effect. The degradations in unloading and reloading stiffness of steel tube due to local buckling are also included. The model is based on fiber element method in which uniaxial stress–strain material laws are used for cross section components. The results obtained from the mathematical model were compared with experimental results for columns under monotonic as well as cyclic loads. It is observed that the proposed model predicts well the columns and beams nonlinear behavior compared with the experimental results.     

Local buckling restraint condition for core plates in buckling restrained braces

Buckling Restrained Braces (BRBs) are commonly used as bracing elements in seismic zones. A key limit state governing BRB design is to prevent flexural buckling. However, when the wall thickness of the steel tube restrainer is relatively small compared to the cross-section of the core plate, the restraint conditions against the local buckling of the core plate can be critical for the stability and strength of the BRB. In this study, cyclic loading tests and numerical analyses of BRBs were carried out using various tube restrainer configurations to investigate the influence of local buckling of the restrainer on BRB strength and ductility.     

Dynamic buckling of thin-walled viscoplastic columns

The purpose of this paper is the analysis of strain-rate effect in dynamic stability of thin-walled orthotropic column of closed rectangular cross-section, subjected to in-plane pulse loading of finite duration. For the solution the first-order shear deformation theory displacement field is employed with the Green–Lagrange strain tensor application. The effect of strain rate sensitivity is included in the framework of the viscoplasticity constitutive Perzyna model for material behaviour under high strain rate loading. The numerical results are obtained with the finite element method application. In the performed analysis the strain-rate effect influence on the dynamic buckling load is examined as well as the initial imperfections of walls, pulse shape and the orthotropy ratio are considered. The results of dynamic criteria application are compared furthermore.     

Numerical evaluation on shell buckling of empty thin-walled steel tanks under wind load according to current American and European design codes

Liquid storage steel tanks are vertical above-ground cylindrical shells and as typical thin-walled structures, they are very sensitive to buckling under wind loads, especially when they are empty or at low liquid level. Previous studies revealed discrepancies in buckling resistance of empty tanks between the design method proposed by the American Standard API 650 and the analytical formulas recommended by the European Standard EN1993-1-6 and EN1993-4-2. This study presents a comparison between the provisions of current design codes by performing all types of numerical buckling analyses recommended by Eurocodes (i.e. LBA-linear elastic bifurcation analysis, GNA-geometrically nonlinear elastic analysis of the perfect tank and GNIA-geometrically nonlinear elastic analysis of the imperfect tank). Such analyses are performed in order to evaluate the buckling resistance of two existing thin-walled steel tanks, with large diameters and variable wall thickness. In addition, a discussion is unfolded about the differences between computational and analytical methods and the conservatism that the latter method imposes. An influence study on the geometric imperfections and the boundary conditions is also conducted. Investigation on the boundary conditions at the foot of the tank highlights the sensitivity to the fixation of the vertical translational degree of freedom. Further, it is indicated that the imperfection magnitude recommended by the EN1993-1-6 is extremely unfavorable when applied to large diameter tanks. Comments and conclusions achieved could be helpful in order to evaluate the safety of the current design codes and shed more light towards the most accurate one.     

Local and distortional buckling of thin-walled short columns

This paper assesses the applicability of Eurocode 3 (EC3) to the prediction of the compression capacity of short fixed-ended columns with different cross-sections. This compression capacity is determined by combining the effective width of plane elements due to local buckling and the effective stiffener thickness due to distortional buckling. Numerical calculations have been carried out in order to compare alternative methods for determining the minimum elastic distortional buckling stress in compression. The method given in EC3 does not correlate as well as Lau and Hancock's method with the results given by Generalized Beam Theory (GBT). The end boundary conditions have a significant influence on the distortional buckling strength, and thus also on the compression capacity of short columns. Selected experimental results from compression tests on C-, Hat- and rack upright-sections are compared with the predictions given by EC3. The procedure in EC3 was modified by determining the distortional buckling stress using GBT, taking into account the actual column length and the end boundary conditions. This lead to better agreement between the experimental results and the theoretical predictions.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

Effective width method to account for the local buckling of steel thin plates at elevated temperatures

The local buckling of thin steel plates exposed to fire is investigated using a finite element model. The reduction of strength and stiffness that occurs at elevated temperatures needs to be taken into account in the design, as it increases the susceptibility to local buckling of the plates thus affecting their load carrying capacity. The obtained results show that the current existing design method of Eurocode 3 to take into consideration the local buckling in the calculation of the ultimate strength of steel thin plates at elevated temperatures needs to be improved. These methods are based on the same principles as for normal temperature but using for the design yield strength of steel, at elevated temperatures, the 0.2% proof strength of the steel instead of its strength at 2% total strain as for the cases where the local buckling is not limiting the ultimate strength of the plates. This consideration, however, leads to an inconsistency if cross-sections are composed simultaneous of plates susceptible and not to local buckling. To address this issue, new expressions for calculating the effective width of internal compressed elements (webs) and outstand elements (flanges) are proposed, which have been derived from the actual expressions of the Part 1.5 of the Eurocode 3 and validated against numerical results. It is also demonstrated that it is not necessary to use for the yield stress at elevated temperatures the 0.2% proof strength of the steel instead of the yield stress at 2% total strain, given that the necessary allowances are considered in these new expressions, thus leading to a more economic design.