Stiffened steel box columns. Part 1: Cyclic behaviour

This paper aims to study the cyclic inelastic behaviour of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. Such columns find broad application in steel bridge piers. The columns are of box sections with longitudinal stiffeners. In the analysis, a modified two‐surface plasticity model developed at Nagoya University is employed to model material non‐linearity. For comparison, analyses using classical isotropic‐ and kinematic‐hardening models are also carried out. Hysteretic curves and buckling modes obtained from analysis using the two‐surface model and classical models are compared with experimental results. Moreover, the progression of deformation from occurrence of local buckling to structural failure is discussed in detail. The comparisons show that the use of an accurate plasticity model is quite important in the prediction of both the cyclic inelastic behaviour and failure characteristic of steel box columns failed by coupled local and overall instability. It is found that the modified two‐surface model is a satisfactory model in predicting the cyclic hysteretic behaviour of both the thin‐ and thick‐walled steel box columns. Copyright © 2000 John Wiley & Sons, Ltd.     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

Stiffened steel box columns. Part 2: Ductility evaluation

The purpose of this study is to evaluate the ultimate strength and ductility capacity of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. In a companion paper, a finite element formulation accounting for both geometrical and material non‐linearity was developed to obtain cyclic hysteretic behaviour of such columns. In this paper, the effect of loading patterns on the cyclic inelastic behaviour is first studied; then, a parametric study is carried out to investigate the effects of flange plate width–thickness ratio parameter, column slenderness ratio parameter, stiffener's equivalent slenderness ratio parameter, magnitude of axial load, and material type of stiffeners on the strength and ductility of the columns. Last but not least, empirical formulae of both the ultimate strength and ductility capacities are proposed for stiffened steel box columns, and the limit values of various parameters for the required ductility demand are also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns

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.     

Influence of deterioration modelling on the seismic response of steel moment frames designed to Eurocode 8

This paper assesses the influence of cyclic and in‐cycle degradation on seismic drift demands in moment‐resisting steel frames (MRF) designed to Eurocode 8. The structural characteristics, ground motion frequency content, and level of inelasticity are the primary parameters considered. A set of single‐degree‐of‐freedom (SDOF) systems, subjected to varying levels of inelastic demands, is initially investigated followed by an extensive study on multi‐storey frames. The latter comprises a large number of incremental dynamic analyses (IDA) on 12 frames modelled with or without consideration of degradation effects. A suite of 56 far‐field ground motion records, appropriately scaled to simulate 4 levels of inelastic demand, is employed for the IDA. Characteristic results from a detailed parametric investigation show that maximum response in terms of global and inter‐storey drifts is notably affected by degradation phenomena, in addition to the earthquake frequency content and the scaled inelastic demands. Consistently, both SDOF and frame systems with fundamental periods shorter than the mean period of ground motion can experience higher lateral strength demands and seismic drifts than those of non‐degrading counterparts in the same period range. Also, degrading multi‐storey frames can exhibit distinctly different plastic mechanisms with concentration of drifts at lower levels. Importantly, degrading systems might reach a “near‐collapse” limit state at ductility demand levels comparable to or lower than the assumed design behaviour factor, a result with direct consequences on optimised design situations where over‐strength would be minimal. Finally, the implications of the findings with respect to design‐level limit states are discussed.     

Loading protocols for European regions of low to moderate seismicity

Existing loading protocols for quasi-static cyclic testing of structures are based on recordings from regions of high seismicity. For regions of low to moderate seismicity they overestimate imposed cumulative damage demands. Since structural capacities are a function of demand, existing loading protocols applied to specimens representative of structures in low to moderate seismicity regions might underestimate structural strength and deformation capacity. To overcome this problem, this paper deals with the development of cyclic loading protocols for European regions of low to moderate seismicity. Cumulative damage demands imposed by a set of 60 ground motion records are evaluated for a wide variety of SDOF systems that reflect the fundamental properties of a large portion of the existing building stock. The ground motions are representative of the seismic hazard level corresponding to a 2 % probability of exceedance in 50 years in a European moderate seismicity region. To meet the calculated cumulative damage demands, loading protocols for different structural types and vibration periods are developed. For comparison, cumulative seismic demands are also calculated for existing protocols and a set of records that was used in a previous study on loading protocols for regions of high seismicity. The median cumulative demands for regions of low to moderate seismicity are significantly less than those of existing protocols and records of high seismicity regions. For regions of low to moderate seismicity the new protocols might therefore result in larger strength and deformation capacities and hence in more cost-effective structural configurations or less expensive retrofit measures.     

