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This paper presents the results of a large parametric study concerning the evaluation of the critical local buckling coefficient for thin-walled rectangular hollow section (RHS) members subjected to combined axial load and biaxial bending, accounting for web-flange interaction. The calculation of the half-wavelength leading to the minimum critical local bifurcation load is performed by means of a Generalized Beam Theory specialization, which makes it possible to quickly solve a large set of cases. In particular, taking advantage of the small half-wavelength of local buckling, it is assumed that the stresses are uniformly distributed along the member length, making it possible to resort to semi-analytical solutions using sinusoidal half-wave amplitude functions for the GBT cross-section deformation modes. On the basis of the results obtained, the key parameters governing local buckling are identified, leading to easy-to-use charts and closed-form formulae to determine the local buckling coefficient. [ABSTRACT FROM AUTHOR]

Abstract: Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account. [Copyright &y& Elsevier]

Abstract: The structural behaviour of elliptical hollow sections has been examined in previous studies under several loading conditions, including pure compression, pure bending and combined uniaxial bending and compression. This paper examines the elastic buckling response of elliptical hollow sections under any linearly varying in-plane loading conditions, including the most general case of combined compression and biaxial bending. An analytical method to predict the elastic buckling stress has been derived and validated against finite element results. The predictive model first identifies the location of the initiation of local buckling based on the applied stress distribution and the section geometry. The critical radius of curvature corresponding to this point is then introduced into the classical formula for predicting the elastic local buckling stress of a circular shell. The obtained analytical results are compared with results generated by means of finite element analysis. The comparisons between the analytical and numerical predictions of elastic buckling stress reveal disparities of less than 2.5% for thin shells and, following an approximate allowance for the influence of shear, less than 7.5% for thick shells. [Copyright &y& Elsevier]

A testing research on the local-biaxial flexural interactive buckling of high strength steel Q460C, Q550D and Q690D welded box slender section beam-columns subjected to combined compression force and biaxial bending is reported. A total of thirteen median long steel columns, of which four manufactured from Q460C steel, five from Q550D steel and four from Q690D steel, were loaded until failure under biaxial eccentric compression forces. The local-biaxial flexural interaction buckling behavior is investigated by analyzing the test results. As an addition to the test data, the finite element parameter analyses are performed. The ultimate bearing capacities obtained from the test in this study and the numerical results presented in this study or in the existent literatures are compared with the calculation results in accordance with the design methods recommended in the American Specification ANSI/AISC 360–16, Eurocodes BS EN 1993-1-1 and BS EN 1993-1-5, and the newly proposed Effective Yield Strength Method (EYSM) and Effective Section Method (ESM) to check whether the current technical provisions and the new methods are suitable to the high strength steel beam-columns examined in this paper. The experimental and numerical results show that after taking the resistance factor into account, the ANSI/AISC 360–16, EN 1993-1-1 and BS EN 1993-1-5 are very conservative for the high strength steel beam-columns with greater member slenderness ratios (λ = 80, 90, 100) or with smaller plate width-to-thickness ratios (square box sections with b/t = 40, or rectangular box sections with h/t = 40 or b/t = 17); the new proposed EYSM provides an excellent prediction of the ultimate bearing capacities of the beam-columns and thus suitable for the high strength steels; but the new proposed ESM gives a very conservative estimate, over the range of steel nominal yield stress f y = 460 MPa ∼ 690 MPa, plate width-to-thickness ratio b/t = 40–80, member slenderness ratio λ = 40–100. • A testing research on the local-biaxial flexural interactive buckling of high strength steel welded box slender section beam-columns subjected to combined compression force and biaxial bending is reported. The local-biaxial flexural interaction buckling behavior is investigated. • The ultimate bearing capacities obtained from the test in this study and the numerical results presented in this paper or in the existent literatures are compared with the calculation results in accordance with the design methods recommended in the American Specification ANSI/AISC 360–16, Eurocodes BS EN 1993-1-1 and BS EN 1993-1-5, and the newly proposed Effective Yield Strength Method (EYSM) and Effective Section Method (ESM) to check whether the current technical provisions and the new methods are suitable to the high strength steel beam-columns examined. • The experimental and numerical results show that after taking the resistance factor into account, the ANSI/AISC 360–16, EN 1993-1-1 and BS EN 1993-1-5 are very conservative for the high strength steel beam-columns with greater member slenderness ratios (λ = 80, 90, 100) or with smaller plate width-to-thickness ratios (square box sections with b/t = 40, or rectangular box sections with h/t = 40 or b/t = 17); the new proposed EYSM provides an excellent prediction of the ultimate bearing capacities of the beam-columns and thus suitable for the high strength steels; but the new proposed ESM gives a very conservative estimate, over the range of steel nominal yield stress f y = 460 MPa ∼ 690 MPa, plate width-to-thickness ratio b/t = 40–80, member slenderness ratio λ = 40–100. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a general formulation for the analysis of steel hollow structural beams subjected to biaxial bending. The model has been developed within the framework of lumped damage mechanics. In this approach, the models are based on methods of continuum damage mechanics and the concept of plastic hinge. The model was implemented in a commercial finite element program. In order to calibrate the model, a set of experimental tests were carried out in the Structural Mechanics Laboratory at the Lisandro Alvarado University. The model was evaluated by the numerical simulation of these tests finding a good agreement between the experimental tests and the numerical simulations. [Copyright &y& Elsevier]

