Spectral Displacement Research Articles

Fragility analysis of R/C frame buildings based on different types of hysteretic model

Estimation of damage probability of buildings under a future earthquake is an essential issue to ensure the seismic reliability. Fragility curves are useful tools for showing the probability of structural damage due to earthquakes as a function of ground motion indices. The purpose of this study is to compare the damage probability of R/C buildings with low and high level of strength and ductility through fragility analysis. Two different types of sample buildings have been considered which represent the building types mentioned above. The first one was designed according to TEC-2007 and the latter was designed according to TEC-1975. The pushover curves of sample buildings were obtained via pushover analyses. Using 60 ground motion records, nonlinear time-history analyses of equivalent single degree of freedom systems were performed using bilinear hysteretic model and peak-oriented hysteretic model with stiffness - strength deterioration for each scaled elastic spectral displacement. The damage measure is maximum inter-story drift ratio and each performance level considered in this study has an assumed limit value of damage measure. Discrete damage probabilities were calculated using statistical methods for each considered performance level and elastic spectral displacement. Consequently, continuous fragility curves have been constructed based on the lognormal distribution assumption. Furthermore, the effect of hysteresis model parameters on the damage probability is investigated.

Rocking-isolated frame structures: Margins of safety against toppling collapse and simplified design approach

This paper aims to explore the limitations associated with the design of “rocking- isolated” frame structures. According to this emerging seismic design concept, instead of over-designing the isolated footings of a frame (as entrenched in current capacity–design principles), the latter are under-designed with the intention to limit the seismic loads transmitted to the superstructure. An idealized 2-storey frame is utilized as an illustrative example, to investigate the key factors affecting foundation design. Nonlinear FE analysis is employed to study the seismic performance of the rocking-isolated frame. After investigating the margins of safety against toppling collapse, a simplified procedure is developed to estimate the minimum acceptable footing width B min , without recourse to sophisticated (and time consuming) numerical analyses. It is shown that adequate margins of safety against toppling collapse may be achieved, if the toppling displacement capacity of the frame δ topl (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand δ dem . With respect to the capacity, the use of an appropriate “equivalent” rigid-body is suggested, and shown to yield a conservative estimate of δ topl . The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SD max is proposed as a conservative measure of δ dem . The validity and limitations of such approximation are investigated for a rigid-block on rigid-base, utilizing rigorous analytical solutions from the bibliography; and for the frame structure on nonlinear soil, by conducting comprehensive nonlinear dynamic time history analyses. In all cases examined, the simplified SD max approach is shown to yield reasonably conservative estimates.

ASSESSMENT OF DAMAGE AND LOSS OF SEISMICALLY EXCITED STRUCTURES BASED ON CONVEX ANALYSIS

Probabilistic results drawn upon inadequate information are suspicious. The convex set theory, which requires much less information, is employed to model the uncertainties of the spectral displacement and damage state medians. Furthermore, a convex model of fragility function is established based on the envelope bound convex models of the spectral displacement and damage state medians. A bound loss estimation method is derived by integrating HAZUS-AEBM module with the convex set theory. The loss bounds of a hotel in southern China are obtained and compared to the loss calculated by HAZUS-AEBM method, which locates in the lower half interval of convex analysis results. The uncertainty propagation is analyzed and damage state medians are found to be the most critical factor to the loss. Finally, the PEER's probabilistic loss estimation methodology is also applied to this example to deduce the probability of loss exceeding the bound values of convex analysis results.

A Bound Fragility Analysis Methodology Based on Convex Model

The spectral displacement and the damage state medians were assumed as deterministic parameters in HAZUS-Advanced Engineering Building Module (AEBM). As the historical material and experimental data were insufficient to establish an exactly probability density function model of uncertain variable, the damage assessment results by probabilistic model derived from many assumptions and simplification were unreliable. The uncertainties of the spectral displacement and damage state medians were modeled by the Envelope Bound Convex Model. Furthermore, a bound fragility analysis methodology is derived by integrating HAZUS-AEBM module with the convex set theory. The fragility of a hotel in southern China are calculated and compared to the damage derived by HAZUS-AEBM method, and the results of fragility analysis are more sensitive to the spectral displacement and the damage state medians.

