A new methodology for energy-based seismic design of steel moment frames

A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom (SDOF) systems are applied to multi-degree-of-freedom (MDOF) steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault-normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design (EBSD) procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.     

Characterization of displacement demand for elastic and inelastic SDOF systems

The results of a research concerning the characterization of elastic and inelastic displacement spectral demand as a function of magnitude, source-to-site distance, and soil type are presented. The displacement spectra were computed for single degree of freedom systems subjected to a large set of strong ground motion records.In the elastic case, design displacement spectra, modeled in a simplified way with a bilinear shape in the period range 0–4 s, are then proposed for the estimation of the displacement demand to structures located on different local soil condition, at different distance from the causative fault, and for different levels of magnitude. In order to evaluate the reliability of the proposed design displacement spectra, probabilistic displacement spectra corresponding to different levels of probability of non-exceedance were also carried out.The inelastic displacement demand to elasto-plastic systems was analyzed through the ratio between inelastic and elastic spectral displacements. Simplified relationships of the inelastic displacement ratio are then proposed as a function of displacement ductility, soil condition and period of vibration. Finally, as a comparison, the inelastic displacement ratios were also estimated considering other constitutive models.     

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.     

Probabilistic seismic demand model for pounding risk assessment

Earthquake‐induced pounding of adjacent structures can cause severe structural damage, and advanced probabilistic approaches are needed to obtain a reliable estimate of the risk of impact. This study aims to develop an efficient and accurate probabilistic seismic demand model (PSDM) for pounding risk assessment between adjacent buildings, which is suitable for use within modern performance‐based engineering frameworks. In developing a PSDM, different choices can be made regarding the intensity measures (IMs) to be used, the record selection, the analysis technique applied for estimating the system response at increasing IM levels, and the model to be employed for describing the response statistics given the IM. In the present paper, some of these choices are analyzed and evaluated first by performing an extensive parametric study for the adjacent buildings modeled as linear single‐degree‐of‐freedom systems, and successively by considering more complex nonlinear multi‐degree‐of‐freedom building models. An efficient and accurate PSDM is defined using advanced intensity measures and a bilinear regression model for the response samples obtained by cloud analysis. The results of the study demonstrate that the proposed PSDM allows accurate estimates of the risk of pounding to be obtained while limiting the number of simulations required. Copyright © 2016 John Wiley & Sons, Ltd.     

An energy-based method for seismic retrofit of existing frames using hysteretic dampers

This paper proposes a method for the seismic retrofitting of existing frames by adding hysteretic energy dissipating devices (EDDs). The procedure is based on the energy balance of the structure, and it is used to determine the lateral strength, the lateral stiffness and the energy dissipation capacity of the EDDs needed in each story to achieve prescribed target performance levels for a given earthquake hazard. The performance levels are governed by the maximum lateral displacement. The earthquake hazard is characterized in terms of input energy and several seismological parameters, and further takes into account the proximity of the earthquake to the source. The proposed method deals with the effect of the EDDs explicitly in terms of hysteretic energy, bypassing equivalent viscous damping approximations, and directly quantifies the cumulative damage induced in the EDDs. The validity of the method is assessed numerically through nonlinear dynamic response analyses with near-fault and far-field ground motions, as well as experimentally through dynamic shaking table tests.     

A comparison of intensity‐based demand distributions and the seismic demand hazard for seismic performance assessment

This paper compares the seismic demands obtained from an intensity‐based assessment, as conventionally considered in seismic design guidelines, with the seismic demand hazard. Intensity‐based assessments utilize the distribution of seismic demand from ground motions that have a specific value of some conditioning intensity measure, and the mean of this distribution is conventionally used in design verification. The seismic demand hazard provides the rate of exceedance of various seismic demand values and is obtained by integrating the distribution of seismic demand at multiple intensity levels with the seismic hazard curve. The seismic demand hazard is a more robust metric for quantifying seismic performance, because seismic demands from an intensity‐based assessment: (i) are not unique, with different values obtained using different conditioning intensity measures; and (ii) do not consider the possibility that demand values could be exceeded from different intensity ground motions. Empirical results, for a bridge‐foundation‐soil system, illustrate that the mean seismic demand from an intensity‐based assessment almost always underestimates the demand hazard value for the exceedance rate considered, on average by 17% and with a large variability. Furthermore, modification factors based on approximate theory are found to be unreliable. Adopting the maximum of the mean values from multiple intensity‐based assessments, with different conditional intensity measures, provides a less biased prediction of the seismic demand hazard value, but with still a large variability, and a proportional increase the required number of analyses. For an equivalent number of analyses, direct computation of the seismic demand hazard is a more logical choice and provides additional performance insight. Copyright © 2013 John Wiley & Sons, Ltd.     

