Capacity Spectrum Method Research Articles

The Extended Adaptive Capacity Spectrum Method for the Seismic Assessment of Plan-Asymmetric Buildings

The use of nonlinear static procedures (NSPs) on the seismic assessment of real existing plan-irregular structures has so far been studied by a limited number of authors. This fact limits the application of such methods to assess current existing structures, the majority of which are irregular in plan. An extended version of the adaptive capacity spectrum method (ACSM) for the seismic assessment of plan-irregular buildings is presented in this paper. The novelty of this proposal is to comprise the most accurate features of commonly used NSPs in order to overcome the problems that subsist in three-dimensional pushover analyses. The accuracy of the procedure is tested in three plan-irregular real buildings. The results are compared with the capacity spectrum method (CSM) with the features proposed in FEMA 440, with the extended N2 method for plan-asymmetric structures, with the adaptive capacity spectrum method (ACSM) and with the most exact nonlinear dynamic analyses. Several seismic intensities are tested, in order to evaluate the performance of the procedure in different stages of structural inelasticity.

Estudio sísmico de los edificios agregados de obra de fábrica utilizando el método del espectro de capacidad

In this work a study about the seismic behaviour of a set of masonry aggregates buildings located in the city of Barcelona, Spain, is presented. Considering the age of these buildings (more than 70 years) two mechanical properties for the masonry were defined. The seismic action considered is defined by elastic response spectrum defined by Eurocode 8 for the seismic acceleration of Barcelona. To analyze these buildings the capacity spectrum method was used, from which the capacity curve and the fragility curves are obtained for evaluating the seismic expected damage. Damage probability matrices quantified the seismic damage and they are obtained from the fragility curves and the performance point. Considering that the city of Barcelona is located in an area of low seismicity, the results show an important seismic damage.

EVALUATION OF CAPACITY SPECTRUM METHOD IN ESTIMATING SEISMIC DEMANDS OF TRIPLE PENDULUM BEARINGS UNDER NEAR-FIELD GROUND MOTIONS

Simplified methods for analyzing seismically isolated structures are always used either as a design procedure or as checking criteria for the results of time history procedure. The main purpose of this study is to evaluate the accuracy of one of these methods, the capacity spectrum method (CSM), in predicting the seismic demands, such as isolator displacement and maximum base shear force, of structures with triple pendulum bearings (TPBs) under bidirectional near-field ground motions. By comparing the results of this method with those of the nonlinear time history analysis (NTHA), it can be concluded that the CSM is able to predict the maximum isolator displacement and base shear of the structure with acceptable accuracy. It should be noted that for softer soil site conditions, the values of demand calculated by CSM are sometimes underestimated compared with the results of NTHA, especially when the effective period of system exceeds 3.0 s or when the TPB works on the fifth regime of its pendulum mechanism.

Pushover Analysis of R.C. Frame Building with Shear Wall

A performance - based design is at controlling the structural damage based on precise estimation of proper response parameter. In performance based seismic analysis evaluates how building is likely to perform. It is an iterative process with selection of performance objective followed by development of preliminary design, an assessment whether or not the design meets the performance objective; In the present study pushover analysis has been done an two multistoried R.C. frame building; In which plan of one building was taken symmetrical and it consist of 2 bay of 5m in x direction & 2 bay of 4m in y direction and second building having L shaped unsymmetrical plan. The shear wall is providing for studying their resisting lateral forces. In this paper highlight the effect of shear wall on R.C frame building when shear wall providing along the longer and shorter side of the building. The base shear and displacement will decreases of building. The comparative study has been done for base shear, story drift, spectral acceleration, spectral displacement, story displacement. Key word: Pushover analysis, Capacity spectrum method, shear wall

Evaluation of Nonlinear Static Procedures in the Assessment of Building Frames

In recent years a number of nonlinear static procedures (NSPs) have been developed and proposed. Such pushover-based seismic assessment procedures are relatively straightforward to employ and are generally chosen over nonlinear dynamic analysis, especially within the realm of design office application. Parametric comparisons between the different NSPs available, however, are still somewhat sparse. In this work, five commonly employed NSPs (the N2 method, capacity spectrum method, modal pushover analysis, adaptive modal combination procedure, and the adaptive capacity spectrum method) are applied in the assessment of 16 frames subjected to a large number of input motions with a view to assess the accuracy level of such approaches through comparison with nonlinear dynamic analysis results. The evaluation shows that all the NSPs are able to accurately predict displacements and to produce reasonable estimates for other response parameters, with limited dispersion. Even though no single NSP tested led to consistently superior results, modal pushover analysis and the adaptive capacity spectrum method seemed to perform slightly better.