Spectral Ground Motion Intensity Based on Capacity and Period Elongation

Ground motion intensity parameters are used to express the relationship between expected structural damage and the seismic forces imposed. The graphical representation of damage probability as a function of ground motion intensity leads to fragility curves that are generally used in loss estimation studies. The most typical parameters used to represent the ground motion intensity are peak ground acceleration, peak ground velocity, spectral acceleration, and spectral displacement. Other parameters obtained from the ground motion trace and response spectra have been recommended in literature, but no consensus on which intensity parameter to use exists because of the various drawbacks of these ground motion intensities. A new spectrum ground motion intensity parameter that relies on the expected elongated period of the structure under seismic forces has been developed. This intensity measure takes into account the approximate yield capacity of the structure and the area between the fundamental and elongated ...

국내 기존 학교건축물의 내진보강 후 비선형 거동특성

본 논문은 내진설계규정이 적용되지 않은 국내 철근콘크리트 학교 건물에 관한 해석적 연구이다. 일본의 내진진단과 비선형 정적 및 동적 해석을 통하여 대상 건축물의 내진 성능을 평가하였다. 일본의 내진진단 방법에 기초하여 철근 콘크리트 학교 건물의 부족한 내진 성능을 파악하였다. 또한, 횡하중을 받는 학교 건물의 내진거동이 해석적으로 평가되었다. 건축물의 내진 보강을 위하여 1,300kN의 내력을 받는 전단벽과 K형 가새골조가 사용되었다. 비선형 정적해석 결과, 보강에 의한 전단내력은 보강 전에 비하여 30%이상의 향상을 보이는 것으로 나타났으며, 전단벽 보강 시 최대 하중 이후에서 가새골조 보강에 비해 큰 강성저하를 나타내었다. 또한, 성능점 산정 결과에서 가새골조로 보강된 건축물이 전단벽으로 보강된 건축물에 비해 30% 이상의 변형능력을 보였다. 한편 비선형 동적해석의 시간이력해석 결과에서는 가새골조와 전단벽에 의해 보강된 건축물의 최대 변위가 보강량이 증가할수록 감소하는 경향을 나타내었다. 본 연구는 이 외에도 지진 지역에서의 건축물의 내진성능 향상을 위해 다양한 지반 조건과 지진파를 고려되어야 한다고 판단된다. This paper describes an analytical study on seismic performance of domestic reinforced concrete (RC) school building not designed by seismic provision. The seismic index and the seismic performance of the building were evaluated through Japanese standard and Midas Gen, respectively. Seismic index (Is) of the RC school buildings in the X-direction is below 0.4. Based on the seismic index, for seismic-strengthening the building, infill shear wall or steel brace with a capacity of 1,300 kN was used. According to nonlinear static analysis results, the contribution of the seismic-strengthening to the shear resistance of the school building was measured to be greater than 30%. However, as expected, shear strength of school building strengthened with infill wall dropt rapidly after peak load and much narrower ductile behavior range was observed compared to steel brace strengthened building. Also, the building strengthened with steel brace showed 30% larger spectral displacement than that strengthened with infill shear wall. In nonlinear dynamic analysis, for the time history analysis, the maximum displacement showed tendency to decrease as amount of reinforcement increased, regardless of strengthening method. It was recommended that variable soil properties and earthquake record should be considered for improving seismic performance of buildings in seismic zone.

The high‐frequency limit of usable response spectral ordinates from filtered analogue and digital strong‐motion accelerograms

AbstractThe range of response frequencies for which spectral ordinates obtained from accelerograms may be considered reliable is limited by several factors, primary among them being the effects of filters that are routinely applied to remove noise from the records. Considerable attention has been focused on the low‐frequency limit of the usable spectral ordinates because of various engineering applications requiring long‐period spectral accelerations or displacements but only recently have rational approaches to selecting the high‐frequency limit been proposed. Since there are applications for which the high‐frequency spectral ordinates are important, the approaches to this issue presented in the recent studies are reviewed and their application to the ground‐motion database from Europe and the Middle East is explored. On the basis of the results of these analyses, it is concluded that a large proportion of this dataset can be used to provide reliable estimates of response spectral ordinates at much shorter periods than may have previously been considered feasible. Copyright © 2011 John Wiley & Sons, Ltd.

