Seismic behavior of asymmetric RC wall buildings: principles and new deformation‐based design method

The seismic design of multi‐story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non‐linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story‐drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story‐drift (performance goals) are discussed. The definition of an eccentricity of the earthquake‐equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake‐equivalent lateral force. A new deformation‐based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story‐drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi‐story asymmetric RC wall building. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of a capacity spectrum seismic design approach against cyclic and seismic experiments on full‐scale precast RC structures

Within the last decades, simplified methods alternative to dynamic nonlinear analysis have been developed to estimate the seismic performance of structures toward a performance‐oriented design. Considering drift as the main parameter correlated with structural damage, its estimation is of main importance to assess the structural performance. While traditional force‐based design deals with calibrated force reduction factors based on the expected structural ductility, other methods are based on the definition of a viscous damping factor defined as a function of the expected energy dissipated by the structure. An example is the capacity spectrum method. This method can be applied even without any a priori calibration or designer arbitrariness. This allows considering several peculiarities of the seismic behavior of precast structures, which may be influenced by nontraditional hysteresis of connections and members, interaction with the cladding panels, P‐δ effects, etc. The paper aims at verifying the soundness and accuracy of this method through the comparison of its predictions against the results of cyclic and pseudodynamic tests on precast structures, including single‐ and multistory buildings either stiff or flexible, obtained on full‐scale building prototypes tested within the framework of recent research projects (namely, “Precast Structures EC8,” “Safecast,” and “Safecladding”). Two simple methodologies of determination of the equivalent viscous damping from a force‐displacement cycle, based on the dissipated energy in relation to 2 different estimates of the elastic strain energy, are addressed and compared. Comments on the possible use of this procedure for the estimation of the seismic performance of precast structures are provided.     

A study on using pre‐bent steel strips as seismic energy‐dissipative devices

Buckling is usually conceived as an unstable structural behavior leading to lateral instability of axially loaded members, if not properly supported. However, a pre‐bent strip would become an excellent seismic energy‐dissipative device if it is deformed in a guided direction and range. Geometrically large lateral deformation of the steel strips in buckling leads to inelastic behavior of the material and dissipates energy as a consequence. The purpose of this study is to propose a new type of seismic damper in the form of braces based on pre‐bent steel strips. The nonlinear elastic stiffness of monotonously loaded pre‐bent strips in both compression and tension is derived. The energy‐dissipative characteristics of the proposed damping device are investigated via component tests under cyclic loads. Experimental results indicate that the force–displacement relationship of pre‐bent strips in cyclic loads exhibits mechanical characteristics of displacement‐dependent dampers. A series of seismic performance tests has been conducted further to verify the feasibility and effectiveness of using the proposed device as seismic dampers. Encouraging test results have been obtained, suggesting feasibility of the proposed device for earthquake‐resistant design. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of seismic energy demand

In this paper, a method is proposed in order to obtain a simplified representation of hysteretic and input energy spectra. The method is based on the evaluation of the equivalent number of cycles correlated to the earthquake characteristics by the proposed seismic index I_D. This procedure allows us to obtain peak values of the hysteretic and input energy that depend on the demanded ductility, on the seismic index I_D and on the peak pseudo‐velocity. The assessment of the input energy represents a first step towards the definition of a damage potential index capable of taking into account the effect of the duration of the ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Design of hysteretic dampers with optimal ductility for the transverse seismic control of cable‐stayed bridges

Cable‐stayed bridges require a careful consideration of the lateral force exerted by the deck on the towers under strong earthquakes. This work explores the seismic response of cable‐stayed bridges with yielding metallic dampers composed of triangular plates that connect the deck with the supports in the transverse direction. A design method based on an equivalent single‐degree of freedom approximation is proposed. This is proved valid for conventional cable‐stayed bridges with 200‐ and 400‐m main spans, but not 600 m. The height of the plates is chosen to (1) achieve a yielding capacity that limits the maximum force transmitted from the deck to the towers, and to (2) control the hysteretic energy that the dampers dissipate by defining their design ductility. In order to select the optimal ductility and the damper configuration, a multi‐objective response factor that accounts for the energy dissipation, peak damper displacement and low‐cycle fatigue is introduced. The design method is applied to cable‐stayed bridges with different spans and deck–support connections. The results show that the dissipation by plastic deformation in the dampers prevents significant damage in the towers of the short‐to‐medium‐span bridges under the extreme seismic actions. However, the transverse response of the towers in the bridge with a 600‐m main span is less sensitive to the dampers. Copyright © 2017 John Wiley & Sons, Ltd.     

Energy demands for seismic design against low‐cycle fatigue

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure is likely to undergo during severe ground motion could lead to unsatisfactory performance. In spite of this, current design procedures do not take into account explicitly the effect of low‐cycle fatigue. Based on the high correlation that exists between the strength reduction factor and the energy demand in earthquake‐resistant structures, simple procedures can be formulated to estimate the cumulative plastic deformation demands for design purposes. Several issues should be addressed during the use of plastic energy within a practical performance‐based seismic design methodology. Copyright © 2006 John Wiley & Sons, Ltd.     