Method of Performance-Based Design

In order to overcome some deficiency of design, American earthquake engineering and structural engineering experts have profound conclusion after the previous earthquakes, improved bearing capacity design method, put forward the theory of performance-based design. Methods of performance-based design mainly include displacement coefficient method; direct displacement based design method, capacity spectrum method and improved capacity spectrum method. Through the understanding of the main methods, enable us to better understand performance-based design, so as to improve the design of civil engineering.

Limit states of RC structures with first floor irregularities

The seismic performance of reinforced concrete (RC) frame structures with irregularities leading to soft first floor is studied using capacity assessment procedures. The soft first story effect is investigated for the cases: (i) slab-column connections without beams at the first floor, (ii) tall first story height and (iii) pilotis type building (open ground story). The effects of the first floor irregularity on the RC frame structure performance stages at global and local level (limit states) are investigated. Assessment based on the Capacity Spectrum Method (ATC-40) and on the Coefficient Method (FEMA 356) is also examined. Results in terms of failure modes, capacity curves, interstory drifts, ductility requirements and infills behaviour are presented. From the results it can be deduced that the global capacity of the structures is decreased due to the considered first floor morphology irregularities in comparison to the capacities of the regular structure. An increase of the demands for interstory drift is observed at the first floor level due to the considered irregularities while the open ground floor structure (pilotis type) led to even higher values of interstory drift demands at the first story. In the cases of tall first story and slab-column connections without beams soft-story mechanisms have also been observed at the first floor. Rotational criteria (EC8-part3) showed that the structure with slab-column connections without beams exhibited the most critical response.

Strength Reduction Factors: A Unified Analytic Expression for Narrowband and Broadband Ground Motion Records

Strength reduction factors are an important component of the force modification factors used in the calculation of seismic code forces, as they account for the effect of the nonlinear hysteretic behavior of the structure. They are expressed as the ratio between the elastic strength demand and the inelastic strength demand induced in a structure by the earthquake. The evaluation of strength reduction factors has applications in the substantiation of seismic force modification factors in building design codes and in the direct application of the capacity spectrum method. The paper presents a study performed on two sets of accelerograms having different spectral content types, i.e. narrow frequency band records and broad frequency band records. Based on constantductility spectra of strength reduction factors, computed with 50% and 10% probability of exceedance, a unified analytic formula is developed, to describe the variation with ductility and vibration period of these factors. By modifying the values of the coefficients of the variables, the formula can be adapted for each type of spectral content. The formula is further refined, by determining a new set of coefficients, to also account for the influence of the predominant period of the ground motion in the case of narrow frequency band records.

Procedure for determining the seismic vulnerability of an irregular isolated bridge

A seismic vulnerability procedure, based on the capacity/demand ratio approach, is applied to an irregular isolated bridge. Special features are incorporated in both, demand estimation and capacity evaluation. The seismic demand is represented by an average pseudo-acceleration spectrum derived from 159 earthquake accelerograms recorded in the region where the bridge is located. The capacity spectrum method is adopted for estimating the structural expected performance for several limit states. The capacity curve derived from a static non-linear procedure is obtained by means of a lateral load pattern that follows the displacement configuration, previously assessed by the use of time history analyses of the bridge supported on non-linear isolator bearings. Based on a moment–curvature analysis of the pier's sections, the maximum curvature ductility was established for each of the four defined performance limit states. Finally, probability density functions of the bridge capacity and demand were assessed and fragility curves were proposed aimed at determining the expected behaviour of the bridge as function of peak ground acceleration (PGA) of the typical strong motions recorded in the area.