光谱共焦位移传感器测量透明材料厚度的应用

The structure and principle of the spectral confocal displacement sensor were described in this paper,and the application to measuring the thickness was analyzed.The paper focused on the feasibility of measuring the parallel plates made of transparent materials.The measurement errors were also analyzed,and the corresponding compensation ways were given.

Probabilistic seismic demand analysis of a slender RC shear wall considering soil–structure interaction effects

Reinforced concrete shear walls are often used to resist the lateral loads imposed by earthquakes. Accurate evaluation of the seismic demands on shear walls requires adequate considerations of the nonlinear behavior of structural and foundation elements, the interaction between them, and the uncertainty and variability associated with earthquake ground motions. This paper presents a comprehensive probabilistic seismic demand analysis of a typical mid-rise slender shear wall in western US with a flexible foundation and evaluates the significance of soil–structure interaction (SSI) effects on their damage probability. Utilizing realistic numerical models for the shear wall and its foundation, the nonlinear time history analyses were conducted with a large number of recorded ground motions. Response quantities such as maximum inter-story drift ratio, base shear, foundation displacement and rotation are monitored and related to the intensity measure of ground motions (i.e. the inelastic spectral displacement S d i ) for the cases with and without considering the SSI effects. Subsequently, the fragility functions of the shear wall are derived and the impact of SSI effects is investigated. It is found that the SSI generally reduces the damage probability of the shear wall, especially when soil nonlinearity is taken into account. The sensitivity of various seismic demands to soil parameters is also discussed. Under strong ground shakings, SSI effects on the maximum inter-story drift are most sensitive to the friction angle of the soil. It is suggested that the damages in foundation and surrounding soil should also be considered in order to systematically evaluate the SSI effects on damage probability of shear wall buildings.

Vibrational spectra of anharmonic oscillators of molecular crystals

This paper discusses the anharmonic vibrations of molecular crystals in the spectral region hν≈10–300cm−1. The wave functions and energy levels of two types of anharmonic oscillators under the conditions of strong anharmonism are calculated. It is shown that such a model correlates well with the observed asymmetry of the bands and their spectral displacement when there is a phase transition.

Convex Model for Earthquake Damage and Loss Estimation of Individual Buildings

Probabilistic results drawn upon inadequate information are suspicious. The convex set theory, which requires much less information, is employed to model the uncertainties of the spectral displacement and damage state medians. Furthermore, a convex model of fragility function is established based on the Envelope Bound Convex Models of the spectral displacement and damage state medians. A bound loss estimation method is derived by integrating HAZUS-AEBM module with the convex set theory. The loss bounds of a hotel in southern China are obtained and compared to the loss calculated by HAZUS-AEBM method, which locates in the lower half interval of convex analysis results. The uncertainty propagation is analyzed and damage state medians are found to be most critical factor to the loss. Finally, the PEER's probabilistic loss estimation methodology is also applied to this example to deduce the probability of loss exceeding the bound values of convex analysis results.

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacitydemand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.

Correlations between Energy and Displacement Demands for Performance-Based Seismic Engineering