This study aims at investigating the biaxial bending capacity of cold-formed steel (CFS) storage rack uprights undergoing global (lateral-torsional) buckling. A previously published and validated biaxial bending numerical model for local and distortional buckling of CFS rack uprights is initially validated in this paper for global buckling and then used to evaluate and analyse the biaxial bending response of nine unperforated upright cross-sections. Nine biaxial bending configurations were considered per cross-section. Results show that a nonlinear interactive relationship typically governs the biaxial bending of the studied uprights. This relationship is discussed and analysed for different cross-sectional slenderness. The numerical capacities are compared with both the classical DSM predictions and the use of inelastic reserve capacity in the DSM. Results show that the classical DSM equations underestimate the biaxial bending capacity by up to 55% but results in better predictions when the inelastic reserve capacity is considered. Finally, an extended range of inelastic reserve strength for global buckling is proposed which results in a 14% improvement of the DSM predictions. The appropriate form of the DSM to estimate the global biaxial bending capacity of unperforated cold-formed steel storage rack uprights is discussed. • Validated Finite Element (FE) model to predict global biaxial bending response of storage rack upright sections • Evaluation of currently available DSM equations to predict global biaxial bending capacity of storage rack upright sections • Newly proposed extended range of inelastic reserve strength for global buckling [ABSTRACT FROM AUTHOR]

Abstract: Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure. [Copyright &y& Elsevier]

Dedicated to Prof. Dr.-Ing. Carl-Alexander Graubner on the occasion of his 60th birthday Masonry members have to resist vertical loads and bending moments about the weak axis due to rotation of adjacent slabs. If the compression member is part of the bracing system, there are also bending moments about the strong axis. This paper deals with the load-bearing capacity of biaxially eccentrically compressed unreinforced compression members with rectangular cross-sections. For linear-elastic material, the principles of an analytical model is presented, which considers geometrical and physical (cracking) non-linearity. The deflections of the wall can be determined by using moment-curvature relations, making possible the analytical analysis of compression members considering the effects of 2nd order theory. For a non-linear stress-strain relation, the calculation of the load carrying capacity of rectangular compression members under biaxial bending is complex and has to be determined numerically. The good accordance of the results of the analytical model with the numeric calculations is also shown for various eccentricities. In addition, a simplified proposal for the calculation of the load-bearing capacity of biaxially eccentrically compressed unreinforced compression members is shown. The proposal is based on the load-bearing capacity of uniaxially eccentrically compressed unreinforced compression members. Therefore it is possible to use the proposal considering existing models, for example according to Eurocode 2 or 6. [ABSTRACT FROM AUTHOR]

