A response spectrum method for seismic response analysis of structures under multi-support excitations

Li, Jian-Hua,Li, Jie Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.21 No.3

Based on the random vibration theory, a response spectrum method is developed for seismic response analysis of linear, multi-degree-of-freedom structures under multi-support excitations is developed. Various response quantities, including the mean and variance of the peak response, the response mean frequency, are obtained from proposed combination rules in terms of the mean response spectrum. This method makes it possible to apply the response spectrum to the seismic reliability analysis of structures subjected to multi-support excitations. Considering that the tedious numerical integration is required to compute the spectral parameters and correlation coefficients in above combination rules, this paper further offers simplified procedures for their computation, which enhance dramatically the computational efficiency of the suggested method. The proposed procedure is demonstrated for tow numerical examples: (1) two-span continuous beam; (2) two-tower cabled-stayed bridge by using Monte Carlo simulation (MC). For this purpose, this paper also presents an approach to simulation of ground motions, which can take into account both mean and variation properties of response spectrum. Computed results based on the response spectrum method are in good agreement with Monte Carlo simulation results. And compared with the MSRS method, a well-developed multi-support response spectrum method, the proposed method has an incomparable computational efficiency.

응답스펙트럼법에 의한 고층 건축물의 탄소성 지진응답해석법

전대한 한국지진공학회 1997 한국지진공학회논문집 Vol.1 No.4

본 논문은 고층건물의 지진응답해석에서 탄성 및 탄소성 응답스펙트럼 해석법에 대하여 고찰한 것이다. 선형 구조물의 지진응답 해석에 널리 사용되고 있는 응답스펙트럼법은 여러 연구자들에 의해 서로 다른 모드 조합방법으로 제안되었으며, 이들 조합방법에 따른 차이점을 상세히 검토하였다. 탄소성 지진응답해석에 응답스펙트럼법은 아직 널리 사용되고 있지 못한 실정이다. 본 연구에서는 장주기를 갖는 고층 건물의 탄소성 지진응답해석에 응답스펙트럼을 확장하여 적용하는 방법을 제시한다. 본 논문에서 제안한 탄소성 응답스펙트럼법을 이용하면, 고층건물의 예비 설계에서 시간이력해석 대신으로 보다 간편히 탄소성 응답치를 예측하는 도구로서 활용할 수 있을 것으로 사료된다. This paper examined various aspects of a linear and a nonlinear response spectrum method in seismic response analysis of multi-story building structures. The response spectrum method that has been widely used in the analysis of linear structures was proposed different mode superposition method by several ivestigators, and the differences between combinations with an elastic modal analysis reviwed closely. It seems, however, that this method is not used to nonlinear seismic analysis. It is the purpose of this paper to propose an alternative method by means of which a nonlinear MDOF structure with long period may be analysed by an extention of response spectrum method. For nonlinear seismic analysis of high-rise building structures using technique proposed in this study, it is intended to serve primarily as a tool in preliminary designs instead of time history analysis.

복합구조물의 하부골조층수 변화에 따른 비선형 약산법의 응답특성

김재웅,강병두,전대한,남영우 대한건축학회지회연합회 2005 대한건축학회지회연합회 학술발표대회논문집 Vol.1 No.1

One of the most accurate earthquake analysis method for the performance evaluation of structure is nonlinear time history analysis, but it is time-consuming and necessitate more efforts. Approximate methods are presented for estimating the capacity of structures while subjecting earthquake ground motions. This is made by exploiting the connection between the nonlinear static response of structure and the dynamic response of SDF system whose backbone matches the structure’s pushover curve. The capacity spectrum method is one of general approximate methods which is based on equivalent linearization where the inelastic deformation is approximated by the maximum deformation of an equivalent linear elastic system having equivalent viscous damping. It requires iterative computations, because the equivalent damping ratio is computed as a function of the maximum deformation. The nonlinear capacity spectrum method estimate the maximum inelastic deformation of SDF system by nonlinear response spectra. The nonlinear direct spectrum method is proposed and studied to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. In this study, it is to compare the accuracy and the reliability of approximate nonlinear methods with respect to upper wall-lower frame system and various earthquakes.