Experimental behavior of transfer story connections for high‐rise SRC structures under seismic loading

Results from an investigation aimed at assessing seismic behavior of transfer story connections for high‐rise building consisting of steel‐reinforced concrete (SRC) frame and reinforced concrete (RC) core tube are presented. Two types of transfer story connections were experimentally evaluated for adequate strength, ductility and energy dissipation. For each type of connection, two large‐scale subassembly tests were carried out under monotonic and cyclic lateral displacement, respectively. Detailed observations and behavior responses were obtained to contrast the differences between monotonic and cyclic performance of the connections. Test results showed that the SRC column failed before connection collapse and that loading types have little effect on the strength but greatly affect the failure modes and the ductility of the connections. All specimens exhibited good properties for earthquake resistance since they all kept a stable inelastic behavior up to the interstory drift demand suggested by the AISC Seismic Provisions. Based on test observations, support stiffeners with appropriate width‐to‐thickness ratio and mechanical connectors connecting bars with the steel plate are recommended for design purposes in order to achieve more ductile and reliable seismic behavior of transfer story connections. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic performance of recycled concrete-filled square steel tube columns

An experimental study on the seismic performance of recycled concrete-filled square steel tube (RCFST) columns is carried out. Six specimens were designed and tested under constant axial compression and cyclic lateral loading. Two parameters, replacement percentage of recycled coarse aggregate (RCA) and axial compression level, were considered in the test. Based on the experimental data, the hysteretic loops, skeleton curves, ductility, energy dissipation capacity and stiffness degradation of RCFST columns were analyzed. The test results indicate that the failure modes of RCFST columns are the local buckling of the steel tube at the bottom of the columns, and the hysteretic loops are full and their shapes are similar to normal CFST columns. Furthermore, the ductility coefficient of all specimens are close to 3.0, and the equivalent viscous damping coefficient corresponding to the ultimate lateral load ranges from 0.323 to 0.360, which demonstrates that RCFST columns exhibit remarkable seismic performance.     

基于纤维模型的空间网架支承体系的优化设计与分析

近年来,民用航空制造业的快速发展给大柱距空间网架结构带来新的契机。本文针对某大柱距厂房设计了无柱间支撑、柱间钢支撑和柱间消能支撑3种抗侧力结构体系。在此基础上,分别建立了3种结构体系的三维整体有限元模型,通过优化设计确立了钢支撑和消能支撑的具体设计参数,并进行了多遇地震作用下的弹性时程对比分析。最后,建立了结构弹塑性分析的纤维模型,对3种结构体系进行了罕遇地震作用下的弹塑性时程分析,对比研究了3种结构体系在大震作用下的倒塌机制。结果表明：采用纤维模型能够较为精确地进行结构的弹塑性时程分析;相较于不加柱间支撑结构体系,柱间钢支撑和柱间消能支撑结构体系在多遇地震作用下的结构层间位移分别衰减约32%和64%,在罕遇地震作用下的结构层间位移分别衰减约12%和46%,且均具有更好的倒塌机制。本文可供大柱距空间结构的设计与分析参考和借鉴。     

Seismic performance of a 3D full‐scale high‐ductile steel–concrete composite moment‐resisting frame—Part II: Test results and analytical validation

This paper presents the results of a multi‐level pseudo‐dynamic seismic test program that was performed to assess the performance of a full‐scale three‐bay, two‐storey steel–concrete composite moment‐resisting frame built with partially encased composite columns and partial‐strength beam‐to‐column joints. The system was designed to develop a ductile response in the joint components of beam‐to‐column joints including flexural yielding of beam end plates and shear yielding of the column web panel zone. The ground motion producing the damageability limit state interstorey drift caused minor damage while the ultimate limit state ground motion level entailed column web panel yielding, connection yielding and plastic hinging at the column base connections. The earthquake level chosen to approach the collapse limit state induced more damage and was accompanied by further column web panel yielding, connection yielding and inelastic phenomena at column base connections without local buckling. During the final quasi‐static cyclic test with stepwise increasing displacement–amplitudes up to an interstorey drift angle of 4.6%, the behaviour was ductile although cracking of beam‐to‐end‐plate welds was observed. Correlations with numerical simulations taking into account the inelastic cyclic response of beam‐to‐column and column base joints are also presented in the paper together. Inelastic static pushover and time history analysis procedures are used to estimate the structural behaviour and overstrength factors of the structural system under study. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of variation in loading protocol on the strength and deformation capacity of ductile reinforced concrete beams

