Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Hysteretic model development and seismic response of unbonded post‐tensioned precast CFT segmental bridge columns

The study investigated the cyclic behavior of unbonded, post‐tensioned, precast concrete‐filled tube segmental bridge columns by loading each specimen twice. Moreover, a stiffness‐degrading flag‐shaped (SDFS) hysteretic model was developed based on self‐centering and stiffness‐degrading behaviors. The proposed model overcomes the deficiency of cyclic behavior prediction using a FS model, which self‐centers with fixed elastic and inelastic stiffnesses. Experimental and analytical results showed that (1) deformation capabilities of the column under the first and second cyclic tests were similar; however, energy dissipation capacities significantly differed from each other, and (2) the SDFS model predicted the cyclic response of the column better than the FS model. Inelastic time‐history analyses were performed to demonstrate the dynamic response variability of a single‐degree‐of‐freedom (SDOF) system using both models. A parametric study, performed on SDOF systems subjected to eight historical earthquakes, showed that increased displacement ductility demand was significant for structures with a low period and low‐to‐medium yield strength ratio and reduced displacement ductility demand in these systems was effectively attained by increasing energy dissipation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Shaking table test and numerical simulation of a 1/2‐scale self‐centering reinforced concrete frame

Self‐centering reinforced concrete frames are developed as an alternative of traditional seismic force‐resisting systems with better seismic performance and re‐centering capability. This paper presents an experimental and computational study on the seismic performance of self‐centering reinforced concrete frames. A 1/2‐scale model of a two‐story self‐centering reinforced concrete frame model was designed and tested on the shaking table in State Key Laboratory of Disaster Reduction in Civil Engineering at Tongji University to evaluate the seismic behavior of the structure. A structural analysis model, including detailed modeling of beam–column joints, column–base joints, and prestressed tendons, was constructed in the nonlinear dynamic modeling software OpenSEES. Agreements between test results and numerical solutions indicate that the designed reinforced concrete frame has satisfactory seismic performance and self‐centering capacity subjected to earthquakes; the self‐centering structures can undergo large rocking with minor residual displacement after the earthquake excitations; the proposed analysis procedure can be applied in simulating the seismic performance of self‐centering reinforced concrete frames. To achieve a more comprehensive evaluation on the performance of self‐centering structures, research on energy dissipation devices in the system is expected. Copyright © 2015 John Wiley & Sons, Ltd.     

Single precast concrete rocking walls as earthquake force‐resisting elements

Precast concrete walls with unbonded post‐tensioning provide a simple self‐centering system. Yet, its application in seismic regions is not permitted as it is assumed to have no energy dissipation through a hysteretic mechanism. These walls, however, dissipate energy imparted to them because of the wall impacting the foundation during rocking and limited hysteretic action resulting from concrete nonlinearity. The energy dissipated due to rocking was ignored in previous experimental studies because they were conducted primarily using quasi‐static loading. Relying only on limited energy dissipation, a shake table study was conducted on four single rocking walls (SRWs) using multiple‐level earthquake input motions. All walls generally performed satisfactorily up to the design‐level earthquakes when their performance was assessed in terms of the maximum transient drift, maximum absolute acceleration, and residual drift. However, for the maximum considered earthquakes, the walls experienced peak lateral drifts greater than the permissible limits. Combining the experimental results with an analytical investigation, it is shown that SRWs can be designed as earthquake force‐resisting elements to produce satisfactory performance under design‐level and higher‐intensity earthquake motions. Copyright © 2016 John Wiley & Sons, Ltd.     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.     