The loads applied to angle beams usually act out of the principal planes so that they cause simultaneous biaxial bending about both principal axes. The general practice for designing unbraced beams against biaxial bending is to consider the separate failure modes of either in-plane bending or lateral buckling under bending about the major principal axis, and in-plane bending about the minor principal axis, and then to use an interaction equation to combine the two principal axis strengths. However, the interaction equations provided by many codes for designing against biaxial bending are largely derived from research on doubly symmetric I-section beams, which may be inappropriate for angle section beams, while the lateral buckling rules of these codes appear to be in error for nonuniform bending with loads acting away from the shear center. This paper investigates the biaxial bending of unbraced steel angle beams. The biaxial bending of compact equal angles in uniform bending is considered first, and a simple interaction equation is developed for their design which utilizes recent proposals for lateral buckling design. A corresponding interaction equation is developed for the design of semicompact and slender equal angles. Suggestions are then made for extending these to the biaxial bending of unequal angles under general shear center loading, and finally, a worked example illustrating the method is provided. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Single-angles are generally loaded parallel to their geometrical axes. And, their cross sections are not symmetrical to their principal axes. Even equal leg angles have only one symmetrical axis. Many loading types cause biaxial bending and axial force in these members. Since single-angles are slender members, they also need to be analyzed under the flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze nominal loads of equal leg angle section beams loaded vertically to the beam axis. It is assumed that axial force is composed of constant and compressive force. Constant axial force is taken into consideration only for the uniform compressive stress and second degree effects caused in the cross section. By this way, only biaxial bending moments are left. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending is calculated with respect to the slenderness and the axial force. The nominal design force on the cross section among these moments is calculated according to the LRFD rules. Analysis procedure presented for constant axial load can also be used for general conditions of axial forces, by using an consecutive calculation procedure. [ABSTRACT FROM AUTHOR]

This work is focused on the design of a structural steel industrial building of double-T type section located in an industrial area of Valladolid (Spain). Firstly, a linear analysis is carried out to dimension the structure and check that it resists according to the established regulations, the Technical Building Code (CTE), the national adaptation of the Eurocodes (ECs). For the analysis of the structure, the 3D model of slender bar bending (Navier-Bernoulli bending theory) and the non-uniform twist or constrained warping model (Vlasov’s torsion theory) are considered. In the second place, a nonlinear analysis is performed with the objective of verifying the Ultimate Limit State of stability of the structural elements and of the industrial building as a whole. All this without the need to estimate buckling coefficients of each of the beams that make up the structure, and without the need for important simplifications. Finally, a linear analysis is once more performed to check the Service Limit State for the frequent combination of actions. The solution of the problem results from an iterative process of searching for the best solution, that is, the one that, with the least amount of steel used, fulfills all the requirements: resistance, stability and displacement limits established by the current regulation. [ABSTRACT FROM AUTHOR]

This paper presents one of the two new proposals for beam-column interaction formulae, which will be made available in the forthcoming EN version of Eurocode 3. It is based on second-order in-plane elasticity, and has been derived in order to exhibit an understandable physical background, as well as accuracy and consistency with the other resistance and stability formulae of the code. The formulae ensure all the required continuities: between the cross-section classes, from plasticity to elasticity when slenderness and axial force are increasing, and continuity between all the individual stability member checks and cross-section verifications. The paper shows how the basic format may be extended to cover a wider range of cases, i.e. spatial elastic–plastic behaviour with possible lateral–torsional buckling. Through an extensive comparison with the results of FEM numerical simulations of about 15 000 beam-columns, the proposal is found to be safe and accurate. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Biaxially loaded high strength rectangular concrete-filled steel tubular (CFST) slender beam-columns with large depth-to-thickness ratios, which may undergo local and global interaction buckling, have received very little attention. This paper presents the verification of a multiscale numerical model described in a companion paper and an extensive parametric study on the performance of high strength thin-walled rectangular CFST slender beam-columns under biaxial loads. Comparisons of computer solutions with existing experimental results are made to examine the accuracy of the multiscale numerical model developed. The effects of the concrete compressive strength, loading eccentricity, depth-to-thickness ratio and columns slenderness on the ultimate axial strength, steel contribution ratio, concrete contribution ratio and strength reduction factor of CFST slender beam-columns under biaxial bending are investigated by using the numerical model. Comparative results demonstrate that the multiscale numerical model is capable of accurately predicting the ultimate strength and deflection behavior of CFST slender beam-columns under biaxial loads. Benchmark numerical results presented in this paper provide a better understanding of the local and global interaction buckling behavior of high strength thin-walled CFST slender beam-columns and are useful for the development of composite design codes. [ABSTRACT FROM AUTHOR]