An adaptive pushover procedure based on effective modal mass combination rule

In order to overcome the major drawbacks of conventional pushover methods, researchers have recently been motivated to develop adaptive pushover procedures by which effect of higher modes as well as progressive damage accumulation are taken into account. In spite of their vigorous theory, these novel methods suffer from the quadratic modal combination rules, in which the sign reversals of load vectors in higher modes are neglected and consequently lead to a positive load pattern. In this paper, a displacement-based adaptive modal pushover method, called APAM, based on effective modal mass combination rule is developed in order to include the sign reversals in the load vectors. In this combination rule a modification factor associated to each mode of interest is determined and applied to the corresponding load vector. The modified modal load vectors are algebraically added and subtracted and result in a range of load pattern and thus, multiple pushover analysis is required. These load patterns are independently applied to the structure within an adaptive framework and the envelope of demand values is considered. These modification factors are updated proportional to the instantaneous dynamic characteristic of structure in each step. Another novel aspect of the proposed method is that the target displacement is estimated during the analysis by implementing the concept of capacity spectrum method recommended by ATC 40. In order to assess the accuracy of this method in predicting the seismic responses, the proposed methodology is applied to three different moment-frame buildings. The obtained results demonstrate that APAM procedure provides well estimation of important seismic demand parameters.

Study on Performance-Based Seismic Performance Method for Masonry-Infilled Frame Structures

Combining with performance grades of reinforced concrete structures at home and abroad, the seismic performance of masonry-infilled frame structures can be induced into five levels: basically normal, slight damage, medium damage, severe damage and collapse prevention. The limit states of all seismic performance levels and their dominating parameters of masonry-infilled frame structures are put forward, and quantified performance index of this structure are obtained on the basis of statistical test data. The seismic response of pure and masonry-infilled frame structures are compared by using capacity spectrum method and equivalent strut model, and the result indicates that the structure could meet predetermined performance objective under the minor and major earthquake levels by comparing the practical story drift and proposed performance index.

Studying higher mode effects on the performance of nonlinear static analysis methods considering near-fault effects

Daily development in civil engineering arena and the importance of economical aspects in the design of structures have motivated the engineers to shift their approaches from designing upon strength to designing upon performance. This is of more importance regarding the forces induced by earthquakes which have unpredicted and random nature. However, it is not possible to design or assess exactly the structural performance against strong ground motion using analytical methods which are applied for static loads and therefore precise dynamic analysis methods are needed. Despite significant progress in the analytical methods and engineering software, using nonlinear time history analysis is very difficult for engineers and designers due to unpredictable nature of future ground motions as well as complicated behaviour of structures. Consequently, the substituting methods are presented upon nonlinear static analysis. Coefficient method and capacity spectrum method, presented by FEMA356 and ATC40, respectively, are of this kind that have been used in the recent years and modified by newer documents such as FEMA440. Despite acceptable results, neglecting some important items, such as higher mode effects which can be decisive in tall and specific structures, made offering other procedures like Modal Pushover Analysis (MPA). In this study, the performance abilities of nonlinear static methods are studied in order to assess the dynamic response of structures under both far- and near-fault earthquake records. For this purpose, two reinforced concrete frames of 5 and 15 stories are analyzed by a series of nonlinear static and dynamic analyses. Analysis results show that conventional nonlinear static analysis methods cannot estimate accurately the deformation demands of tall building structures, particularly in the higher stories, due to the effects of higher modes. Although MPA method has almost improved the results, yet it has not high accuracy regarding near-fault earthquake records.

A design procedure of dissipative braces for seismic upgrading structures

The research presented in this paper deals with the seismic protection of existing frame structures by means of passive energy dissipation. A displacement-based procedure to design dissipative bracings for the seismic protection of frame structures is proposed and some applications are discussed. The procedure is based on the displacement based design using the capacity spectrum method, no dynamic non linear analyses are needed. Two performance objective have been considered developing the procedure: protect the structure against structural damage or collapse and avoid non-structural damage as well as excessive base shear. The compliance is obtained dimensioning dissipative braces to limit global displacements and interstorey drifts. Reference is made to BRB braces, but the procedure can easily be extended to any typology of dissipative brace. The procedure has been validated through a comparison with nonlinear dynamic response of two 2D r.c. frames, one bare and one infilled. Finally a real application, on an existing 3D building where dissipative braces available on market are used, is discussed.

