Story Drift Demands Research Articles

An equivalent SDOF system model for estimating the response of R/C building structures with proportional hysteretic dampers subjected to earthquake motions

AbstractFor the purpose of estimating the earthquake response, particularly the story drift demand, of reinforced concrete (R/C) buildings with proportional hysteretic dampers, an equivalent single‐degree‐of‐freedom (SDOF) system model is proposed. Especially in the inelastic range, the hysteretic behavior of an R/C main frame strongly differs from that of hysteretic dampers due to strength and stiffness degradation in R/C members. Thus, the proposed model, unlike commonly used single‐spring SDOF system models, differentiates the restoring force characteristics of R/C main frame and hysteretic dampers to explicitly take into account the hysteretic behavior of dampers. To confirm the validity of the proposed model, earthquake responses of a series of frame models and their corresponding equivalent SDOF system models were compared. 5‐ and 10‐story frame models were studied as representative of low‐ and mid‐rise building structures, and different mechanical properties of dampers—yield strength and yield deformation—were included to observe their influence on the effectiveness of the proposed model. The results of the analyses demonstrated a good correspondence between estimated story drift demands using the proposed SDOF system model and those of frame models. Moreover, the proposed model: (i) led to better estimates than those given by a single‐spring SDOF system model, (ii) was capable of estimating the input energy demand and (iii) was capable of estimating the total hysteretic energy and the participation of dampers into the total hysteretic energy dissipation, in most cases. Results, therefore, suggest that the proposed model can be useful in structural design practice. Copyright © 2010 John Wiley & Sons, Ltd.

모멘트골조의 내진설계를 위한 부재 소성변형 요구량 예측

안전한 내진설계를 위해서는 각 부재에 요구되는 소성변형 요구량을 정확히 예측하여야 한다. 본 연구에서는 등가정적내진설계에 쉽게 활용할 수 있도록, 복잡한 비선형해석 없이 탄성해석을 사용하여 모멘트골조 부재의 소성변형을 평가하는 방법을 개발하였다. 각 부재의 소성변형은 부재 강성과 탄성해석 결과로부터 직접 결정되는 층간변위비 요구량 및 모멘트 재분배 등의 설계 변수로부터 결정된다. 제안된 방법을 8층 2경간의 모멘트골조에 적용하고, 비선형해석을 통하여 제안된 방법의 정확성을 검증하였다. 검증결과, 제안된 방법은 비선형거동에 의한 층간변위비 요구량과 각 부재의 소성변형 요구량을 정확히 평가하였다. 제안된 방법은 부재연성설계와 같은 신축건물의 내진설계에 활용할 수 있을 뿐만 아니라 기존건물의 내진성능평가에도 활용될 수 있을 것으로 기대된다. To secure the structural safety of structures and members against earthquakes, the plastic deformation capacity demand of members should be accurately predicted. In the present study, a method for the evaluation of the plastic deformations of members for moment frames was developed. To facilitate the practical use of the proposed method in equivalent seismic design, the plastic deformations of members were evaluated based on the results of elastic analysis, without using nonlinear analysis. The plastic deformation demands of members were formulated as functions of story drift demand, redistributed moment and member stiffness. Story drift demand and moment redistribution were directly determined from elastic analysis. The proposed method was applied to an 8 story-2 bay moment frame, and the predicted plastic deformations were verified using nonlinear analysis. The results showed that the proposed method could be used to accurately predict the member plastic rotations with simple calculations. The proposed method can be applied both to the earthquake design of new structures and to the performance evaluation of existing structures.

Investigation of Effects of Nonlinear Static Analysis Procedures to Performance Evaluation on Low-Rise RC Buildings

The aim of the study is to compare and evaluate structural response demands obtained from nonlinear static analysis procedures (NSPs) which are displacement coefficient method (DCM) recommended in FEMA 356 and capacity spectrum method (CSM) recommended in ATC 40. For these reasons, three of three-dimensional low-rise RC buildings with different characteristics are investigated. In order to determine nonlinear behavior of the buildings under lateral loads, the base shear-roof displacement relationships (capacity curves) are obtained by pushover analysis including P-delta effects. Then by considering four different seismic hazard levels, building performances are determined by using the CSM and by using from DCM results determined in a previous study. In order to determine performance levels of the buildings, maximum beam and column plastic rotation demands and maximum story drift demands are determined in the related maximum displacement demands. Plastic strains in the equivalent diagonal struts, representing the nonstructural infill walls, are also determined, similarly. Comparing structural response quantities (such as plastic rotations, story drifts, etc.) obtained from the NSPs for considered low-rise RC buildings, effects of different NSPs in performance evaluations of the buildings are investigated comparatively, as well.