The aim of this article is to describe problems of members subjected to biaxial bending and axial compression force and the methods of their design. Members subjected to bending moments about two axes and axial compression force exhibit complex behavior. It is necessary to consider second order theory and imperfections when designing members like that, since they have noticeable influence on resistance in instability. There are examples shown in the article, using methods present in current European standards EN 1993-1-1 and EN 1999-1-1. Attention is drawn to differences in methods, both in applicability and practicality, in design of members with constant and linear bending moment. The purpose of presented paper is to show if the method, which is currently used in Eurocode for aluminum structures, can be also used for steel structures. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

This paper presents a comprehensive experimental and numerical investigation on hysteretic behavior of thin-walled circular steel tubes as loaded members in reticulated shells. The experimental setup available for constant compression and biaxial bending loading was designed to examine the failure process, failure modes, load bearing capacity, ductility, stiffness degradation and energy dissipation capacity of sixteen thin-walled circular steel tubes. Also, the effects of the loading condition, axial load ratio, slenderness and steel strength on hysteretic behavior of specimens were investigated. The study showed that test results of specimen loaded in two directions might overestimate hysteretic characteristic of this member. Premature local buckling may be caused by the high axial load ratio and the recommended axial load ratio may be n ≤ 0.2 to ensure the load bearing capacity, deformation capacity and ductility of circular steel tubes and to prevent the premature local buckling occurring in engineering practice. Slenderness affects the load bearing capacity, ductility, and energy dissipation capacity of specimens, and with an increasing slenderness, the stiffness degraded considerably and quickly. Specimens with high strength steel exhibited higher load bearing capacity and better stiffness but lower energy dissipation capacity than those made by low strength steel. Furthermore, the nonlinear finite element analysis was performed to simulate hysteretic behavior of test specimens, and the results got a satisfactory agreement with those of test. [ABSTRACT FROM AUTHOR]

In this paper, the stressing state modeling analysis of the residual strain data of H-steel columns reveals three characteristic points that exist during the failure of H-steel columns. Also, the correctness of the stressing state analysis method, residual, and buckling characteristic pairs was verified. First, the experimental residual strains were transformed into generalized strain energy density (GSED) values as the state variables for establishing the stressing state mode and characteristic parameters (characteristic pairs). The Mann-Kendall (M-K) criterion is applied to the normalized GSED sum-j curves to reveal the characteristic points P, Q, and U of the evolving stressing state of the H-steel column. Characteristic point P is defined as the elastic-plastic branch point of the H-steel column, characteristic point Q is defined as the failure starting point, and characteristic point U is defined as the progressive failure point. Around the characteristic points of the H-steel columns, the directly modeled stressing state characteristic pairs, residual characteristic pairs, and buckling characteristic pairs produce significant mutation characteristics. This phenomenon verifies the correctness of the revealed H-steel column characteristic points and the rationality of this paper's stressing state modeling method. Then, it is proposed that the elastic-plastic branch point P can be directly used as the design reference point, and it is compared with the design point given by Code EN1993–1–5. In conclusion, this paper provides new ideas for analyzing steel structures and opens up the value of residual strain data in structural analysis.

Abstract: The theory and algorithms of a performance-based analysis (PBA) technique for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam–columns with local buckling effects were presented in a companion paper. Initial local buckling and effective strength/width formulas for steel plates are incorporated in the PBA program to account for local buckling effects. Performance indices are used in the PBA program to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam–columns. This paper presents the verification and applications of the PBA program developed. The axial load–strain curves, ultimate axial loads and moment–curvature curves for thin-walled CFST columns predicted by the PBA program are verified by experimental data. The PBA program is then utilized to investigate the effects of local buckling, depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility performance of thin-walled CFST beam–columns under axial load and biaxial bending. The PBA technique developed is shown to be efficient and accurate and can be used directly in the performance-based design of thin-walled CFST beam–columns and implemented in advanced analysis programs for composite columns and frames. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