Scaling of strength reduction factors for degrading elasto‐plastic oscillators

The inelastic (design) spectra characterizing a seismic hazard are generally obtained by the scaling‐down of the elastic (design) spectra via a set of response modification factors. The component of these factors, which accounts for the ductility demand ratio, is known as the strength reduction factor (SRF), and the variation of this factor with initial period of the oscillator is called an SRF spectrum. This study considers scaling of the SRF spectrum in the case of an elasto‐plastic oscillator with strength and stiffness degradation characteristics. Two models are considered: one depending directly on the characterization of source and site parameters and the other depending on the normalized design spectrum characterization of the seismic hazard. The first model is the same as that proposed earlier by the second author, and is given in terms of earthquake magnitude, strong‐motion duration, predominant period, geological site conditions, ductility demand ratio, and ductility supply‐related parameter. The second model is a new model proposed here in terms of the normalized pseudo‐spectral acceleration values (to unit peak ground acceleration), ductility demand ratio and ductility supply‐related parameter. For each of these models, least‐square estimates of the coefficients are obtained through regression analyses of the data for 956 recorded accelerograms in western U.S.A. Parametric studies carried out with the help of these models confirm the dependence of SRFs on strong‐motion duration and earthquake magnitude besides predominant period and site conditions. It is also seen that degradation characteristics make a slight difference for high ductility demands and may lead to lower values of SRFs, unless the oscillators are very flexible. Copyright © 2004 John Wiley & Sons, Ltd.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Establishing absorbed energy spectra—an attenuation approach

For energy‐based seismic design, energy demand in the form of absorbed energy spectra was established by an attenuation relationship. The absorbed energy is proposed for evaluating the energy demand in an inelastic system because the absorbed energy is directly related to the pseudo‐velocity in the elastic case. Based on a total of 273 ground motion records from 15 significant earthquakes in California, an attenuation relationship of the absorbed energy was established from a two‐stage non‐linear regression analysis. This relationship was established for a given earthquake magnitude, source‐to‐site distance, site class, and ductility factor. A similar expression for the normalized absorbed energy was also developed. This study showed that the absorbed energy for near‐field ground motions can be significantly larger than that predicted by the attenuation relationship for normal ground motions. Copyright © 2000 John Wiley & Sons, Ltd.     

基于位移的概率极限状态设计

尽管近年来国内外学者提出了多种基于位移的抗震设计方法，但采用的与位移相关的反应谱大多是平均谱，设计过程可以看作是确定性的。基于位移的抗震设计应该建立在可靠度理论基础之上。利用作者在概率延性需求谱方面已有的研究成果和可靠度分析方法——验算点法，本文提出了根据基于位移的目标可靠指标直接进行结构设计的方法，并给出了设计流程图。为便于工程应用，在进行了大量分析计算之后，本文建议了基于位移的概率极限状态分项系数设计表达式，并确定了其中的分项系数。最后，本文对一8层框架结构采用建议的分项系数设计表达式进行了设计，并对有待于进一步研究的问题进行了简要分析。     

Experimental and analytical investigations of steel panel dampers for seismic applications in steel moment frames

A ductile Vierendeel frame can be constructed by incorporating steel panel dampers (SPDs) into a moment‐resisting frame (MRF). Thus, the stiffness, strength, and ductility of the lateral force–resisting system can be enhanced. The proposed 3‐segment SPD possesses a center inelastic core (IC) and top and bottom elastic joints. This paper discusses the mechanical properties, capacity design method, and buckling‐delaying stiffeners for the SPDs through the use of cyclic loading tests on 2 specimens. Tests confirm that SPDs' cyclic force vs deformation relationships can be accurately predicted using either the Abaqus or PISA3D model analyses. The paper also presents the capacity design method for boundary beams connected to the SPDs of a typical SPD‐MRF. The seismic performance of an example 6‐story SPD‐MRF is evaluated using nonlinear response history analysis procedures and 240 ground accelerations at 3 hazard levels. Results indicate that under 80 maximum considered earthquake ground accelerations, the mean‐plus‐one standard deviation of the shear deformation of the ICs in the SPDs is 0.055 rad, substantially less than the 0.11 rad deformational capacity observed from the SPD specimens. The experimental cumulative plastic deformation of the proposed SPD is 242 times the yield deformation and is capable of sustaining a maximum considered earthquake at least 8 times before failure. This paper introduces the method of using one equivalent beam‐column element for effective modeling of the 3‐segment SPD. The effects of the IC's relative height and stiffness on the overall SPD's elastic and postelastic stiffness, elastic deformation limits, and inelastic deformational demands are discussed.     