Earthquake Damage Assessment for RC Structures Based on Fuzzy Sets

A global damage index based on multiple linear force-deformation curves in pushover analysis is presented to evaluate the integrated damage of reinforced concrete structure. The modified coefficient is provided considering the cyclic load and hysteresis energy. The number of inelastic cycles and the coefficient of hysteresis energy concentration are also introduced as damage indices. Hence, multiple damage indices about displacement and energy for performance-based design are considered. The relation of multiple damage indices or factors and the fuzzy damage set is presented by comprehensive fuzzy evaluation; hence, a performance-based multiple fuzzy seismic damage-assessment method for reinforced concrete frame structures is established. The method can be accomplished based on pushover analysis, code spectrum, and capacity spectrum method. The fuzzy seismic damage-assessment method is verified through nonlinear analysis four different structures and the corresponding results and assessment conclusions are accurate.

Capacity Spectrum Method for RC Building with Cracked and Uncracked Section

one of the most widespread procedures for the assessment of building behavior, due to earthquake, is the Capacity Spectrum Method (CSM). In the scope of this procedure, capacity of the structure compares with the demands of earthquake ground motion on the structure. The capacity of the structure is represented by a nonlinear force-displacement curve, referred to as a pushover curve. The base shear forces and roof displacements are converted to equivalent spectral accelerations and spectral displacements, respectively, by means of coefficients that represent effective modal masses and modal participation factors. These spectral values define the capacity spectrum. The demands of the earthquake ground motion are represented by response spectra. A graphical construction that includes both capacity and demand spectra, results in an intersection of the two curves that estimates the performance of the structure to the earthquake. In this study, for determination of the performance levels, G+10 R.C.C. Building with cracked and uncracked section were taken. The structural Capacity of cracked and uncracked section compared with performance point value, which shows the structural capacity of building having cracked section is lesser than the uncracked section. Different modeling issues were analyzed to study the effect on Capacity of the structure with cracked

Damage seismic scenarios for Angra do Heroísmo, Azores (Portugal)

Angra do Heroismo, located in Terceira Island, is the main town of the Central Group of Azores Archipelago and it is classified as World Heritage by Unesco. The preservation of this patrimony, located inside a seismic region, includes the implementation of a policy to protect it against earthquakes. The development of credible damage scenarios could help this objective, as they can be used in prevention measures to minimize the impact of future earthquakes. Two methods were used for seismic damage estimation: the capacity spectrum method and a new method, based on the direct response of a 1D non-linear oscillator to simulate the building seismic performance. Both methods seem to overestimate the damages for the near sources, but this could be due to the empirical model used to estimate the input ground motion. Comparison with the damage observed after the January 1st, 1980 earthquake show a large discrepancy with an underestimation bias, which can be explained, mainly, by the difference of building performance and on the plausible hypothesis of 2D site effects.

Displacement-Based Seismic Design of Steel Frames Strengthened by Buckling-Restrained Braces

This study presents a displacement-based design procedure for seismic retrofitting of steel frames using buckling-restrained braces (BRB) to meet a given target displacement in the framework of the capacity spectrum method. The seismic performance of a six-storey steel frame equipped with BRB is investigated. Different storey-wise BRB distribution methods are proposed and the influence on the results of the design procedure is analyzed. Nonlinear dynamic analyses demonstrate the efficacy of the design procedure showing the improvements achieved by the retrofitting intervention using BRB. The maximum top displacement registered for the retrofitted frame under earthquake excitation coincides with the target displacement obtained in accordance with the design procedure. The introduction of buckling-restrained braces enhances the earthquake resistance of the steel frame, providing significant energy dissipation and the stiffness needed to satisfy structural drift limits.