Constant-ductility strength demand spectra for seismic design of structures

In displacement-based seismic design, constant-ductility strength demand spectra （CDSDS） are very useful for preliminary design of new structures where the global displacement ductility capacity is known. The CDSDS can provide the required inelastic lateral strength of new structures from the required elastic lateral strength. Based on a statistical study of nonlinear time-history for an SDOF system, the mean CDSDS corresponding to four site conditions are presented and approximate expressions of the inelastic spectra are proposed, which are functions of the structural period and ductility level. The effects of site conditions, structural period, level of ductility, damping and post-yield stiffness of structures on CDSDS are also investigated. It is concluded that site conditions, ductility level and structural period have important effects on the CDSDS and damping, post-yield stiffness effects are rather complex and of minor importance. The damping, post-yield stiffness effects depend on both the level of ductility and the natural period of structures.     

Sensitivity analysis on the input parameters in probabilistic seismic hazard assessment

A project has been implemented in recent years for assessing seismic hazard in the Italian territory on probabilistic bases, to be used as scientific background for the revision of the current seismic zonation. A consolidated approach was considered for the purpose; seismic hazard was estimated in terms of peak ground acceleration and macroseismic intensity. As the computer code employed allows the user to make specific choices on some input data, some rather unorthodox decisions were taken regarding earthquake catalogue completeness, seismicity rates, boundaries of the seismogenic zones, definition of the maximum magnitude, attenuation relation, etc. The overwhelming amount of geological and seismological data for Italy (just consider, for example, that the earthquake catalogue collects events which occurred over the last ten centuries) permits the operator to make different choices, more or less cautiously. It is quite interesting, then, to evaluate the influence of the specific choices on the final hazard results as a comparison to traditional possibilities. The tests performed clearly indicate the critical choices and quantify their contribution. In particular, we consider thorough comprehension of the space geometry of the earthquake source boundaries and the adequacy of the attenuation relation in modelling the radiation pattern very important.     

An energy-based procedure for the assessment of seismic capacity of existing frames: Application to RC wide beam systems in Spain

A methodology for assessing the seismic capacity of existing frames in terms of energy is proposed. It estimates the global amount of input energy—in form of a factor AE_IU—and hysteretic energy that the overall structure can dissipate until collapse under earthquake-type loadings. The method requires static pushover analyses to determine the ductility factor and energy shape of an equivalent single-degree-of-freedom system for the first—two or more—modes. The procedure accounts for the relation between the frequency content of the earthquake expected at the site and the dynamic properties of the existing structure. It can be useful for evaluating the possible deficit on energy dissipation capacity of existing structures, and for designing seismic retrofit solutions. Finally, the methodology is applied to reinforced concrete frames with wide beam-column connections representative of existing post-1970 buildings located in the earthquake-prone southern part of Spain.     

近断层区的输入能量设计谱及其在基于能量抗震设计中的应用

研究并确定输入能量设计谱是建立基于性能抗震设计和评估能量方法的必要基础。选取断层15km投影距离内的224条强震记录讨论场地类型和断层距等因素的影响,建议了近场地震的输入能量设计谱(EIDS),在与实际记录及日本等国已有抗震规范比较后表明,所建议的设计能量谱能较好地反映近断层区潜在能量需求,在此基础上形成了基于能量的桥梁结构抗震评估设计方法,并用3座实际RC桥墩进行算例验证证明了所建议方法的可行性,表明基于既有抗震规范设计的桥梁结构仍有必要进行考虑近断层效应的耗能能力验算。     