Hybrid experimental performance of a full‐scale two‐story buckling‐restrained braced RC frame

This paper proposes a novel implementation of buckling‐restrained braces (BRB) in new reinforced concrete (RC) frame construction. Seismic design and analysis methods for using a proposed steel cast‐in anchor bracket (CAB) to transfer normal and shear forces between the BRB and RC members are investigated. A full‐scale two‐story RC frame with BRBs (BRB‐RCF) is tested using hybrid and cyclic loading test procedures. The BRBs were arranged in a zigzag configuration and designed to resist 70% of the story shear. The gusset design incorporates the BRB axial and RCF actions, while the beam and column members comply with ACI 318‐14 seismic design provisions. Test results confirm that the BRBs enhanced the RCF stiffness, strength, and ductility. The hysteresis energy dissipation ratios in the four hybrid tests range from 60% to 94% in the two stories, indicating that BRBs can effectively dissipate seismic input energy. When the inter‐story drift ratio for both stories reached 3.5% in the cyclic loading test, the overall lateral force versus deformation response was still very stable. No failure of the proposed steel CABs and RC discontinuity regions was observed. This study demonstrates that the proposed design and construction methods for the CABs are effective and practical for real applications. Copyright © 2016 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.     

A study on using wide‐flange section web under out‐of‐plane flexure for passive energy dissipation

It is not common to purposely subject the web of wide‐flange or I‐sections to out‐of‐plane bending. However, yielding the web under this loading condition can be a stable source of energy dissipation as the transition at the corner from the web to the flanges is smooth and weld‐free; this prevents stress concentrations causing premature failure and eliminates uncertainties and imperfections associated with welding. Further, short segments of wide‐flange or I‐sections constitute a simple and inexpensive energy dissipating device as minimum manufacturing is required and leftovers not useful for other structural purposes can be re‐utilized. This paper proposes a new type of seismic damper in the form of braces based on yielding the web of short length segments of wide‐flange or I‐shaped steel sections under out‐of‐plane bending. The hysteretic behavior and ultimate energy dissipation capacity is investigated via component tests under cyclic loads. The experimental results indicate that the damping device has stable restoring force characteristics and a high energy dissipation capacity. Based on these results, a simple hysteretic model for predicting the load–displacement curve of the seismic damper is proposed, along with a procedure for predicting its ultimate energy dissipation capacity and anticipating its failure under arbitrarily applied cyclic loads. The procedure considers the influence of the loading path on the ultimate energy dissipation capacity. Finally, shaking table tests on half‐scale structures are conducted to further verify the feasibility and effectiveness of the new damper, and to assess the accuracy of the hysteretic model and the procedure for predicting its failure. Copyright © 2010 John Wiley & Sons, Ltd.     

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy (R_E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude.Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio.The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.     

Earthquake‐resistant structural design through energy demand and capacity

An energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 John Wiley & Sons, Ltd.     

A procedure for evaluating seismic energy demand of framed structures

Energy serves as an alternative index to response quantities like force or displacement to include the duration‐related seismic damage effect. A procedure to evaluate the absorbed energy in a multistorey frame from energy spectra was developed. For low‐ to medium‐rise frames, it required a static pushover analysis of the structure to determine the modal yield force and ductility factor of an equivalent single‐degree‐of‐freedom system for the first two modes. The energy spectra were then used to determine the energy contribution of each mode. A procedure was also developed to distribute the energy along the frame height based on energy shapes. This study showed that the second‐mode response in some cases needs to be considered to reflect the energy (or damage) concentration in the upper floors. Copyright © 2002 John Wiley & Sons, Ltd.     

Design method and behavior factor for steel frames with buckling restrained braces

Buckling restrained braces (BRBs) are very effective in dissipating energy through stable tension–compression hysteretic cycles and have been successfully experimented in the seismic protection of buildings. Their behavior has been studied extensively in the last decades and today the level of performance guaranteed by these devices and the technological constrains that have to be fulfilled to optimize their behavior are well known. Furthermore, several companies in the world have developed their own BRBs and are now producing them. In spite of this, many seismic codes (for instance, the EuroCode 8) do not stipulate provisions for the design and construction of earthquake‐resistant structures equipped with BRBs. This discourages the structural engineering community from using these devices and seriously limits their use in structural applications. In this paper a procedure for the seismic design of steel frames equipped with BRBs is proposed. Furthermore, the paper presents a numerical investigation aimed at validating this design procedure and proposing the value of the behavior factor q that should be used for this structural type. To this end, a set of frames with BRBs is first designed by means of several values of q. Then, the obtained frames are subjected to a set of accelerograms compatible with the elastic response spectrum considered in design. The seismic response of the frames is determined by nonlinear dynamic analysis and represented in terms of the ductility demand of BRBs and the internal force demand of nondissipative members (beams and columns). Finally, the largest value of q that leads to acceptable seismic performance of the analyzed frames is assumed as adequate. The value of q is given in the paper as a continuous function of the assumed ductility capacity of the BRBs. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.