The development of a scientific framework for performance-based seismic engineering requires, among other steps, the evaluation of ground motion intensity measures at a site and the characterization of their relationship with suitable engineering demand parameters (EDPs) which describe the performance of a structure. In order to be able to predict the damage resulting from earthquake ground motions in a structural system, it is first necessary to properly identify ground motion parameters that are well correlated with structural response and, in turn, with damage. Since structural damage during an earthquake ground motion may be due to excessive deformation or to cumulative cyclic damage, reliable methods for estimating displacement demands on structures are needed. Even though the seismic performance is directly related to the global and local deformations of the structure, energy-based methodologies appear more helpful in concept, as they permit a rational assessment of the energy absorption and dissipation mechanisms that can be effectively accomplished to balance the energy imparted to the structure. Moreover, energy-based parameters are directly related to cycles of response of the structure and, therefore, they can implicitly capture the effect of ground motion duration, which is ignored by conventional spectral parameters. Therefore, the identification of reliable relationships between energy and displacement demands represents a fundamental issue in both the development of more reliable seismic code provisions and the evaluation of seismic vulnerability aimed at the upgrading of existing hazardous facilities. As these two aspects could become consistently integrated within a performance-based seismic design methodology, understanding how input and dissipated energy are correlated with displacement demands emerges as a decisive prerequisite. The aim of the present study is the establishment of functional relationships between input and dissipated energy (that can be considered as parameters representative of the amplitude, frequency content and duration of earthquake ground motions) and displacement-based response measures that are well correlated to structural and non-structural damage. For the purpose of quantifying the EDPs to be related to the energy measures, for comprehensive range of ground motion and structural characteristics, both simplified and more accurate numerical models will be used in this study for the estimation of local and global displacement and energy demands. Parametric linear and nonlinear time-history analyses will be performed on elastic and inelastic SDOF and MDOF systems, in order to assume information on the seismic response of a wide range of current structures. Hysteretic models typical of frame force/displacement behavior will be assumed for the local inelastic cyclic response of the systems. A wide range of vibration periods will be taken into account so as to define displacement, interstory drift and energy spectra for MDOF systems. Various scalar measures related to the deformation demand will be used in this research. These include the spectral displacements, the peak roof drift ratio, and the peak interstory drift ratio. A total of about 900 recorded ground motions covering a broad variety of condition in terms of frequency content, duration and amplitude will be used as input in the dynamic analyses. The records are obtained from 40 earthquakes and grouped as a function of magnitude of the event, source-to-site condition and site soil condition. In addition, in the data-set of records a considerable number of near-fault signals is included, in recognition of the particular significance of pulse-like time histories in causing large seismic demands to the structures.

An improvement to linear‐elastic procedures for seismic performance assessment

AbstractAn improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.

Drift Demand Predictions in Low to Moderate Seismicity Regions

This paper presents results obtained from a recent study that is aimed at assessing the drift demand on buildings for a range of projected earthquake scenarios in Australia. Parameters considered that may affect the response of buildings included building height, structural systems, and mass and stiffness distributions. It has been found that, for the range of buildings studied, the maximum angle of drift is 2.6–4.4 times the maximum response spectral displacement of the earthquake divided by the building height. This can be checked against the limiting drift capacity of the building to enable various levels of damage to be predicted for given earthquake scenarios.

Tentative seismic design guidelines for rocking structures

Many new and existing buildings have insufficient weight to resist overturning loads due to earthquakes without uplift. Previous versions of the New Zealand loadings code allowed simplified procedures for the design of rocking structures provided the ductility factor was limited to not more than two. The new loadings code, NZS 1170.5, removed this exemption and requires that a special study be performed whenever energy dissipation through rocking occurs. This paper presents a tentative design procedure intended to substitute for the special study required by the code. The resistance function of rocking walls was developed from the principles of engineering mechanics. The results from a series of time history analyses were used to develop a procedure to estimate maximum seismic displacements and empirical equations were derived to estimate the dynamic amplification of inertia forces. A substitute structure approach, using spectral displacements at an effective period calculated from the ductility factor, provided accurate predictions of the displacements from more sophisticated nonlinear analyses. Four example designs were completed and the predicted response compared to time history results. The procedure provided a satisfactory estimate of response for regular structures, but it was less accurate where torsional effects were significant.

A spectral displacement study of cyclodextrin/naphthenic acids inclusion complexes

The spectral displacement technique has been used to obtain 1:1 β-cyclodextrin (β-CD)/carboxylate anion equilibrium binding constants (K2) for some complex mixtures of naphthenic acids (NAs) and some examples of single-component NAs in aqueous solution. Three specific examples of single-component NAs were chosen with variable Z values as follows: 2-hexyldecanoic acid (Z = 0; S1), trans-4-pentylcyclohexanecarboxylic acid (Z = –2; S2), and dicyclohexylacetic acid (Z = –4; S3). The estimated K2 values for S1, S2, and S3 are as follows: 1.42 × 103 M–1, 52.2 × 104 M–1, and 13.1 × 104 M–1, respectively. The corresponding K2 values are 2.34 × 104 M–1 and 1.27 × 104 M–1 for commercial (Fluka) and industrial (Syncrude) sourced NAs, respectively. The magnitude of K2 for 1:1 complexes formed between β-CD and S1, S2, or S3 did not correlate with the degree of hydrogen deficiency (Z-series) but there was a correlation with the size of the guest molecules (n) examined in this study. The correlation between complex stability and the relative size of the lipophilic fragments of the guest molecule are related to the importance of the hydrophobic effect for inclusion of such carboxylic acid guest molecules within β-CD.

