Capacity Spectrum Method Research Articles

Seismic performance evaluation of steel frame-steel plate shear walls system based on the capacity spectrum method

This paper presents some methods that the standard acceleration design response spectra derived from the present China code for seismic design of buildings are transformed into the seismic demand spectra, and that the base shear force-roof displacement curve of structure is converted to the capacity spectrum of an equivalent single-degree-of-freedom (SDOF) system. The capacity spectrum method (CSM) is programmed by means of MATLAB7.0 computer language. A dual lateral force resisting system of 10-story steel frame-steel plate shear walls (SPSW) is designed according to the corresponding China design codes. The base shear force-roof displacement curve of structure subjected to the monotonic increasing lateral inverse triangular load is obtained by applying the equivalent strip model to stimulate SPSW and by using the finite element analysis software SAP2000 to make Pushover analysis. The seismic performance of this dual system subjected to three different conditions, i.e. the 8-intensity frequently occurred earthquake, fortification earthquake and seldom occurred earthquake, is evaluated by CSM program. The excessive safety of steel frame-SPSW system designed according to the present China design codes is pointed out and a new design method is suggested.

Performance of precast concrete load-bearing panel structures in regions of low to moderate seismicity

The performance of jointed precast concrete load-bearing panel structures is evaluated using the capacity spectrum method for Australian seismic conditions which is typical of low to moderate seismicity regions. The critical element in the load path is the connection between the floor slab and the wall panel, and sub-assemblage tests are carried out in order to calibrate a finite element model for typical load displacement characteristics. The calibrated model is used to evaluate the performance of a full scale structure using the demand spectra given in the Australian code for various soil conditions. It is found that the seismic performance is inadequate under deep soil and very soft soil conditions for the structure detailed with deep embedment connections. In comparison for the structure with shallow embedment connections, local damage to the concrete topping slab would be expected for ground motions on shallow soil or very soft soil, but overall structural stability would be maintained for the ultimate limit state event.

Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona

Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for seismic evaluation of structures. The capacity spectrum method and the way of obtaining seismic damage scenarios for urban areas starting from capacity and fragility curves are then discussed. The determination of capacity curves for buildings using non-linear structural analysis tools is then explained, together with a simplified expeditious procedure allowing the development of fragility curves. The seismic risk of the buildings of Barcelona, Spain, is analyzed in the paper, based on the application of the capacity spectrum method. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. The information on the buildings was obtained by collecting, arranging, improving and completing a broad database of the dwellings and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled-slab floors. The ArcView software was used to create a GIS tool for managing the collected information in order to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant in Barcelona and, therefore, in spite of the low-to-moderate seismic hazard in the region, the expected seismic risk is considerable.

Design of supplemental viscous dampers in inelastic SDOF system based on improved capacity spectrum method

A simplified yet effective design procedure for viscous dampers was presented based on improved capacity spectrum method in the context of performance-based seismic design. The amount of added viscous damping required to meet a given performance objective was evaluated from the difference between the total demand for effective damping and inherent damping plus equivalent damping resulting from hysteretic deformation of system. Application of the method is illustrated by means of two examples, using Chinese design response spectrum and mean response spectrum. Nonlinear dynamic analysis results indicate that the maximum displacements of structures installed with supplemental dampers designed in accordance with the proposed method agree well with the given target displacements. The advantage of the presented procedure over the conventional iterative design method is also highlighted.

Earthquake damage estimation in Metro Manila, Philippines based on seismic performance of buildings evaluated by local experts’ judgments

Building damage due to a scenario earthquake in Metro Manila, Philippines is estimated based on seismic performance of the buildings evaluated by local experts’ judgments. For the damage estimation, building capacity curves and fragility curve are developed from questionnaire to the local experts of structural engineering. The Delphi method is used to integrate the experts’ opinions. The derived capacity curves are validated by comparing with the result of pushover analysis for typical buildings. Building responses due to simulated ground motions are estimated by the capacity spectrum method. Damage ratios are calculated from the fragility curves and the building responses. Distributions of the damaged buildings are computed by multiplying the damage ratios and the building inventory. The distribution and the amount of the damaged buildings in this study show significant difference from the estimation with the capacity curves of HAZUS, suggesting the importance of evaluation of the region-specific building performance.