An isolation system for limited seismic gaps in near‐fault zones

The ability of a recently proposed seismic isolation system, with inherent self‐stopping mechanism, to mitigate or even eliminate seismic pounding of adjacent structures is investigated under severe near‐fault earthquakes. The isolation system is referred to as roll‐in‐cage (RNC) isolator. It is a rolling‐based isolator that provides in one unit the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, hysteretic energy dissipation, and resistance to minor vibration loads. In addition, the RNC isolator is distinguished by a self‐stopping (buffer) mechanism to limit the bearing displacement under excitations stronger than a design earthquake or at limited seismic gaps, and a linear gravity‐based self‐recentering mechanism to prevent permanent bearing displacement without causing vertical fluctuation of the isolated structure. A previously developed multifeature SAP2000 model of the RNC isolator is improved in this paper to account for the inherent buffer mechanism's damping. Then, the effectiveness of the isolator's buffer mechanism in limiting peak bearing displacements is studied together with its possibly arising negative influence on the isolation efficiency. After that, the study investigates how to alleviate or even eliminate those possibly arising drawbacks, due to the developed RNC isolator's inner pounding as a result of its buffer activation, to achieve efficient seismic isolation with no direct structure‐to‐structure pounding, considering limited seismic gaps with adjacent structures and near‐fault earthquakes. The results show that the RNC isolator could be an efficient solution for aseismic design in near‐fault zones considering limited seismic gaps. Earthquake Engineering and Structural Dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

Cyclic behavior and failure mechanism of self‐centering energy dissipation braces with pre‐pressed combination disc springs

A new type of bracing system composed of friction energy dissipation devices for energy dissipation, pre‐pressed combination disc springs for self‐centering and tube members as guiding elements is developed and experimentally studied in this paper. The mechanics of this system are explained, the equations governing its hysteretic responses are outlined and large‐scale validation tests of two braces with different types of disc springs are conducted under the condition of low cyclic reversed loading. The experimental results demonstrate that the proposed bracing system exhibits a stable and repeatable flag‐shaped hysteretic response with an excellent self‐centering capability and effective energy dissipation throughout the loading protocol. Furthermore, the maximum bearing force and stiffness are predicted well by the equations governing its mechanical behavior. Fatigue and destructive test results demonstrate that the proposed bracing system can maintain stable energy dissipation and self‐centering capabilities under large deformation cyclic loading even when the tube members exceed the elastic limit and that a larger bearing capacity is achieved by the system that has disc springs without a bearing surface. Copyright © 2016 John Wiley & Sons, Ltd.     

Restoring capability of bilinear hysteretic seismic isolation systems

The restoring capability (or re‐centering capability) is identified by the current design codes as a fundamental feature of seismic isolation systems. In this paper, the restoring capability of bilinear hysteretic or frictional seismic isolation systems is investigated in some detail. Certain energy considerations are examined first in order to provide insight into and reveal governing parameters on individual aspects of the problem. The restoring capability is then investigated through an extensive parametric study of smooth bilinear single‐degree‐of‐freedom hysteretic systems, with parameters covering a range of typical seismic isolation systems, subjected to a large group of recorded earthquakes. The results of the parametric analyses are processed statistically and regression analysis relations are derived that show the dependence of the residual displacement after the earthquake and the cumulative build up of displacements after a series of successive earthquakes on the governing parameters. Based on the analysis results, the features of the bilinear system that ensure sufficient restoring capability are identified. Copyright © 2007 John Wiley & Sons, Ltd.     

Using Bézier curves to model gradual stiffness transitions in nonlinear elements: Application to self‐centering systems

A number of techniques are available for modelling nonlinear elements, but most available hysteretic rules do not capture the gradual stiffness changes that are typical of physical systems. In particular, there has not previously been a hysteretic rule with rounded hysteretic corners that could be used to model self‐centering elements, where multiple stiffness changes occur within one loading cycle. This paper presents a new hysteretic rule that allows the gradual stiffness transitions that occur in real systems to be modelled. In this paper, the rule is formulated for flag‐shaped hystereses, but it is shown that the same model also produces hystereses that can be used to model systems that are not self‐centering. The same technique could also be applied to round the corners of different backbone hystereses. A previous study has shown how abrupt stiffness changes can cause very large acceleration spikes, particularly in self‐centering systems. This paper shows that acceleration spikes due to stiffness changes may be reduced by designing systems to change stiffness more gradually, and that this typically has little effect on other aspects of the seismic response. When modelling structural systems, especially if they are self‐centering, sharp‐cornered hysteretic models may be used for initial analysis, but round‐cornered hysteretic models should be considered when using nonlinear rotational springs or when accelerations are of particular importance. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic design procedure and seismic response of post‐tensioned self‐centering steel frames