Prediction of spatially distributed seismic demands in specific structures: Structural response to loss estimation

AbstractA companion paper has investigated the effects of intensity measure (IM) selection in the prediction of spatially distributed response in a multi‐degree‐of‐freedom structure. This paper extends from structural response prediction to performance assessment metrics such as probability of structural collapse; probability of exceeding a specified level of demand or direct repair cost; and the distribution of direct repair loss for a given level of ground motion. In addition, a method is proposed to account for the effect of varying seismological properties of ground motions on seismic demand that does not require different ground motion records to be used for each intensity level. Results illustrate that the conventional IM, spectral displacement at the first mode, Sde(T1), produces higher risk estimates than alternative velocity‐based IM's, namely spectrum intensity, SI, and peak ground velocity, PGV, because of its high uncertainty in ground motion prediction and poor efficiency in predicting peak acceleration demands. Copyright © 2009 John Wiley & Sons, Ltd.

On Baseline Corrections and Uncertainty in Response Spectrafor Baseline Variations Commonly Encounteredin Digital Accelerograph Records

Most digital accelerograph recordings are plagued by long-period drifts, best seen in the velocity and displacement time series obtained from integration of the acceleration time series. These drifts often result in velocity values that are nonzero near the end of the record. This is clearly unphysical and can lead to inaccurate es- timates of peak ground displacement and long-period spectral response. The source of the long-period noise seems to bevariations in the acceleration baseline in many cases. These variations could be due to true ground motion (tilting and rotation, as well as local permanent ground deformation), instrumental effects, or analog-to-digital con- version. Very often the trends in velocity are well approximated by a linear trend after the strong shaking subsides. The linearity of the trend in velocity implies that no vari- ations in the baseline could have occurred after the onset of linearity in the velocity time series. This observation, combined with the lack of any trends in the pre-event motion, allows us to compute the time interval in which any baseline variations could occur. We then use several models of the variations in a Monte Carlo procedure to derive a suite of baseline-corrected accelerations for each noise model using records from the 1999 Chi-Chi earthquake and several earthquakes in Turkey. Comparisons of the mean values of the peak ground displacements, spectral displacements, and resid- ual displacements computed from these corrected accelerations for the different noise models can be used as a guide to the accuracy of the baseline corrections. For many of the records considered here the mean values are similar for each noise model, giving confidence in the estimation of the mean values. The dispersion of the ground-motion measures increases with period and is noise-model dependent. The dispersion of in- elastic spectra is greater than the elastic spectra at short periods but approaches that of the elastic spectra at longer periods. The elastic spectra from the most basic proces- sing, in which only the pre-event mean is removed from the acceleration time series, do not diverge from the baseline-corrected spectra until periods of 10-20 sec or more for the records studied here, implying that for many engineering purposes elastic spec- tra can be used from records with no baseline correction or filtering.

Ground-Motion Prediction Equations (GMPEs) for inelastic displacement and ductility demands of constant-strength SDOF systems

The objective of this paper is to present ground-motion prediction equations for ductility demand and inelastic spectral displacement of constant-strength perfectly elasto-plastic single-degree-of-freedom (SDOF) oscillators. Empirical equations have been developed to compute the ductility demand as a function of two earthquake parameters; moment magnitude, and source-to-site distance; one site parameter, the ground type; and three oscillator parameters, an undamped natural period, critical damping ratio, and the mass-normalized yield strength. In addition, a comparative study of the proposed model with selected previous studies and recommendations of Eurocode 8 is presented. Proposed equations can easily be incorporated in existing probabilistic seismic hazard analysis (PSHA) software packages with the introduction of an additional parameter. This leads to hazard curves for inelastic spectral displacement, which can provide better estimates of target displacement for nonlinear static procedures and an efficient intensity measure for probabilistic seismic demand analysis (PSDA). Proposed equations will be useful in performance evaluation of existing structures.