公路简支梁桥的地震能量响应分析

利用有限元软件SAP2000建立了某公路简支梁桥的有限元模型,以7条典型强震记录为输入,研究了公路简支梁桥的地震能量响应及其分配规律。结果表明:①地基柔性效应对公路简支梁桥的地震能量响应及其分配规律的影响较小;②当场地土质变软时,地震总输入能、结构阻尼耗能和结构阻尼耗能比均呈递增趋势,而结构滞回耗能和结构滞回耗能比则不断减小,即地基土体作为桥梁动力系统的一部分,增大了系统阻尼,并分担了部分非弹性变形;③随着PGA增大,输入结构的地震能量也增加,导致塑性铰的非弹性变形增加,即结构滞回耗能和结构阻尼耗能增大。     

Stochastic energy analysis of seismic isolated bridges

In this paper, a parametric stochastic analysis of isolated bridge is proposed with the aim to assess isolation performance and to investigate effects of energetic influence on protection efficiency. The analysis has been carried out in terms of two stochastic parameters of pear-deck maximum displacement and hysteretic energy response, of which a qualitative trend has been observed.Isolated bridge is described by a simple two degree of freedom (TDoF) Bouc–Wen hysteretic model, which has been introduced for its intrinsic ability in reproducing a wide range of real devices behavior. With the aim of taking into consideration intrinsic stochastic nature of seismic events, the ground motion and the structural response have been described by random vibration approach. Results obtained show that protection achieved by shifting structural natural period and reducing input energy by devices dissipation have counteracting effects if related to deck lateral displacement.     

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.     

A simplified methodology for the seismic assessment of masonry buildings with RC slabs

The present paper aims to contribute to the knowledge concerning the seismic assessment of load bearing masonry buildings with reinforced concrete slabs. The final goal of the present research was to propose a simple, yet accurate, methodology to assess the seismic safety of existing masonry buildings. The methodology here presented was based on the so-called ICIST/ACSS methodology with major improvements such as the extension to load bearing masonry wall buildings and the consideration of the effects of one of the most common strengthening solutions for masonry walls, here referred to as reinforced plastering mortar, as well as the possibility of considering four levels of increasing refinement: global, by alignment, by wall panel and by wall element. An extended research was performed on the existing methodologies to evaluate the seismic structural risk of load bearing masonry buildings, briefly describing methodologies similar to the one proposed, namely all of those that have in common the fact that they are based in the physical comparison between the resisting and acting shear forces at all storeys and along the two orthogonal horizontal directions. A case study is presented to check the applicability of the proposed methodology. The case study showed that the proposed methodology is relatively simple to apply and has a sufficiently good accuracy when compared with alternative methodologies. The degree of refinement of the analysis (global, by alignment, by wall panel and by wall element) must be taken into consideration and successively more complex analyses may be required when the results of simpler analyses are inconclusive.     

New methodology for urban seismic risk assessment from a holistic perspective

The seismic risk evaluation usually works with a fragmented concept of risk, which depends on the scientific discipline in charge of the assessment. To achieve an effective performance of the risk management, it is necessary to define risk as the potential economic, social and environmental consequences due to a hazardous phenomenon in a period of time. This article presents a methodology which evaluates the seismic risk from a holistic perspective, which means, it takes into account the expected physical damage and also the conditions related to social fragility and lack of resilience, which favour the second order effects when a hazard event strikes an urban centre. This seeks to obtain results which are useful in the decision making process for risk reduction. The proposed method for urban seismic risk evaluation uses the fuzzy sets theory in order to handle qualitative concepts and variables involved in the assessment, the physical risk level and aggravation level, related to the social fragility and the lack of resilience, are evaluated and finally a total risk level is determinate.     

Assessment of the seismic non-linear behavior of ductile wall structures due to synthetic earthquakes