현수교의 지진응답 평가

김호경,유동호 주석범 한국지진공학회 2003 한국지진공학회논문집 Vol.7 No.1

현수교의 지진응답 산정 시 몇 가지 해석법 간에 발생될 수 있는 차이를 파악하고자 하나의 예제 현수교에 대해 비교 연구를 수행하였다. 주된 검토항목은 선형과 비선형 응답응답스펙트럼법과 동적해석법, 그리고 감쇠율과 감쇠고려 방안이다. 검토 결과 대상 물리량이나 가진 방향에 따라 약간의 차이는 있지만 전체적으로 감쇠율과 감쇠 고려방안 등 감쇠와 관련된 변수가 지진응답에 큰 영향을 미치고 있음을 확인하였다. 반면 응답스펙트럼과 동적해석법, 선형 및 비선형해석법 등 구조해석법에 관련된 변수는 상대적으로 지진응답에 미치는 영향이 적은 것으로 확인되었다. 대상 현수교의 경우에도 응답스펙트럼법이 안전측의 결과를 줄 수 있을 것으로 기대되지만 이 경우 도로교설계기준에 제시된 설계응답스펙트럼을 감쇠율에 따라 적절히 보정하는 사전 작업이 필요랄 것으로 판단되었다. A comparative study was performed for a suspension bridge to grasp the possible differences in seismic responses evaluated by several analytical methods. The items mainly investigated are the linear vs. nonlinear response, the response spectrum method vs. the linear dynamic analysis method, and the damping ratio and it's implementation into analysis procedures. According to the numerical example, it is found that the seismic responses are considerably affected by the damping-related parameters even though slight differences are shown depending on the response quantities and the exciting directions. On the other hand, it is also confirmed that the seismic responses are less affected by the analysis method-related parameters such as the response spectrum method vs. the linear dynamic analysis method, and the linear and nonlinear analysis method. The response spectrum method is expected to give conservative results for the examined bridge, provided that the design response spectrum in the Korean Highway Design Specification is modified according to the proper damping ratio.

Response spectrum analysis considering non-classical damping in the base-isolated benchmark building

Huating Chen,Ping Tan,Haitao Ma,Fulin Zhou 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.4

An isolated building, composed of superstructure and isolation system which have very different damping properties, is typically non-classical damping system. This results in inapplicability of traditional response spectrum method for isolated buildings. A multidimensional response spectrum method based on complex mode superposition is herein introduced, which properly takes into account the non-classical damping feature in the structure and a new method is developed to estimate velocity spectra from the commonly used displacement or pseudo-acceleration spectra based on random vibration theory. The error of forced decoupling method, an approximated approach, is discussed in the viewpoint of energy transfer. From the baseisolated benchmark model, as a numerical example, application of the procedure is illustrated companying with comparison study of time-history method, forced decoupling method and the proposed method. The results show that the proposed method is valid, while forced decoupling approach can’t reflect the characteristics of isolated buildings and may lead to insecurity of structures.

한반도 지진원의 특성을 고려한 응답스펙트럼

신재철,이두한,정인수,이창원 충남대학교 산업기술연구소 2003 산업기술연구논문집 Vol.18 No.1

The response spectrum is the best representation of earthquake for engineering purposes because it takes account of the natural frequencies of structures. In general PGA(Peak Ground Acceleration) is used to scale the standard response spectrum. But it is likely to lead to serious error, because the shapes of response spectra depend on magnitude, source distance and site conditions. Therefore, theoretical prediction called stochastic source models have been used for predicting ground motion and response spectrum by magnitude and distance in regions where strong ground motion data are sparse. The deterministic method that PGA scales the design spectrum is prescribed in Korea, so unexpected error can be occured. Therefore the stochastic simulation method is employed to predict ground motion and to estimate the response spectrum for comparison with the design spectrum in this study. Stochastic source model that the shape is controlled by two corner frequency is computed and verified by comparing with Gyeongju earthquake using site-amplification(Boor & Joyner, 1997) to consider site condition. And it is proved how much this difference has an effect on response of structure such as steel box girder bridge.

최대 비탄성 변위 응답 예측을 위한 기존 능력스펙트럼법들의 유효성 평가 및 비교

김홍진 민경원,이상현,박민규 한국지진공학회 2004 한국지진공학회논문집 Vol.8 No.2

탄성응답스펙트럼을 사용하는 능력스펙트럼법은 비선형 시스템을 등가의 선형시스템으로 치환하여 주어진 지진 하중에 대한 구조물의 최대 비선형 거동을 예측한다. 본 연구의 목적은 이러한 능력스펙트럼법들의 정확성을 검증하고, 예측 특성을 비교하는 것이다. 이를 위해, ATC-40, G lkan, Kowalsky, 그리고 Iwan이 제시한 방법을 이용하여 등가주기와 등가감쇠비를 산정한 후, ATC-40에서 제시한 절차B에 따라 성능점을 산정 하였다. 전반적으로 ATC-40 방범은 구조물의 응답을 과소 평가하여 안전하지 못한 설계결과를 가져 올 수 있으며, G lkan과 Kowalsky의 방법은 과대 평가하는 경향을 가지고 있다. Iwan이 제시한 방법은 ATC-40 방법과 G lkan과 Kowalsky 방법의 중간 값을 예측함으로써, 비교적 정확한 값에 가까운 최대 변위를 산출하였다. 그리고, Kowalsky 방법은 항복 후 강성비에 따라 등가감쇠비를 음수로 산정함으로써 예측 값을 제시하지 못하는 경우가 있음을 확인하였다. In the capacity spectrum method(CSM) using a linear response spectrum, the peak response of an inelastic system under a given earthquake load is estimated transforming the system into the equivalent elastic one. The CSM for estimating the peak inelastic response is evaluated in this paper. The equivalent period and damping ratio are calculated using the ATC-40, G lkan, Kowalsky, and Iwan methods, and the performance points are obtained according to the procedure B of ATC-40. Analysis results indicate that the ATC-40 method generally underestimates the peak response resulting in the unsafe design, while the G lkan and Kowalsky methods overestimate the responses. The Iwan method produces the values between those by the ATC-40 method and the G lkan and Kowalsky methods, and estimates the responses relatively closer to the exact ones. Further, it is found that the Kowalsky method gives the negative equivalent damping ratios depending on the hardening ratios, and thereby can not be used to estimate the responses in some cases.

