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1.
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.  相似文献   

2.
Estimation of design forces in ductility‐based earthquake‐resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo‐spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto‐plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period‐dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

3.
In current seismic design procedures, base shear is calculated by the elastic strength demand divided by the strength reduction factor. This factor is well known as the response modification factor, R, which accounts for ductility, overstrength, redundancy, and damping of a structural system. In this study, the R factor accounting for ductility is called the ‘ductility factor’, Rμ. The Rμ factor is defined as the ratio of elastic strength demand imposed on the SDOF system to inelastic strength demand for a given ductility ratio. The Rμ factor allows a system to behave inelastically within the target ductility ratio during the design level earthquake ground motion. The objective of this study is to determine the ductility factor considering different hysteretic models. It usually requires large computational efforts to determine the Rμ factor. In order to reduce the computational efforts, the Rμ factor is prepared as a functional form in this study. For this purpose, statistical studies are carried out using forty different earthquake ground motions recorded at a stiff soil site. The Rμ factor is assumed to be a function of the characteristic parameters of each hysteretic model, target ductility ratio and structural period. The effects of each hysteretic model to the Rμ factor are also discussed. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

4.
Numerical and analytical solutions are presented for the elastic and inelastic response of single‐degree‐of‐freedom yielding oscillators to idealized ground acceleration pulses. These motions are typical of near‐fault earthquake recordings generated by forward rupture directivity and may inflict damage in the absence of substantial structural strength and ductility capacity. Four basic pulse waveforms are examined: (1) triangular; (2) sinusoidal; (3) exponential; and (4) rectangular. In the first part of the article, a numerical study is presented of the effect of oscillator period, strength, damping, post‐yielding stiffness and number of excitation cycles, on inelastic response. Results are presented in the form of dimensionless graphs and regression formulas that elucidate the salient features of the problem. It is shown that conventional R–µ relations may significantly underestimate ductility demand imposed by near‐fault motions. The second part of the article concentrates on elastic‐perfectly plastic oscillators. Closed‐form solutions are derived for post‐yielding response and associated ductility demand. It is shown that all three ground motion histories (i.e. acceleration, velocity, and displacement) control oscillator response—contrary to the widespread view that ground velocity alone is of leading importance. The derived solutions provide insight on the physics of inelastic response, which is often obscured by the complexity of numerical algorithms and actual earthquake motions. The model is evaluated against numerical results from near‐field recordings. A case study is presented. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

5.
The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor Rμ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

6.
A predictive model is presented for estimating the peak inelastic oscillator displacements (Sd,ie) from peak ground velocity (PGV). The proposed model accounts for the variation of Sd,ie for bilinear hysteretic behavior under constant ductility (µ) and normalized lateral strength ratio (R) associated with postyield stiffness ratios of α=0 and 5%. The regression coefficients are based on a ground‐motion database that contains dense‐to‐stiff soil site recordings at distances of up to 30 km from the causative fault. The moment magnitude ( M ) range of the database is 5.2? M ?7.6 and the ground motions do not exhibit pulse‐dominant signals. Confined to the limitations imposed by the ground‐motion database, the model can estimate Sd,ie by employing the PGV predictions obtained from the attenuation relationships (ground‐motion prediction equations). In this way, the influence of important seismological parameters can be incorporated to the variation of Sd,ie in a fairly rationale manner. This feature of the predictive model advocates its implementation in the probabilistic seismic hazard analysis that employs scalar ground‐motion intensity indices. Various case studies are presented to show the consistent estimations of Sd,ie by the proposed model. The error propagation in the Sd,ie estimations is also discussed when the proposed model is associated with attenuation relationships. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

7.
Modern seismic design allows a structure to develop inelastic response during moderate to severe earthquakes. The emerging performance-based design requires more clearly defined levels of inelastic response, or damage, to be targeted for different earthquake hazard levels. While there are a range of factors that could influence the level of damage and hence the performance, the design strength remains to be a fundamental design parameter that is inherently related to the structural performance. In this paper, the response reduction factor, which is a normalized form of the design strength, is investigated on a direct damage basis. The implications of the damage-based strength reduction factor (SRF), denoted as RD factor, on multiple performance targets are discussed. A series of RD spectra are generated from a large set of ground motions in different groupings to examine the effects of local site condition, earthquake magnitude and distance to rupture on the RD spectra. The overall mean and standard deviation of the RD spectra for different levels of damage are obtained, and simple empirical formulas are proposed.  相似文献   

8.
This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a2 dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio EHEI) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio EH/EI is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and EH/EI  相似文献   

9.
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10.
A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASAR), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASAR shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASAR a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

11.
A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, ML 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.  相似文献   

12.
Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (Tin/Tel). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, Ry), post‐yield stiffness (ay) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of Tin/Tel are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (Ry, ay and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of Ry and Tel. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