In this paper, different methods for generating synthetic earthquakes are compared in terms of related non-linear seismic response of ductile structures. The objective of the investigation is to formulate recommendations for the use of synthetic earthquakes for reliable seismic analysis. The comparison is focused on the accuracy of the reproduction of the characteristics of the structural non-linear response due to recorded earthquakes. First the investigations are carried out for non-linear single-degree-of-freedom systems. Later, the results are validated for a set of realistic buildings modelled as multi-degree-of-freedom systems. Various options of the classical stationary simulation procedure of SIMQKE and a non-stationary simulation procedure proposed by Sabetta and Pugliese are examined and compared. The adopted methodology uses a set of recorded earthquakes as a reference. Hundred synthetic accelerograms are generated for each examined simulation option with the condition that the related elastic responses are similar to those of the reference set. The non-linear single-degree-of-freedom systems are defined using six recognized hysteretic models and four levels of increasing non-linearity. The non-linear responses computed for the reference set and the studied simulation options are then statistically compared in terms of displacement ductility and energy. The results show that the implementation of the classical stationary procedure always leads to a significant underestimation of the ductility demand and a significant overestimation of the energy demand. By contrast, non-stationary time histories produce much better results. The results with the multi-degree-of-freedom systems are shown to confirm these conclusions.     

An energy-based envelope function for the stochastic simulation of earthquake accelerograms

An energy-based envelope function is developed for use in the stochastic simulation of earthquake ground motion. The envelope function is directly related to the Arias intensity of the ground motion as well to the manner in which this Arias intensity is built-up over time. It is shown that this build-up, represented by a Husid plot, can be very well modelled using a simple lognormal distribution. The proposed envelope makes use of parameters that are commonly available in seismic design situations, either following a deterministic scenario-type analysis or following a more comprehensive probabilistic seismic hazard analysis (PSHA), either in terms of Arias intensity or the more common spectral acceleration. The shape parameters of the envelope function are estimated following the calculation of the analytic envelopes for a large number of records from PEER Next Generation of Attenuation (NGA) database. The envelope may also be used to predict the distribution of peak ground acceleration values corresponding to an earthquake scenario. The distribution thus obtained is remarkably consistent with those of the recent NGA models.     

Numerical efficiency assessment of energy dissipators for seismic protection of buildings

This paper presents a two-dimensional numerical study on the nonlinear seismic response of buildings equipped with two types of energy dissipators: Constant Friction Slip Braces (CFSB) and Adding Damping and Stiffness (ADAS). Three types of reinforced concrete buildings with 3, 7 and 15 storeys, representatives of the short-medium- and long-period ranges, are considered. Dissipators are placed in steel diagonal braces in all the floors. The sliding threshold (or yielding) forces for each mechanism are selected using two different criteria: (i) they are taken as 50, 75 and 100 per cent of those generated by the equivalent static lateral forces recommended by the UBC-91 for a ductile moment resisting frame and (ii) they are constant in the whole building (this constant value is chosen equal to the maximum forces obtained with the previous criterion). The input consists of ten recorded earthquakes (normalized with respect to their Housner intensity) corresponding to medium and stiff local soil conditions. Average values on the ten registers are given for the maximum horizontal displacement, the base shear, the energy dissipated and the interstorey drift. The possibility of failure in some devices has been numerically simulated to assess the robustness of the system. The obtained results show that both devices are useful to reduce the response compared to the bare frame and that CFSB is more efficient than ADAS; for 7- and 15-storey frames the lateral displacement with CFSB is even smaller than the one for the braced frame (rigid connections instead of dissipators). The conclusions are expected to provide simple design guidelines. © 1998 John Wiley & Sons, Ltd.     

Probabilistic seismic demand model for nonstructural components

Past earthquakes have shown the importance for critical facilities to remain functional during seismic events. In the performance assessment of these facilities, it is therefore essential to accurately evaluate the seismic demand of nonstructural components. Evaluation of these components is also important when estimation of nonstructural repair costs is a concern. In this paper, the use of a multivariate demand model for nonstructural components is proposed, in which demand is expressed in terms of both interstory drifts and floor acceleration spectra. A model is built using statistics of the demand vector derived from the results of a limited number of inelastic response history analyses of a structure. The model is then used to simulate any number of additional realizations of the demand vector required for an accurate estimation of the probability of functionality loss. A new proposal for a predictive equation to generate approximate realizations of floor response spectra is presented. A reinforced concrete frame is selected as an illustrative example to show the implementation of the probabilistic seismic demand model and to evaluate the proposed predictive equation for the floor response spectra. The results of the case study are used to demonstrate the importance of accounting for the correlation among the demand parameters when realizations of the seismic demand of nonstructural components are simulated. Copyright © 2015 John Wiley & Sons, Ltd.