Post‐tensioned (PT) self‐centering moment‐resisting frames (MRFs) have recently been developed as an alternative to welded moment frames. The first generation of these systems incorporated yielding energy dissipation mechanisms, whereas more recently, PT self‐centering friction damped (SCFR) moment‐resistant connections have been proposed and experimentally validated. Although all of these systems exhibited good stiffness, strength and ductility properties and stable dissipation of energy under cyclic loading, questions concerning their ultimate response still remained and a complete design methodology to allow engineers to conceive structures using these systems was also needed. In this paper, the mechanics of SCFR frames are first described and a comprehensive design procedure that accounts for the frame behavior and the nonlinear dynamics of self‐centering frames is then elaborated. A strategy for the response of these systems at ultimate deformation stages is then proposed and detailing requirements on the beams in order to achieve this response are outlined. The proposed procedure aims to achieve designs where the interstory drifts for SCFR frames are similar to those of special steel welded moment‐resisting frames (WMRFs). Furthermore, this procedure is adapted from current seismic design practices and can be extended to any other PT self‐centering steel frame system. A six‐story building incorporating WMRFs was designed and a similar building incorporating SCFR frames were re‐designed by the proposed seismic design procedure. Time‐history analyses showed that the maximum interstory drifts and maximum floor accelerations of the SCFR frame were similar to those of the WMRF but that almost zero residual drifts were observed for the SCFR frame. The results obtained from the analyses confirmed the validity of the proposed seismic design procedure, since the peak drift values were similar to those prescribed by the seismic design codes and the SCFR frames achieved the intended performance level under both design and maximum considerable levels of seismic loading. Copyright © 2008 John Wiley & Sons, Ltd.     

Shake table test and numerical study of self‐centering steel frame with SMA braces

Given their excellent self‐centering and energy‐dissipating capabilities, superelastic shape memory alloys (SMAs) become an emerging structural material in the field of earthquake engineering. This paper presents experimental and numerical studies on a scaled self‐centering steel frame with novel SMA braces (SMAB), which utilize superelastic Ni–Ti wires. The braces were fabricated and cyclically characterized before their installation in a two‐story one‐bay steel frame. The equivalent viscous damping ratio and ‘post‐yield’ stiffness ratio of the tested braces are around 5% and 0.15, respectively. In particular, the frame was seismically designed with nearly all pin connections, including the pinned column bases. To assess the seismic performance of the SMA braced frame (SMABF), a series of shake table tests were conducted, in which the SMABF was subjected to ground motions with incremental seismic intensity levels. No repair or replacement of structural members was performed during the entire series of tests. Experimental results showed that the SMAB could withstand several strong earthquakes with very limited capacity degradation. Thanks to the self‐centering capacity and pin‐connection design, the steel frame was subjected to limited damage and zero residual deformation even if the peak interstory drift ratio exceeded 2%. Good agreement was found between the experimental results and numerical simulations. The current study validates the prospect of using SMAB as a standalone seismic‐resisting component in critical building structures when high seismic performance or earthquake resilience is desirable under moderate and strong earthquakes. Copyright © 2016 John Wiley & Sons, Ltd.     

考虑自复位影响的预应力节段拼装桥墩地震损伤模型

预应力节段拼装桥墩在地震作用下具有良好的自复位能力,而既有的损伤模型无法准确评估预应力节段桥墩的地震损伤。鉴于此,有必要研究预应力节段拼装桥墩的地震损伤模型。从预应力节段桥墩的自复位特点和损伤机理出发,对自复位性能表征方法进行简化,提出采用自复位修正因子来对桥墩在地震作用下的累积耗能进行修正,从而获得考虑桥墩自复位性能的地震损伤评估模型。在此基础上,划分预应力节段拼装桥墩的损伤状态,最后验证该地震损伤模型及损伤分级方法的适用性。结果表明：预应力节段桥墩的自复位性能与耗能损伤之间呈现明显的相关性,考虑桥墩自复位的地震损伤模型和分级方法适用于不同的预应力节段拼装桥墩,为定量评估预应力节段拼装桥墩在地震作用下的损伤程度打下基础。     