기존 비선형약산법들의 신뢰성 개선을 위한 비선형직접스펙트럼법

김재웅,강병두,전대한 한국지진공학회 2006 한국지진공학회논문집 Vol.10 No.4

본 연구에서는 강성골격곡선으로부터 산정한 구조물의 초기 탄성진동주기 T_1와 응답스트럼으로부터 산정한 비선형 유사가속도 A_{1y}/g 및 연성비 {\mu}를 사용하여, 반복적인 계산과정 없이 복합구조물의 내진성능을 평가하는 비선형직접스펙트럼법(NDSM)을 고려한다. 다양한 지진과 복합구조물에 대한 NDSM의 신뢰성과 실용성을 비선형시각이력해석(NRHA) 결과와 비교 검토하였다. 본 연구의 결론은 다음과 같다. (1) NDSM은 강성골격곡선으로부터 기본진동주기와 비선형 항복강도를 구하면, 비선형 응답스펙트럼으로부터 직접적으로 구조물의 비선형 최대응답을 산정할 수 있는 실용적인 방법으로 사료된다. (2) NDSM의 응답을 정산해와 비교한 결과, 대부분의 모델이 단순평균의 관점에서 전체 해석모델 중 3/4이 약 20% 이하의 오차를 나타내었고, 일반적으로 비선형시각이력해석의 응답보다 크게 산정되는 것으로 나타났다. This paper considers the nonlinear direct spectrum method to estimate seismic performance of mixed building structures without iterative computations, given dynamic property T_1 from stiffness skeleton curve and nonlinear pseudo acceleration A_{1y}/g and/or ductility ratio p from response spectrum. Nonlinear response history analysis has been performed and analysed with various earthquakes for evaluation of correctness and confidence of nonlinear direct spectrum method. The conclusions of this study are as follows; (1) Nonlinear direct spectrum method is considered as a practical method which is applicable to compute the structural initial elastic period and the yielding strength from stiffness skeleton owe and calculate the nonlinear maximum response of structure directly from nonlinear response spectrum. (2) The comparison of the analysis results from NDSM and NRHA showed that the average errors were less than 20% in about 3/4 of the analysis cases, and that the results obtained from NDSM turned out to be generally larger than those from NRHA.

능력스펙트럼을 이용한 최대 비탄성 변위 응답의 정확성 평가

박민규,민경원,김홍진 대한건축학회 2004 대한건축학회 학술발표대회 논문집 - 계획계/구조계 Vol.24 No.1(구조계)

In the capacity spectrum method (CSM) using a linear response spectrum, the peak response of an inelastic system under a given earthquake load is estimated transforming the system into the equivalent elastic one. The CSM for estimating the peak inelastic response is evaluated in this paper. The equivalent period and damping ratio are calculated using the A TC-40, Gulkan, Kowalsky, and Iwan methods, and the performance points are obtained according the procedure B of ATC-40. Analysis results indicate that the ATC-40 method generally underestimates the peak response resulting in the unsafe design, while the Gulkan and Kowalsky methods overestimate the responses. The Iwan method produces the values between those by the A TC-40 method and the Gulkan and Kowalsky methods, and estimates the responses relatively closer to the exact ones.

계측 기록의 설계스펙트럼 부합 가상 지진 변환 방법

지혜연,최다슬,김정한 한국지진공학회 2021 한국지진공학회논문집 Vol.25 No.1

The design response spectrum presented in the seismic design standard reflects the characteristics of the tectonic environment at a site. However, since the design response spectrum does not represent the ground motion with a specific earthquake magnitude or distance, input ground motions for response history analysis need to be selected reasonably. It is appropriate to use observed ground motions recorded in Korea for the seismic design. However, recently recorded ground motions in the Gyeongju (2016) or Pohang (2017) earthquakes are not compatible with the design response spectrum. Therefore, it is necessary to convert the recorded ground motion in Korea to a model similar to the design response spectrum. In this study, several approaches to adjust the spectral acceleration level at each period range were tested. These are the intrinsic and scattering attenuation considering the earthquake environment, magnitude, distance change by the green function method, and a rupture propagation direction's directivity effect. Using these variables, the amplification ratio for the representative natural period was regressed. Finally, the optimum condition compatible with the design response spectrum was suggested, and the validation was performed by converting the recorded ground motion.