비선형동적해석을 통한 국내 철골 모멘트골조의 내진성능 평가

국내 철골모멘트골조를 이전 KBC2005 및 현 KBC2009 기준에 따라 설계한 후 비선형동적해석을 이용하여 FEMA355F의 내진성능평가 절차에 따라 성능을 평가하였다. 그 결과 비선형정적 Push-over 해석을 이용한 역량스펙트럼법과 차이가 있었다. 특히 국내 철골모멘트골조는 약패널존을 가지기 때문에 비선형동적해석을 통해서만 보다 정확한 거동을 예측할 수 있었다. 국내 철골모멘트골조는 지반 조건 SB 또는 SC에 위치한다면 층수 및 R값에 관계없이 성능목표를 만족하는 것으로 나타났다. 하지만 지반 조건 SD 또는 SE에 위치한다면 성능목표 만족 여부는 명확하지 않았다. 따라서 KBC2005나 KBC2009 어떤 기준을 사용하더라도 지반 조건이 상대적으로 좋다면 국내 철골모멘트골조는 내진성능을 충분히 확보하고 있다고 볼 수 있다. Domestic steel moment resisting frames were designed in accordance with the former KBC2005 and the current KBC2009, and then their seismic performance was evaluated in accordance with FEMA355F by utilizing nonlinear dynamic analysis. The results from the procedure in FEMA355F were different with those from the capacity spectrum method utilizing nonlinear static push-over analysis. In particular, the domestic steel moment resisting frames have a weak panel zone, so their behavior can be estimated more precisely by nonlinear dynamic analysis. The domestic steel moment resisting frames satisfied the performance goal if located at a site class <TEX>$S_B$</TEX> or <TEX>$S_C$</TEX>, regardless of the story number and the response modification factor. However, if they are located at a site class <TEX>$S_D$</TEX> or <TEX>$S_E$</TEX>, performance goal satisfaction cannot be guaranteed. No matter what standard is used for the design, KBC2005 or KBC2009, the domestic steel moment resisting frames may possess satisfactory seismic performance if the site condition is relatively good.

Shaking table tests of structures with hysteretic dampers: experimental results versus prediction using non-linear static methods

The use of seismic hysteretic dampers for passive control is increasing exponentially in recent years for both new and existing buildings. In order to utilize hysteretic dampers within a structural system, it is of paramount importance to have simplified design procedures based upon knowledge gained from theoretical studies and validated with experimental results. Non-linear Static Procedures (NSPs) are presented as an alternative to the force-based methods more common nowadays. The application of NSPs to conventional structures has been well established; yet there is a lack of experimental information on how NSPs apply to systems with hysteretic dampers. In this research, several shaking table tests were conducted on two single bay and single story 1:2 scale structures with and without hysteretic dampers. The maximum response of the structure with dampers in terms of lateral displacement and base shear obtained from the tests was compared with the prediction provided by three well-known NSPs: (1) the improved version of the Capacity Spectrum Method (CSM) from FEMA 440; (2) the improved version of the Displacement Coefficient Method (DCM) from FEMA 440; and (3) the N2 Method implemented in Eurocode 8. In general, the improved version of the DCM and N2 methods are found to provide acceptable accuracy in prediction, but the CSM tends to underestimate the response.

Damage‐dependent vulnerability curves for existing buildings

SUMMARYSeismic behavior of damaged buildings may be expressed as a function of their REsidual Capacity (REC), which is a measure of seismic capacity, reduced by damage. REC can be interpreted as the median value of collapse vulnerability curves. Its variation owing to damage is a useful indication of increased building vulnerability. REC reduction, indicating the lowering of seismic safety after an earthquake (performance loss, PL), represents an effective index for assessing the need of seismic repair/strengthening after earthquakes. The study investigates the applicability of a pushover‐based method in the analysis of damaged structures for the case of existing under‐designed RC buildings. The paper presents a systematization of the procedure in an assessment framework that applies the capacity spectrum method based on inelastic demand spectra; furthermore, the vulnerability variation of a real building is investigated with a detailed case study. The behavior of damaged buildings is simulated with pushover analysis through suitable modification of plastic hinges (in terms of stiffness, strength and residual drift) for damaged elements. The modification of plastic hinges has been calibrated in tests on nonconforming columns. The case study analysis evidenced that, for minor or moderate damages, the original structural displacement capacity was only slightly influenced, but the ductility capacity was significantly reduced (up to 40%) because of the increased structure deformability. This implied performance loss in the range 10%–20%. For severe damages the PL ranged between 41% and 56%. Local mechanism types exhibit PL nearly double with respect to global mechanism types. Copyright © 2012 John Wiley &amp; Sons, Ltd.