Nonlinear Static Methods vs. Experimental Shaking Table Test Results

Three different Nonlinear Static Methods (NSM's), based on pushover analysis, are applied to a 3-story, 2-bay, RC frame. They are (i) the Capacity Spectrum Method (CSM), described in ATC-40, (ii) the Displacement Coefficient Method (DCM), presented in FEMA-273 and further developed in FEMA 356, and (iii) the N2 Method, implemented in the Eurocode 8. Pushover analyses are conducted with DRAIN-3DX by using four different lateral force distributions, according to the acceleration profile assumed along the height of the structure: uniform, triangular, modal-proportional, and multimodal fully adaptive. In the numerical model, RC members are modeled as fiber elements. The numerical predictions of each method are compared to the experimental results of the shaking table tests carried out on two similar 1:3.3-scale structural models, with and without infilled masonry panels, respectively. The comparison is made in terms of maximum story displacements, interstory drifts, and shear forces. All the NSM's are found to predict with adequate accuracy the maximum seismic response of the structure, provided that the associated parameters are properly estimated. The lateral load pattern, instead, is found to little affect the accuracy of the results for the three-story model considered, even if collapse occurs with a soft story mechanism.

Evaluation of nonlinear static analysis methods and software tools for seismic analysis of highway bridges

The response of bridges when subjected to seismic excitation can be evaluated by a number of analysis methods. The traditional approach is to employ linear static or dynamic analyses coupled with appropriate modifiers to account for inelastic response while current design practice is moving towards an increased emphasis on nonlinear static analysis methods. In this study, a preliminary seismic response analysis of a two-span highway bridge was performed using linear dynamic analysis procedures to identify the potential for inelastic response. The bridge was subsequently analyzed in accordance with two nonlinear static analysis methods (capacity spectrum and inelastic demand spectrum methods) in an effort to evaluate the difference in global response predicted by the two methods and the effectiveness of various software programs for performing nonlinear static analysis. The results demonstrated that, for the two nonlinear static analysis methods used in this study, different predictions of nonlinear response occurred with neither method being regarded as producing correct results due to a number of simplifications inherent in the methods. Furthermore, the analysis revealed that some software programs are well suited to performing nonlinear static analysis, both from the point-of-view of performing comprehensive analyses and providing a graphical depiction of the evolution of damage (i.e. the behaviour of plastic hinges).

Assessment of Improved Nonlinear Static Procedures in FEMA-440

Nonlinear static procedures (NSPs) presented in the FEMA-440 document are evaluated for nondegrading three- to nine-story reinforced concrete moment-resisting frame systems. Evaluations are based on peak single-degree-of-freedom displacement, peak roof, and interstory drifts estimations. A total of 78 soil site records and 24 buildings with fundamental periods varying between 0.3s–1.3s are used in 2,832 linear and nonlinear response-history analyses to derive the descriptive statistics. The moment magnitude of the ground motions varies between 5.7 and 7.6. All records are within 23km of the causative fault representing near-fault ground motions with and without pulse signals. The statistics presented suggest that lateral loading patterns used in pushover analysis to idealize the building systems play a role in the accuracy of NSPs investigated. Both procedures yield fairly good deformation demand estimations on the median. Displacement coefficient method (DCM) tends to overestimate the global deformation demands with respect to the capacity spectrum method (CSM). The conservative deformation demand estimations of DCM are correlated with the normalized lateral strength ratio, R. The CSM tends to overestimate the deformation demands for the increasing displacement ductility, μ.

Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects (PASSI) is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights (3, 9 and 20) including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis (NL-RHA) method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ‘Code for Seismic Design of Buildings.’ The feasibility of the proposed procedure is verified.

Inelastic Demand Spectra of Bi-Linear Models for Capacity Spectrum Method and Response of Simple Structures under Near-Source Records

A very useful tool for the preliminary design of structures is the elastic demand spectrum that can be used in the capacity spectrum method. A pseudo-acceleration relationship has to be assumed when constructing a demand spectrum. This assumption results in large errors for long period structures with large damping ratios and the conventional demand spectra require a substitute elastic structure. In the present study, the conventional demand spectra are extended to bi-linear models. Pseudo-acceleration is still assumed but results in acceptably small errors, when a constant viscous damping coefficient for a single-degree-of-freedom (SDF) structure is calculated from the tangent stiffness and the damping ratio is set at 5% in both elastic and yield phases. For nonlinear structures, tangent stiffness dependency of damping force could be acceptable because energy absorption is primarily the result of structural nonlinear deformation. To extend the conventional demand spectra to a bi-linear model, effective period calculated from the secant stiffness has to be used. The use of effective period introduces no approximation because the peak displacement of the SDF structure is computed from nonlinear analysis in the time domain. The method presented in this study is also valid if damping coefficient proportional to initial elastic spectra is used. In this case, the pseudo-acceleration is defined as the base shear coefficient that is required to produce the peak displacement of the SDF structure in a static manner. We present demand spectra of bi-linear models for a number of near-source records from large earthquakes, and spectral ratios of two horizontal components. The effects of different types of ground motion on the response reduction factor due to inelastic deformation are investigated.