Seismic behaviour of self‐centring braced frame buildings with reusable hysteretic damping brace

This paper presents the seismic behaviour of a concentrically braced frame system with self‐centring capability, in which a special type of bracing element termed reusable hysteretic damping brace (RHDB) is used. The RHDB is a passive energy dissipation device with its core energy‐dissipating component made of superelastic Nitinol wires. Compared with conventional bracing in steel structures, RHDB has a few prominent performance characteristics: damage free under frequent and design basis earthquakes in earthquake prone areas; minimal residual drifts due to the self‐centring capability of RHDB frame; and ability to survive several strong earthquakes without the need for repair or replacement. This paper also includes a brief discussion of the RHDB's mechanical configuration and analytical model for RHDB. The seismic performance study of RHDB frame was carried out through a non‐linear time history analysis of 3‐storey and 6‐storey RHDB frame buildings subjected to two suites of 20 earthquake ground motions. The analysis results were compared with buckling‐restrained brace (BRB) frames. This study shows that RHDB frame has a potential to outperform BRB frames by eliminating the residual drift problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison of web plate numerical models for self‐centering steel plate shear walls

Previous research has shown that self‐centering steel plate shear walls (SC‐SPSWs) are capable of achieving enhanced seismic performance at multiple hazard levels, including recentering following design‐level earthquakes. When modeling SC‐SPSWs numerically, these studies considered an idealized tension‐only steel plate shear wall (SPSW) web plate behavior. Research has shown that web plate behavior is more complex than predicted by the idealized model, and web plates can provide more strength, stiffness, and energy dissipation than predicted by the idealized model. The idealized model of web plate behavior is used widely in SPSW numerical models where the moment‐resisting boundary frame provides supplemental hysteretic damping and stiffness; however, in SC‐SPSWs, where the post‐tensioned boundary frame is designed to remain elastic during an earthquake, accounting for the more complex web plate behavior can have a significant impact on seismic performance estimates from numerical simulation. This paper presents different methods for modeling SC‐SPSWs. Responses from these models are compared with experimental results. A simple modification of the tension‐only model, referred to as the tension‐compression strip model, is shown to provide a reasonable approximation of SC‐SPSW behavior. Results from nonlinear response history analyses of SC‐SPSWs with the tension‐only and tension‐compression web plate models are compared to assess how the approximation of web plate behavior affects SC‐SPSW seismic performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance‐based earthquake engineering assessment of a self‐centering,post‐tensioned concrete bridge system

Highway bridges in highly seismic regions can sustain considerable residual displacements in their columns following large earthquakes. These residual displacements are an important measure of post‐earthquake functionality, and often determine whether or not a bridge remains usable following an earthquake. In this study, a self‐centering system is considered that makes use of unbonded, post‐tensioned steel tendons to provide a restoring force to bridge columns to mitigate the problem of residual displacements. To evaluate the proposed system, a code‐conforming, case‐study bridge structure is analyzed both with conventional reinforced concrete columns and with self‐centering, post‐tensioned columns using a formalized performance‐based earthquake engineering (PBEE) framework. The PBEE analysis allows for a quantitative comparison of the relative performance of the two systems in terms of engineering parameters such as peak drift ratio as well as more readily understood metrics such as expected repair costs and downtime. The self‐centering column system is found to undergo similar peak displacements to the conventional system, but sustains lower residual displacements under large earthquakes, resulting in similar expected repair costs but significantly lower expected downtimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

Force reduction factor for building structures equipped with added viscous dampers

This research work focuses on the analysis of the hysteretic seismic behaviour of inelastic SDOF systems equipped with viscous dampers. In detail, it is aimed at obtaining a practical tool useful for the seismic design of building structures with added dampers, within the framework of the traditional seismic design based on ductility. The objective is to evaluate the appropriate force reduction factor for highly damped (i.e. damping ratio greater than 5 %) SDOF systems able to guarantee a prescribed level of structural safety.