Understanding the impact of prior earthquake damage on residual capacity is important for postearthquake damage assessment of buildings; however, interpretation of such impact is challenging when based on tests using traditional reversed‐cyclic loading protocols. A new loading protocol, consisting of a dynamic earthquake displacement history followed by quasi‐static reversed‐cyclic loading to failure, is presented as an alternative to traditional simulated seismic loading protocols. Data are analyzed from a set of 12 nominally identical ductile reinforced concrete beams that were tested by using variations of this protocol and traditional reversed‐cyclic and monotonic protocols. Differences in the cycle content of the earthquake displacement histories applied to the test specimens allowed for the effects of load history variation below 2.2% drift to be isolated. It is found that such variation had no effect on the beam deformation capacities. The effects of dynamic loading rates are also analyzed and compared against control quasi‐static specimens. Relative strength increases due to dynamic loading are found to be more significant at yield than at ultimate. Dynamic loading rates led to modest reductions in the beam deformation capacities, but the presence of causality between these variables remains uncertain.     

不同支撑形式高强钢组合偏心支撑抗震性能研究

耗能梁段作为偏心支撑结构的耗能元件,在大震作用下通过弹塑性变形吸收地震能量,保护主体结构处于弹性受力状态。现行规范基于强度的设计理论,为了保证耗能梁段进入塑性或破坏,梁柱构件需要进行放大内力设计,导致截面过大,而且基于强度的设计方法很难保证结构的整体破坏状态。目前,抗震设计越来越重视基于性能的设计思想,该方法能够评估结构的弹塑性反应。对于高强钢组合偏心支撑,其中耗能梁段和支撑采用Q345钢,框架梁柱采用Q460或者Q690高强度钢材,高强钢不仅带来良好的经济效益,而且能够推广高强钢在抗震设防区的应用。利用基于性能设计方法设计了4种不同形式的高强钢组合偏心支撑钢框架,包括K形、Y形、V形和D形,考虑4层、8层、12层和16层的影响。通过Pushover分析和非线性时程分析评估该结构的抗震性能,研究结果表明:4种形式的高强钢组合偏心支撑钢框架具有类似的抗震性能,在罕遇地震作用下,几乎所有耗能梁段均参与耗能,而且层间侧移与耗能梁段转角沿高度分布较为均匀。其中:D形偏心支撑具有最大的抗侧刚度,但延性较差,而Y形偏心支撑的抗侧刚度最弱,但延性最佳。     

Effects of column axial force – bending moment interaction on inelastic seismic response of steel frames

It is well known that axial force – bending moment interaction (N–M interaction) affects to a large extent the cyclic inelastic behaviour of structural elements, especially columns in framed structures, with reduction in bending capacity and loss of available ductility. A few studies have also shown that significant inelastic axial shortening affects the response of column elements subjected to medium–high levels of axial loads and cyclic bending. This paper is primarily aimed at evaluating the effects of column N–M interaction on the inelastic seismic response of steel frames. By considering the contemporaneous action of vertical loads, due to gravity, and of horizontal seismic excitation, it is shown that the progressive axial shortening of adjacent columns may differ substantially, thus inducing significant relative settlements at the ends of the connecting beams and, then, remarkable amplifications in beam plastic rotations. An evaluation of additional beam plastic rotations induced by column N–M interaction is carried out for real structures by investigating the inelastic response of steel frames designed according to European standards under horizontal and vertical earthquake excitations. Copyright © 2003 John Wiley & Sons, Ltd.     

Loading protocols for experimental seismic qualification of members in conventional and emerging steel frames

Quasi-static testing is one of the most commonly used experimental methods for examining the seismic performance of structural members. However, consistent loading protocols for experimental seismic qualification of members in emerging steel frames such as self-centering braced frames (SCBFs) as well as in some conventional ones including buckling-restrained braced frames (BRBFs) are still lacking. This paper aims to propose standardized loading protocols based on time-history dynamic analysis on a series of prototype building frames, including steel SCBFs, BRBFs, and moment-resisting frames (MRFs), where both far-field and near-fault earthquakes are considered. The methodology for the development of the loading protocols involves ground motion selection and scaling, design and analysis of prototype buildings, analysis results processing, and rainflow cycle counting, together with extra justification steps. The proposed loading protocols are consistently derived based on the MCE-level seismic hazard and 84^th percentile values of key seismic demand parameters. These parameters are number of damaging cycles N_t, maximum inter-story drift θ_max, inter-story drift range Δθ_i, sum of inter-story drift range ΣΔθ_i, and residual inter-story drift θ_r. The analysis confirms the variations in these seismic demands imposed on the different structural systems under different types of ground motions, highlighting the necessity of developing separate loading protocols for the different cases. The assumptions, decisions, and judgments made during the development of the loading protocols are elaborated, and the conditions and restrictions are outlined. The rationality of the proposed loading protocols is further justified through demonstrating the cumulative distribution function and energy dissipation demand of the systems.     