This paper proposes a simplified method to design slender rectangular reinforced concrete columns with doubly symmetric reinforcement subjected to combined axial loads and biaxial bending, which is valid for short-time and sustained loads and for both normal and high strength concretes. The method is based on the so-called moment magnifier method (ACI-318-02) and EuroCode-2 (draft for stage 49) and it is only suitable for columns with equal effective buckling lengths in the two principal bending planes. A new equation of the column stiffness EI is proposed with which to obtain the moment magnification factor for single and double curvature. The method was compared with 371 experimental tests from the literature and a good degree of accuracy was obtained. Precision for sustained loads was improved in comparison with the method proposed by the American ACI-318 (02) and the European EC-2 (September 2003). The method allows slender reinforced concrete columns to be both checked and designed with enough accuracy for practice engineering. [Copyright &y& Elsevier]

Concrete exposed to fire can experience spalling when the pore pressure increases due to water evaporation resulting in damage to part of the concrete cross-section which causes the loss of the initial cross-sectional symmetry, both thermal and geometrical. This may lead to what is, in essence, a biaxial bending problem in reinforced concrete columns. This study does not deal with the prediction of the occurrence of spalling for which a fully coupled hygro-thermo-mechanical analysis would be required. This work evaluates the consequences that corner spalling and surface spalling have on the fire resistance of reinforced concrete columns and presents a methodology based on the determination of a modified fire resistance time. An advanced fiber based numerical model for evaluating the fire resistance of RC sections exposed to fire is used as a tool to analyse the effect that spalling has on the performance of the columns. The model is able to generate the interaction surfaces of the columns subjected to uniaxial or biaxial bending and 4-sided exposed to the standard fire curve ISO 834. After a parametric analysis, it is observed that the negative effect of spalling can be quantified by means of an additional fire exposure time, which ranges between 0–35 min and depends on the column cross-section configuration, dimensions and load level. Finally, a proposal for the calculation of the modified fire resistance time for the effect of spalling is presented, which may be beneficial for practitioners in design. [ABSTRACT FROM AUTHOR]

• The local buckling of steel corrugated-plates is considered in the load-carrying capacity. • The moment capacity is evaluated based on the plastic stress distribution. • Simplified interaction equations with good accuracy are proposed. • The interaction curves of biaxial bending are almost exclusively related to the axial compression ratio. This paper studies the load-carrying capacity of concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs) under axial compression and biaxial bending. T-CDSCWs are composed of flange and web walls and boundary elements. The T-section is mono-symmetric and exhibits different interaction curves of load-carrying capacity when subjected to axial load and different direction bending. Based on the finite element (FE) model established by the previous study, the local buckling of the steel corrugated-plates is considered in the load-carrying capacity. Subsequently, this paper investigates the behaviours of T-CDSCWs under axial compression and uniaxial bending, including stress distribution, load–displacement curves, and interaction curves. Based on the numerical results, the pure moment capacity is found to be evaluated by reducing the plastic moment capacity, and the interaction equations of N –positive M x , N –negative M x , and N – M y are proposed in the bilinear, linear, and parabolic form. For biaxial bending, the shape of the interaction curves is almost exclusively related to the axis compression ratio. Accordingly, this paper proposes the interaction equations of M x – M y subjected to certain axial compression. Moreover, the local buckling of steel corrugated-plates has no significant influence on the shape of the interaction curves no matter the bending direction. The global stability of T-CDSCWs is not involved in the study, and with the interaction equations obtained above, the global stability design of T-CDSCWs can be investigated by introducing the magnification factor of the bending moment caused by the secondary effect. [ABSTRACT FROM AUTHOR]

To investigate the seismic performance of hollow reinforced concrete (RC) bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges (JTG/T B02-01-2008). The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns. [ABSTRACT FROM AUTHOR]

The results of an extensive experimental campaign on centric and eccentric compressive behavior of thin-walled steel uprights of pallet-rack systems are presented. The analyzed cold-formed profiles are perforated through their whole length and have open, mono-symmetric cross-sections. Experimental results are extended through finite-element simulations, including geometrical and material nonlinearities, to obtain detailed three-dimensional compression-bending-bending strength-domains, which are compared to building-code prescriptions. Regulations are safety preserving, with an average difference of about 10%, and maximum difference for bending about the weak axis. Unlike in regulatory prescriptions, the experimental-numerical results show unsymmetrical behavior about the weak axis and nonlinear, convex bending-bending interaction. [ABSTRACT FROM AUTHOR]

