• Title, Summary, Keyword: demand and capacity spectra

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Capacity spectrum method based on inelastic spectra for high viscous damped buildings

  • Bantilas, Kosmas E.;Kavvadias, Ioannis E.;Vasiliadis, Lazaros K.
    • Earthquakes and Structures
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    • v.13 no.4
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    • pp.337-351
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    • 2017
  • In the present study a capacity spectrum method based on constant ductility inelastic spectra to estimate the seismic performance of structures equipped with elastic viscous dampers is presented. As the definition of the structures' effective damping, due to the damping system, is necessary, an alternative method to specify the effective damping ratio ${\xi}eff$ is presented. Moreover, damping reduction factors (B) are introduced to generate high damping elastic demand spectra. Given the elastic spectra for damping ratio ${\xi}eff$, the performance point of the structure can be obtained by relationships that relate the strength demand reduction factor (R) with the ductility demand factor (${\mu}$). As such expressions that link the above quantities, known as R - ${\mu}$ - Τ relationships, for different damping levels are presented. Moreover, corrective factors (Bv) for the pseudo-velocity spectra calculation are reported for different levels of damping and ductility in order to calculate with accuracy the values of the viscous dampers velocities. Finally, to evaluate the results of the proposed method, the whole process is applied to a four-storey reinforced concrete frame structure and to a six-storey steel structure, both equipped with elastic viscous dampers.

Ductility and inelastic deformation demands of structures

  • Benazouz, Cheikh;Moussa, Leblouba;Ali, Zerzour
    • Structural Engineering and Mechanics
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    • v.42 no.5
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    • pp.631-644
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    • 2012
  • Current seismic codes require from the seismically designed structures to be capable to withstand inelastic deformation. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformation and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the performance-based seismic design through capacity-spectrum methods. In this paper, the median of the ductility demand ratio for 80 ground motions are presented for different levels of normalized yield strength, defined as the yield strength coefficient divided by the peak ground acceleration (PGA). The influence of the post-to-preyield stiffness ratio on the ductility demand is investigated. For fixed levels of normalized yield strength, the median ductility versus period plots demonstrated that they are independent of the earthquake magnitude and epicentral distance. Determined by regression analysis of the data, two design equations have been developed; one for the ductility demand as function of period, post-to-preyield stiffness ratio, and normalized yield strength, and the other for the inelastic deformation as function of period and peak ground acceleration valid for periods longer than 0.6 seconds. The equations are useful in estimating the ductility and inelastic deformation demands for structures in the preliminary design. It was found that the post-to-preyield stiffness has a negligible effect on the ductility factor if the yield strength coefficient is greater than the PGA of the design ground motion normalized by gravity.

Seismic Upgrading of Multi-Span continuous Bridges using Shear Keys (전단키를 이용한 다경간 연속교의 내진성능 향상 방법)

  • 김재관
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.313-318
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    • 1999
  • The seismic performance of multi-span bridge without seismic detailing is found to be insufficient in longitudinal direction. Shear keys and stoppers can be introduced as an alternative to enhance seismic capacity. The capacity curve of bridge with shear keys is obtained considering two extreme contact conditions of shear keys. Its curve is converted into ADRS spectra and compared with demand spectra. It is concluded that seismic performance can be improved effectively by shear keys and its performance can be evaluated graphically on the ADRS specta.

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A study on determination of target displacement of RC frames using PSV spectrum and energy-balance concept

  • Ucar, Taner;Merter, Onur;Duzgun, Mustafa
    • Structural Engineering and Mechanics
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    • v.41 no.6
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    • pp.759-773
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    • 2012
  • The objective of this paper is to present an energy-based method for calculating target displacement of RC structures. The method, which uses the Newmark-Hall pseudo-velocity spectrum, is called the "Pseudo-velocity Spectrum (PSVS) Method". The method is based on the energy balance concept that uses the equality of energy demand and energy capacity of the structure. First, nonlinear static analyses are performed for five, eight and ten-story RC frame structures and pushover curves are obtained. Then the pushover curves are converted to energy capacity diagrams. Seven strong ground motions that were recorded at different soil sites in Turkey are used to obtain the pseudo-acceleration and the pseudo-velocity response spectra. Later, the response spectra are idealised with the Newmark-Hall approximation. Afterwards, energy demands for the RC structures are calculated using the idealised pseudo-velocity spectrum. The displacements, obtained from the energy capacity diagrams that fit to the energy demand values of the RC structures, are accepted as the energy-based performance point of the structures. Consequently, the target displacement values determined from the PSVS Method are checked using the displacement-based successive approach in the Turkish Seismic Design Code. The results show that the target displacements of RC frame structures obtained from the PSVS Method are very close to the values calculated by the approach given in the Turkish Seismic Design Code.

A mechanical model for the seismic vulnerability assessment of old masonry buildings

  • Pagnini, Luisa Carlotta;Vicente, Romeu;Lagomarsino, Sergio;Varum, Humberto
    • Earthquakes and Structures
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    • v.2 no.1
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    • pp.25-42
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    • 2011
  • This paper discusses a mechanical model for the vulnerability assessment of old masonry building aggregates that takes into account the uncertainties inherent to the building parameters, to the seismic demand and to the model error. The structural capacity is represented as an analytical function of a selected number of geometrical and mechanical parameters. Applying a suitable procedure for the uncertainty propagation, the statistical moments of the capacity curve are obtained as a function of the statistical moments of the input parameters, showing the role of each one in the overall capacity definition. The seismic demand is represented by response spectra; vulnerability analysis is carried out with respect to a certain number of random limit states. Fragility curves are derived taking into account the uncertainties of each quantity involved.