Inelastic displacement ratios for evaluation of structures built on soft soil sites

This paper summarizes the results of a comprehensive statistical study aimed at evaluating peak lateral inelastic displacement demands of structures with known lateral strength and stiffness built on soft soil site conditions. For that purpose, empirical information on inelastic displacement ratios which are defined as the ratio of peak lateral inelastic displacement demands to peak elastic displacement demands are investigated. Inelastic displacement ratios were computed from the response of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to 118 earthquake ground motions recorded on bay‐mud sites of the San Francisco Bay Area and on soft soil sites located in the former lake‐bed zone of Mexico City. Mean inelastic displacement ratios and their corresponding scatter are presented for both ground motion ensembles. The influence of period of vibration normalized by the predominant period of the ground motion, the level of lateral strength, earthquake magnitude, and distance to the source are evaluated and discussed. In addition, the effects of post‐yield stiffness and of stiffness and strength degradation on inelastic displacement ratios are also investigated. It is concluded that magnitude and distance to the source have negligible effects on constant‐strength inelastic displacement ratios. Results also indicate that weak and stiffness‐degrading structures in the short spectral region could experience inelastic displacement demands larger than those corresponding to non‐degrading structures. Finally, a simplified equation obtained using regression analyses aimed at estimating mean inelastic displacement ratios is proposed for assisting structural engineers in performance‐based assessment of structures built on soft soil sites. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic behavior and strength capacity of steel tube‐reinforced concrete composite columns

The steel tube‐reinforced concrete (ST‐RC) composite column is a novel type of composite column, which consists of a steel tube embedded in RC. In this paper, the seismic behavior of ST‐RC columns is examined through a series of experiments in which 10 one‐third scale column specimens were subjected to axial forces and lateral cyclic loading. The test variables include the axial force ratio applied to the columns and the amount of transverse reinforcement. All specimens failed in a flexural mode, showing stable hysteresis loops. Thanks to the steel tube and the high‐strength concrete it is filled with, the ST‐RC column specimens had approximately 30% lower axial force ratios and 22% higher maximum bending moments relative to the comparable RC columns when subjected to identical axial compressive loads. The amount of transverse reinforcement made only a small difference to the lateral load‐carrying capacity but significantly affected the deformation and energy dissipation capacity of the ST‐RC columns. The specimens that satisfied the requirements for transverse reinforcement adopted for medium ductile RC columns as specified by the Chinese Code for Seismic Design of Buildings (GB 50011‐2010) and EuroCode 8 achieved an ultimate drift ratio of around 0.03 and a displacement ductility ratio of approximately 5. The design formulas used to evaluate the strength capacity of the ST‐RC columns were developed on the basis of the superposition method. The predictions from the formulas showed good agreement with the test results, with errors no greater than 10%. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic analysis of long multiple-span highway bridges

Mathematical models and three-dimensional non-linear dynamic analysis procedures are described for determining the seismic response of long, curved (or straight), multiple-span, reinforced concrete highway bridges. Under the action of strong earthquakes, the columns (or piers) of such structures may experience large cyclic inelastic deformations of a coupled form. Also, cyclic slippage of the Coulomb type can take place in the expansion joints of the deck causing multiple impacts and separations to occur. These separations may be sufficiently large to cause tensile yielding of the longitudinal expansion joint restrainer bars (or cables) and, if not controlled, can permit deck spans to fall off their supports resulting in partial or total collapse of the structure. In this paper, a three-dimensional elasto-plastic mathematical model suitable for representing the coupled inelastic flexural behaviour of reinforced concrete columns under cyclic deformations is presented along with a non-linear mathematical model for simulating the non-linear discontinuous behaviour of expansion joints. The procedures used for non-linear seismic response analysis are described and a numerical example is given to illustrate the method.     

同级位移多次循环作用下型钢混凝土柱抗震性能试验研究

为研究远场长周期地震动作用下SRC柱的抗震性能,对5个不同含钢率和配箍率的SRC柱进行同级位移循环加载10次的拟静力试验,分析其抗震性能指标。结果表明:同级位移循环次数对SRC柱抗震性能的影响与循环位移幅值有关。位移角不大于1/50时,同级位移循环次数对SRC柱的裂缝发展、承载力退化和耗能能力的影响均很小;位移角1/40时,随着位移循环次数的增加,SRC柱的裂缝不断发展,角部混凝土逐渐掉落,承载力退化幅度开始加大,耗能能力逐渐增强,损伤程度增长较快;位移角1/33时,同级位移多次循环导致SRC柱的损伤急剧发展,承载力快速降低,耗能能力明显增强,破坏程度显著加重。提高含钢率和配箍率均可以改善SRC柱的抗震性能。