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

An analysis of the damage observed in 24 reinforced concrete (RC) columns tested under uniaxial and biaxial horizontal loading is presented. The test results show that for biaxial loading conditions specific damage occurs for lower drift demands when compared with the corresponding uniaxial demand (a reduction of 50-75 % was found). The damage distribution observed in each column is also analysed. No significant differences are found in the plastic hinge length for uniaxial and biaxial loading. The drift demands associated with each damage state are compared with reference values proposed in international guidelines. Finally, and based on the philosophy of the Park and Ang uniaxial damage index, two new expressions are proposed for the evaluation of damage in RC elements under biaxial loading. The results of the application of these expressions to the experimental results are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In the recent codes for the design of steel structures, the elastic–plastic methods of analysis are recognised to provide an efficient estimation of the ultimate resistance of some of these structures. These methods are usually based on some basic hypotheses, such as the creation of plastic hinges in the most stressed cross-sections, for instance. As the development of these plastic hinges depends on the interaction between the internal forces and on the cross-section shape, specific equations are required for the analysis of different types of cross-sections. However, most frequently, these equations are not available, or they are expressed by means of simplified expressions; this is usually the case when biaxial bending is involved. This paper presents new interaction criteria for the analysis of steel rectangular hollow sections subjected to an axial force and biaxial bending moments, at the elastic or the plastic limit states (as long as buckling phenomena are not involved). The plastic interaction criteria are presented, in a first step, for some particular combinations of the internal forces, such as axial loading with bending about a main axis, and biaxial bending without axial loading. Then, the global solution for the simultaneous combination of an axial force and bending moments about both the main axes of inertia are described in detail. All these plastic interaction criteria are compared with the corresponding plastic criteria adopted in the Eurocode 3 (EC3). Some suggestions are presented in order to improve the results given by these EC3 criteria. [Copyright &y& Elsevier]

Abstract: The plastic criteria for the verification of steel cross-sections resistance are usually based on some basic hypotheses such as the development of plastic hinges, which depend on the interaction between the internal forces and the cross-section shape; therefore, specific equations are required for each type of cross-section. This paper presents new alternative interaction criteria for the analysis of steel I-sections subjected to an axial force and biaxial bending moments, at the elastic or the plastic limit states (as long as buckling phenomena are not involved). The plastic interaction criteria are presented, in a first step, for some particular combinations of the internal forces, such as axial loading with bending about a main axis, and biaxial bending without axial loading. In these cases, they are given by exact equations (within the frame of the hypotheses adopted in this study). All these plastic interaction criteria are compared with the corresponding plastic criteria adopted in the Eurocode 3 (EC3). Afterwards, a simplified global criterion is proposed for the simultaneous combination of an axial force and bending moments about both the main axes of inertia. This new simplified plastic criterion and the corresponding plastic criterion adopted in the EC3 are compared with the exact solution, obtained by a mixed numerical and analytical integration procedure. This comparison shows that this simplified criterion usually leads to results closer to the exact solutions. Some suggestions are then presented to improve the results given by the EC3. [Copyright &y& Elsevier]

Abstract: 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) , 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. [Copyright &y& Elsevier]

This paper presents a new proposal for beam-column interaction formulae initially based on second-order in-plane elastic theory, as an alternative to those proposed in the Eurocode 3 pre-standard . It has been derived according to the following requirements: theoretical background, clear physical meaning, consistency with the other related formulae of Eurocode 3 and accuracy. Besides that, the suggested formulae cover all required continuities: between the cross-section classes, from plasticity to elasticity as slenderness and axial force increase, and continuity between all the individual stability member checks and cross-section verifications. Further to the presentation of the formulae and their background, the good agreement of the proposal is shown through an extensive comparison with more than 15,000 results of finite element numerical simulations. [Copyright &y& Elsevier]