Seismic Capacity of a Reinforced Concrete Structure without Seismic Detailing and Implication to the Seismic Design in the Region of Moderate Seismicity (비내진상세 철근콘크리트 구조물의 내진성능 및 중약진지역 내진설계에의 적용)

  • 김익현
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.305-312
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    • 1999
  • A four-story reinforced concrete frame building model is designed for the gravity loads. only Static nonlinear pushover analyses are performed in two orthogonal horizontal directions. The overall capacity curves are converted into ADRS spectra and compared with demand spectra. At several points the deformed shape moment and shear distribution are calculated. It is observed that the seismic capacity may not meet the design requirements in soft soil condition and may collapse in MCE. It is concluded that limited but adequate amount of ductility need be provided in the seismic design in low to moderate seismicity regions.

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Seismic Energy Absorption Capacity in R.C. Structures (R.C. 구조물의 지진에너지 흡수능력 연구)

  • 김장훈
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.217-224
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    • 1997
  • One way in which a comparison can be mode between various reinforced concrete structures is to compare the rate of energy absorption capacity. It is useful to use a well-known standard hysteretic rule as a benchmark for comparisons. The concept of energy absorption efficiency with respect to an elaste-perfectly plastic (EPP) system has been adopted. The normalized cumulative energy, cumulative plastic drift and energy response spectra are used for the method. The previous study using the energy spectra developed by Chang and Mander (1994) indicates the cumulative plastic demand for most earthquakes to be 0.1 rad., but a conservative upper bound of 0.2 rad. could be expected for a maximum credible earthquake. From the present study, the energy absorption efficiency in R.C. structures with respect to the EPP system may range in 30%-45% for most cases.

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Seismic structural demands and inelastic deformation ratios: a theoretical approach

  • Chikh, Benazouz;Mebarki, Ahmed;Laouami, Nacer;Leblouba, Moussa;Mehani, Youcef;Hadid, Mohamed;Kibboua, Abderrahmane;Benouar, Djilali
    • Earthquakes and Structures
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    • v.12 no.4
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    • pp.397-407
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    • 2017
  • To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

Simplified procedure for seismic demands assessment of structures

  • Chikh, Benazouz;Mehani, Youcef;Leblouba, Moussa
    • Structural Engineering and Mechanics
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    • v.59 no.3
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    • pp.455-473
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    • 2016
  • Methods for the seismic demands evaluation of structures require iterative procedures. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformations and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the Performance-Based Seismic Design (PBSD) through Capacity-Spectrum Method (CSM). For instance, the Modal Pushover Analysis (MPA) has been proved to provide accurate results for inelastic buildings to a similar degree of accuracy than the Response Spectrum Analysis (RSA) in estimating peak response for elastic buildings. In this paper, a simplified nonlinear procedure for evaluation of the seismic demand of structures is proposed with its applicability to multi-degree-of-freedom (MDOF) systems. The basic concept is to write the equation of motion of (MDOF) system into series of normal modes based on an inelastic modal decomposition in terms of ductility factor. The accuracy of the proposed procedure is verified against the Nonlinear Time History Analysis (NL-THA) results and Uncoupled Modal Response History Analysis (UMRHA) of a 9-story steel building subjected to El-Centro 1940 (N/S) as a first application. The comparison shows that the new theoretical approach is capable to provide accurate peak response with those obtained when using the NL-THA analysis. After that, a simplified nonlinear spectral analysis is proposed and illustrated by examples in order to describe inelastic response spectra and to relate it to the capacity curve (Pushover curve) by a new parameter of control, called normalized yield strength coefficient (${\eta}$). In the second application, the proposed procedure is verified against the NL-THA analysis results of two buildings for 80 selected real ground motions.

Seismic Design of Structures in Low Seismicity Regions

  • Lee, Dong-Guen;Cho, So-Hoon;Ko, Hyun
    • Journal of the Earthquake Engineering Society of Korea
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    • v.11 no.4
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    • pp.53-63
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    • 2007
  • Seismic design codes are developed mainly based on the observation of the behavior of structures in the high seismicity regions where structures may experience significant amount of inelastic deformations and major earthquakes may result in structural damages in a vast area. Therefore, seismic loads are reduced in current design codes for building structures using response modification factors which depend on the ductility capacity and overstrength of a structural system. However, structures in low seismicity regions, subjected to a minor earthquake, will behave almost elastically because of the larger overstrength of structures in low seismicity regions such as Korea. Structures in low seismicity regions may have longer periods since they are designed to smaller seismic loads and main target of design will be minor or moderate earthquakes occurring nearby. Ground accelerations recorded at stations near the epicenter may have somewhat different response spectra from those of distant station records. Therefore, it is necessary to verify if the seismic design methods based on high seismicity would he applicable to low seismicity regions. In this study, the adequacy of design spectra, period estimation and response modification factors are discussed for the seismic design in low seismicity regions. The response modification factors are verified based on the ductility and overstrength of building structures estimated from the farce-displacement relationship. For the same response modification factor, the ductility demand in low seismicity regions may be smaller than that of high seismicity regions because the overstrength of structures may be larger in low seismicity regions. The ductility demands in example structures designed to UBC97 for high, moderate and low seismicity regions were compared. Demands of plastic rotation in connections were much lower in low seismicity regions compared to those of high seismicity regions when the structures are designed with the same response modification factor. Therefore, in low seismicity regions, it would be not required to use connection details with large ductility capacity even for structures designed with a large response modification factor.