Seismic performance of viaducts with probabilistic method

Due to the uncertainty of both ground motions and structural capacity, it is necessary to consider the seismic performance of viaduct structures using the probabilistic method. The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves. A group of ground motions, Large Magnitude-Short Distance Bin (LMSR-N), selected specially due to its response spectra, is accorded well with the corresponding spectra of the Chinese code for seismic design. The characteristic values of the curvature ductility factors for the serviceability and the damage control limit states are obtained, and two equations for estimating the characteristic values of the curvature ductility factors are developed through regression analysis. Then, the serviceability and damage control limit states were proposed. Three damage states were constituted according the results of the experiment by Pacific Earthquake Engineering Research (PEER) Center. The analytical fragility curves were obtained specifically, using both Capacity Spectrum Method (CSM) (non-linear static) analysis and Ineremental Dynamic Method (IDM) (non-linear dynamic) analysis, respectively, in this paper. The structural fragility curves developed by CSM method can help make the structural analysis simple and quick, avoiding the implementation of the dynamic response history analysis (RHA). Although the dynamic RHA requires a lot of complicated analysis for the structure, the results from RHA are reliable and accurate. Fragility curves are powerful tools for use in performance-based seismic bridge design.

기존 철근콘크리트 벽식 공동주택의 내진 성능 예비 평가법에 관한 연구

In Korea, the seismic design regulations was established since 1988 about regularity scale of structures. However, It was not established about seismic performance and evaluation method as the most existing buildings was constructed before Earthquake-Resistant Design(1988). In this study, for model structures which are 4 units of non-seismic designed apartment and 3 units of seismic designed in Korea performed seismic performance evaluation by suggested KISTC (2004). And the result compare to evaluate Capacity Spectrum Method by using MIDAS Gen and SDS. As a result, we observed that suggested KISTC's method have overestimated for shear stress and drift index. The purpose of this study provides most conformity seismic performance evaluation process and the appropriate method of calculating the seismic performance index in Korea.

Variability of seismic demands according to different sets of earthquake ground motions

AbstractIt is a challenging task to predict seismic demands for earthquake resistant design, particularly for tall buildings. In current seismic design provisions, seismic demands are expressed as a design base shear of which the key components are linear elastic design response spectra, force reduction factor (‘R factor’), and building weight. For tall buildings, response spectrum analysis or response history analysis is recommended in current design provisions. In recent years, new methods for predicting seismic demands have been developed, such as the capacity spectrum method (CSM) and displacement coefficient method. This study investigates the effect of different earthquake ground motion (EQGM) sets on seismic demands. Key components of the base shear and performance points in the CSM are considered as the seismic demands to be tested. For this purpose three EQGM sets are collected independently at rock sites. This study found that seismic demands can vary significantly according to different EQGM sets even though those sets were obtained at sites with similar soil conditions. This study also attempts to provide a criterion for reducing the variability in seismic demands according to different EQGM sets. Copyright © 2007 John Wiley & Sons, Ltd.

Estimating the confidence of earthquake damage scenarios: examples from a logic tree approach

Earthquake loss estimation is now becoming an important tool in mitigation planning, where the loss modeling usually is based on a parameterized mathematical representation of the damage problem. In parallel with the development and improvement of such models, the question of sensitivity to parameters that carry uncertainties becomes increasingly important. We have to this end applied the capacity spectrum method (CSM) as described in FEMA HAZUS-MH. Multi-hazard Loss Estimation Methodology, Earthquake Model, Advanced Engineering Building Module. Federal Emergency Management Agency, United States (2003), and investigated the effects of selected parameters. The results demonstrate that loss scenarios may easily vary by as much as a factor of two because of simple parameter variations. Of particular importance for the uncertainty is the construction quality of the structure. These results represent a warning against simple acceptance of unbounded damage scenarios and strongly support the development of computational methods in which parameter uncertainties are propagated through the computations to facilitate confidence bounds for the damage scenarios.

Inelastic demand spectra for bi-linear seismic isolation systems based on nonlinear time history analyses and the response of lead-rubber bearing isolation systems subjected to near-source ground motions

In this study, we present an inelastic demand spectrum for the design of seismically-isolated structures using lead-rubber bearings or other types of isolators with bi-linear hysteresis loops and the inelastic spectrum can be used in the design of seismically-isolated structures in a very similar manner to capacity spectrum method. The inelastic demand spectrum is a very useful design tool for visual selection of optimal isolation parameters, and eliminates the use of equivalent linear-elastic substitute structures as the displacement demand is obtained from nonlinear time history analysis. The responses of seismically-isolated structures subjected to near-source ground motions with either large forward-directivity pulses or fault-fling pulses are presented. Our analyses suggest that seismic isolation can be used to protect structures subjected to recorded ground motions currently available to us, with acceptable levels of base shear coefficient and isolator displacement, except for one component of the TCU068 record from the 1999 Chichi, Taiwan, earthquake (which contained a large permanent displacement of nearly 10 m).