Steel-concrete composite columns are strong and efficient structural members. However, their strength is not consistently recognized within design standards. In particular, current provisions regarding the strength of composite columns under combined axial compression and biaxial bending are overly simplistic and conservative. This paper presents a study of the biaxial behavior of square and rectangular, filled and encased composite columns and methods of evaluating their strength. Analyses of composite cross sections confirm the conservative nature of current design provisions and form the basis for modified strength equations that better capture the shape of the three-dimensional interaction surface. Analyses of composite columns confirm that the proposed design equations are suitable for use within the direct analysis method for evaluating members with length effects. The proposed design equations are further validated against published experimental results. This paper provides key insights on the behavior of composite columns subjected to axial compression and biaxial bending and offers an improved yet practical method of evaluating strength under these conditions that will enable more efficient designs. [ABSTRACT FROM AUTHOR]

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For design situations in case of ambient temperature, both EN1992-1-1 and ACI318 provide guidelines for the design of columns, and for evaluating the structural capacity in case of biaxial bending. However, the effect of fire on these columns subjected to biaxial bending is not mentioned in the provisions. Hence, it is important to evaluate the mechanical behavior of columns in case of biaxial bending combined with fire and to provide guidelines for fire resistance design. In this paper, first a simplified method proposed by Bresler is presented for design under ambient temperature in order to predict the interaction curves of concrete columns subjected to biaxial bending and axial loading, based on a calculation of the uniaxial bending capacity. In order to verify whether this method can be adopted in case of fire, a cross-sectional calculation tool is introduced and validated with experimental data. Further, the results from the simplified method are compared with those obtained with the calculation tool. Subsequently, the simplified method is elaborated further in order to take into account the effect of an ISO 834 standard fire for a column loaded by a symmetrical biaxial load. Finally, the results of a parametric study are presented. Suggestions are given for implementing this method for design of relatively short concrete columns subjected to biaxial bending in case of an ISO 834 fire. [ABSTRACT FROM AUTHOR]

Available capacity models for the assessment of seismic capacity of RC columns are mainly based on experimental tests under axial load and uniaxial bending. Furthermore, experimental tests have been mainly performed on columns representative of new constructions. To analyze the effects of biaxial bending on the seismic performances of existing RC columns with design characteristics nonconforming to present day seismic codes and practices, this paper presents the results of a first stage of tests on RC columns under both axial load and biaxial bending, which effectively simulate the seismic actions. In particular, this paper presents results of four tests on full-scale square columns reinforced with plain bars subjected to constant axial load and biaxial cyclic actions. Two different cyclic displacement paths were investigated: horizontal displacements with an inclination angle of 45 or 30°, with respect to the cross-section principal axes. The influence of biaxial bending actions on the global behavior of existing RC columns in terms of stiffness, strength, deformation capacity, and the effects of different horizontal displacements orientation on their performances are herein investigated and discussed; the comparison with experimental outcomes provided by uniaxial bending tests on companion specimens are also presented. Experimental findings showed that biaxial bending actions affect columns rotational capacity more than strength. The rotational capacity reduction because of biaxial bending actions, even if more significant than the flexural capacity reduction, is not currently taken into account in the available seismic guidelines related to existing RC buildings. [ABSTRACT FROM AUTHOR]

This paper presents an analytical model for the analysis of reinforced concrete (RC) members with rectangular cross sections, strengthened in flexure with various types of externally applied reinforcement (near-surface-mounted [NSM] or externally bonded [EBR]), in combination with composite material confining jackets. The model takes into account simple but realistic constitutive laws for the constituent materials and yields, through a simplified procedure, the resistance of cross sections subjected to biaxial bending combined with axial loading. Verification of the analytical approach is provided by comparing the model predictions with existing test results published in the literature. The analytical formulation is then implemented in a user-friendly computer program, which is used to perform a number of parametric studies on the role of various factors (for example, reinforcing ratios, level of axial force, level of confinement, type of external reinforcement, and confining materials) in section resistance. [ABSTRACT FROM AUTHOR]

The performance of different nonlinear modelling strategies to simulate the response of RC columns subjected to axial load combined with cyclic biaxial horizontal loading is compared. The models studied are classified into two categories according to the nonlinearity distribution assumed in the elements: lumped-plasticity and distributed inelasticity. For this study, results of tests on 24 columns subjected to cyclic uniaxial and biaxial lateral displacements were numerically reproduced. The analyses show that the global envelope response is satisfactorily represented with the three modelling strategies, but significant differences were found in the strength degradation for higher drift demands and energy dissipation. [ABSTRACT FROM AUTHOR]