Improved probabilistic quantification of drift demands for seismic evaluation

This study deals with the evaluation and formulation of methods to improve the probabilistic quantification of maximum story drift demands for structural systems exposed to severe ground motions. The focus is on flexible structures that are prone to dynamic instability. The quantification of drift demands is based on the probability distribution of the maximum story drift over the height, for a given ground motion hazard level, which in this study is represented by the spectral acceleration at the first mode period of the building. Improvements in the probabilistic estimation of maximum story drift demands are illustrated with a nine-story, moment-resisting frame building exposed to a set of 40 ground motions. It is concluded that (1) the three-parameter LN distribution more rationally describes maximum story drifts at higher values of spectral acceleration; (2) statistically adding values to replace truncated data points provides better goodness-of-fit in maximum drift demand prediction when the structure is close to the onset of dynamic instability, and (3) the least-squares fitting of the LN distribution yields parameters that provide an improved fit compared to that from maximum likelihood estimation and the method of moments.

Seismic behavior of asymmetric RC wall buildings: principles and new deformation-based design method

The seismic design of multi-story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non-linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story-drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story-drift (performance goals) are discussed. The definition of an eccentricity of the earthquake-equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake-equivalent lateral force. A new deformation-based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story-drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi-story asymmetric RC wall building. Copyright © 2005 John Wiley & Sons, Ltd.

Relating the Seismic Drift Demands of SMRFs to Element Deformation Demands

A procedure is outlined and evaluated for estimation of beam and panel zone deformation demands for given estimates of story drift demands for regular steel moment resisting frame (SMRF) structures. The total story drift demand is related to the story plastic drift demand by estimating the story yield drift based on the weakest element at the connection. The story plastic drift demand is related to the panel zone and beam plastic deformation demands by a function based on story geometry and member properties. The procedure is verified for a series of code compliant SMRFs. It complements a process presented in the literature that permits the estimation of seismic drift demand for frame structures from the spectral displacement demand at the first mode period of the structure. The combined process should prove useful in conceptual design, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behavior of steel frame structures.

Spectral story drift demand analysis for building structures during the 1999 Chi‐Chi Taiwan earthquake

The 921 Chi‐Chi earthquake caused a very significant number of building collapses and damage of various degrees. Many collapsed buildings had pedestrian corridors and open fronts on the ground floors. Using a modified modal participation factor and the generalized shape function computed from the nonlinear push over analysis, story drift demands imposed on soft first story building systems are studied in this paper. Generalized shape functions are constructed from the nonlinear static push over analysis of shear buildings having specific distributions of story stiffness and strength. Nonlinear response spectrum analyses were performed on the ground acceleration recorded from 51 sites located in the Taipei Basin and 62 sites in the Taichung Region. Analytical results indicate that soft first story buildings are likely to have story drift demands significantly greater than regular buildings of short fundamental period. Results of the nonlinear dynamic analysis of a 6‐story structure indicate that the maximum story drift demand can be satisfactorily predicted by the story spectral drift constructed from the generalized shape functions.

Effects of Connection Fractures on SMRF Seismic Drift Demands

A central portion of an extensive investigation into the effects of beam-column connection fractures on seismic interstory drift demands for steel moment-resisting frame (SMRF) structures is summarized. Nonlinear dynamic analyses are carried out for six SAC Phase II buildings modeled with brittle connections and subjected to the SAC ground motions at two probability levels. Story drift demand statistics for the model structures with brittle connections are compared with those for the model structures with ductile connections. An empirical analysis model for connection fracture is employed, with values for the parameters of the model calibrated by field and laboratory data. The sensitivities of story drift demands to variations in the fracture parameters are explored. In particular, the case when only bottom beam-flange-connections fracture is contrasted with the case of both top- and bottom-flange fractures. Whereas the effects of single-flange (e.g., bottom-flange) fractures alone on story drift demands ...

Estimation of seismic drift demands for frame structures

A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi-degree-of-freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P-delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.

Behavior of Ductile SMRFs at Various Seismic Hazard Levels

A summary is presented of a comprehensive study on the seismic behavior of ductile steel moment resisting frame (SMRF) structures with fully restrained connections. The study focuses on the seismic behavior of code compliant structures of different heights (3-, 9-, and 20-stories), located in regions of different seismicity (Los Angeles, Seattle, and Boston), and subjected to sets of ground motions representative of various hazard levels (return periods of 72, 475, and 2,475 years). Structural behavior characteristics are illustrated by means of inelastic static (pushover) analysis results. Dynamic performance characteristics are evaluated from story drift demand predictions obtained through nonlinear time history analysis. The sensitivity of the response to analytical modeling is appraised. The performance of the model structures is found to be in fair agreement with general expectations for conventional design events and more frequent earthquake events. For rare events larger than expected inelastic def...