Nonlinear Static Procedure for Seismic Vulnerability Assessment of Bridges

Abstract: The impact of an earthquake event on the performance of a highway transportation network depends on the extent of damage sustained by its individual components, particularly bridges. Seismic damageability of bridges expressed in the form of fragility curves can easily be incorporated into the scheme of risk analysis of a highway network under the seismic hazard. In this context, this article focuses on a nonlinear static method of developing fragility curves for a typical type of concrete bridge in California. The method makes use of the capacity spectrum method (CSM) for identification of spectral displacement, which is converted to rotations at bridge column ends. To check the reliability of this current analytical procedure, developed fragility curves are compared with those obtained by nonlinear time history analysis. Results indicate that analytically developed fragility curves obtained from nonlinear static and time history analyses are consistent.

An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action

Estimating seismic demands on structures, to predict their performance level with confidence, requires explicit consideration of the structural inelastic behav- iour: to this end, the use of nonlinear static procedures is inevitably going to be favoured over complex nonlinear time-history methods. The currently available assessment procedures have been tested predominantly against building frames. A newly derived assessment procedure is proposed within the scope of bridge applications, based on an innovative displacement-based adaptive pushover technique. The procedure, which can be incorporated into a performance- based engineering philosophy, is applicable to MDOF continuous span bridges with flexible or rigid superstructures, and for varying degrees of abutment restraint. As a first application to determine the viability of the proposed procedure, a para- metric study is conducted on a ensemble of bridges subjected to earthquake motion. It is shown that, compared to the seismic demand estimated by means of the more accurate nonlinear dynamic analysis tool, the novel static assessment method can lead to the attainment of satisfactory predictions, both in terms of displacement as well as moment demand on members.

Seismic Design Codes for Buildings in Japan

Two revised seismic design codes in the Building Standard Law of Japan, which were revised in 1981 and 2000, are simply reviewed with the transition of Japanese seismic design code in this paper. The central feature of the seismic code revised in 1981 was the introduction of a two-phase earthquake design. Allowable stress design was employed for first-phase earthquake design targeting the safety and serviceability of buildings during medium-level earthquake activity. Second-phase earthquake design, which is ultimate strength design, was added to provide safety against severe earthquake motion. On the other hand, the seismic code revised in 2000 precisely defines performance requirements and verification based on accurate earthquake response and limit states of a building. The capacity spectrummethod is used for evaluating the earthquake response. The code is applicable to any type of material and buildings such as seismic isolation systems as long as material properties are well defined and structural behavior is appropriately estimated.

Adaptive Modal Combination Procedure for Nonlinear Static Analysis of Building Structures

A new pushover analysis procedure derived through adaptive modal combinations (AMC) is proposed for evaluating the seismic performance of building structures. The methodology offers a direct multimode technique to estimate seismic demands and attempts to integrate concepts built into the capacity spectrum method recommended in ATC-40 (1996), the adaptive method originally proposed by Gupta and Kunnath (2000) and the modal pushover analysis advocated by Chopra and Goel (2002). The AMC procedure accounts for higher mode effects by combining the response of individual modal pushover analyses and incorporates the effects of varying dynamic characteristics during the inelastic response via its adaptive feature. The applied lateral forces used in the progressive pushover analysis are based on instantaneous inertia force distributions across the height of the building for each mode. A novel feature of the procedure is that the target displacement is estimated and updated dynamically during the analysis by incorporating energy-based modal capacity curves in conjunction with constant-ductility capacity spectra. Hence it eliminates the need to approximate the target displacement prior to commencing the pushover analysis. The methodology is applied to two existing steel moment-frame buildings and it is demonstrated that the AMC procedure can reasonably estimate critical demand parameters such as roof displacement and interstory drift for both far-fault and near-fault records, and consequently provides a reliable tool for performance assessment of building structures.

Seismic risk of R.C. building classes

Seismic risk assessment on a large scale may be defined as the prediction of the fraction of buildings expected to reach a conventional limit state in the region and time period of interest. This definition is the frequentistic interpretation of the failure probability for a homogeneous class of structures. Empirical post-event survey methods for vulnerability evaluation may not fit the purpose of seismic risk analysis at class level and a pure analytical approach may be required. To this aim this paper proposes the extension of structure-specific reliability procedures, but without assuming a single structure as representative of the class. The class-capacity function is approximated by regression of significant cases analyzed by Static Push-Over (SPO); the seismic demand is obtained by Probabilistic Seismic Hazard Analysis (PSHA). The seismic risk is computed by simulation of the former being exceeded by the latter via the Capacity Spectrum Method (CSM). Explanatory application refers to six classes of Italian rectangular R.C. buildings; three classes are of pre-code constructions, designed only for gravity loads, whereas the other three considered are of seismic buildings designed with old codes not accounting for capacity design rules.