13.
This paper focuses on constant-ductility inelastic displacement ratios of self-centering single-degree-of-freedom (SDF) systems with two different levels of energy dissipation capacity, in the presence of 5% viscous damping ratio. A statistical analysis is developed considering an earthquake database composed of 228 ground motions recorded in California with magnitudes greater than six and organized for NEHRP soil class, ground motion duration, and peak ground acceleration. The response of self-centering SDF systems with large variability of initial periods, ductility levels, and postyield stiffness ratios is investigated and compared with the responses of SDF systems with bilinear plastic, Clough, and Takeda hysteresis. The inelastic demand variation with soil class, initial period, postyield stiffness ratio, unloading stiffness degradation, ductility level, and hysteretic behavior is highlighted. Simple and conservative analytical estimates of constant-ductility inelastic displacement ratios for mean and 90th percentile values in terms of initial period, ductility level, and postyield stiffness ratio are proposed to allow the extension of the Displacement-Based Design via Inelastic Displacement Ratio (CμDBD) to self-centering structural systems.  相似文献   

14.
This paper examines the observed directionality of ground motions in the Christchurch urban area during the 2010–2011 Canterbury, New Zealand earthquakes. A dataset of ground motions recorded at 20 strong motion stations over 10 different earthquake events is utilized to examine the ratios of various response spectral directionality definitions and the orientation of the maximum direction. Because the majority of previous related studies have utilized overlapping ground motion datasets from the NGA database, the results of this study provide a largely independent assessment of these ground motion aspects. It is found that the directionality ratio between the maximum (100th percentile) and 50th percentile orientation‐independent spectral acceleration is similar to that obtained from recent studies. Ground motions from the 4 September 2010 Darfield earthquake are shown to exhibit strong directionality for source‐to‐site distances up to Rrup = 30 km, notably further than results from a previous study, which suggests that such effects are generally limited to Rrup < 5 km. The adopted dataset also offers the unique potential to consider site‐specific effects on directionality ratios and maximum direction orientations; however, in both cases, site‐specific effects are found not to be significant in the observed empirical results. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

15.
Estimation of structural damage from a known increase in the fundamental period of a structure after an earthquake or prediction of degradation of stiffness and strength for a known damage requires reliable correlations between these response functionals. This study proposes a modified Clough–Johnston single‐degree‐of‐freedom oscillator to establish these correlations in the case of a simple elasto‐plastic oscillator. It is assumed that the proposed oscillator closely models the response of a given multi‐degree‐of‐freedom system in its fundamental mode throughout the duration of the excitation. The proposed model considers the yield displacement level and ductility supply ratio‐related parameter as two input parameters which must be estimated over a narrow range of ductility supply ratio from a frequency degradation curve. This curve is to be identified from a set of recorded excitation and response time‐histories. Useful correlations of strength and stiffness degradation with damage have been obtained wherein a simple damage index based on maximum and yield displacements and ductility supply ratio has been considered. As an application, the proposed model has been used to demonstrate that ignoring the effects of aftershocks in the case of impulsive ground motions may lead to unsafe designs. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

16.
A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.  相似文献   

17.
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18.
A procedure for the determination of inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor has been developed. All the spectra are consistent (interrelated and based on the same assumptions). This is the first of two companion papers which deals with the ‘classical’ structural parameters: strength and displacement. The input data are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum. Simple, approximate expressions for the strength reduction factor R are proposed. The value of R depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour, damping and ground motion. Fairly accurate approximations to the inelastic spectra for strength and displacement can be derived from the elastic spectrum using the proposed values for R.  相似文献   

19.
This study investigates the seismic design factors for three reinforced concrete (RC) framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code (IBC’09). Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years (10/50 and 2/50, respectively) are used. The nonlinear dynamic responses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor (R), deflection amplification factor (Cd), system overstrength factor (Ωo), and response modification factor for ductility (Rd) in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion (10/50 versus 2/50). Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the Ωo factor, which shows a mere 30% increase. Based on the observed trends, period-dependent R and Cd factors are recommended if consistent collapse probability (or collapse prevention performance) in moment frames with varying heights is to be expected.  相似文献   

20.
A statistical analysis is performed to investigate the significance of peak ground acceleration to velocity ratio (a/v) on the displacement ductility demand of simple bilinear hysteretic systems. Three groups of earthquake records representative of low, normal and high<a/v ranges are used as input ground motions. The design yield strength of the inelastic systems is specified from the base shear formula in the 1980 National Building Code of Canada (NBCC 1980) and that in NBCC 1985 respectively. The former case represents the common practice of specifying seismic design base shear based on a peak site acceleration, while in the latter case the base shear is specified based on peak ground velocity and a/v ratio. Mean displacement ductility demands are obtained for the three groups of ground motions; and the corresponding dispersion characteristics are examined. The results show that the ground motion<a/v range has a significant effect on the displacement ductility demand, and it should be accounted for in design strength specification.  相似文献   

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