년 - 년
축회전 다이아그리드 구조시스템의 내진성능평가에 관한 연구 KCI 등재
대한건축학회지회연합회 대한건축학회연합논문집 제17권 제1호 통권 65호 2015.02 pp.187-194
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4,000원
최근 초고층 구조물은 단순 생활공간이 아닌 도시의 랜드마크적인 기능을 할수 있도록 점차 그 형태가 다양해지고 있다. 다이아그리드 구조시스템은 외부에 위치하는 반복된 삼각 트러스 형태로서 수평하중 및 수직하중에 저항하는 시스템이고, 외부기둥을 제거하여 비정형 형상을 자유롭게 표현할수 있다. 최근에 다이아그리드 구조시스템에 대한 연구는 활발하게 진행 중이지만, 비정형 형태인 다이아그리드 구조시스템에 대한 연구는 상대적으로 설계경험이나 연구가 미흡하다. 따라서 본 연구는 비정형 구조물 형태중 twisted(뒤틀림)을 적용하여 축회전 다이아그리드 구조시스템의 내진성능평가에 관한 연구를 하였다. 선형시간이력해석과 비선형정적해석을 수행하여 층간변위와 최대밑면전단력 통해 가새각도와 구조시스템 평면의 회전각도 변화에 따른 다이아그리드 구조시스템의 내진성능평가에 관한 연구를 하였다.
Since the high-rise structures have been played a role the city's Landmarks, the form of high-rise structures are becoming diverse. Diagrid structural system resists horizontal loads and vertical loads as a repeated triangular truss type along the entire exterior perimeter surfaces of the building. Due to eliminate vertical columns in exterior. This system can express complex shape buildings. Recently, diagrid structural system has been studied actively in many field. But study of atypical diagrid structural system, and experience of the design is relatively lack. Therefore, In this study the seismic performance of axial rotation-diagrid structure system was evaluated by applying the one twist in the form of atypical structures. Seismic performance of diagrid structural system was evaluated by change of the rotation angle of structural system plane and angle of external braces throught story drift and maximum base shear performed nonlinear static and linear time history analysis
일방향 정적해석을 통한 필로티형 RC 건물의 지진거동 연구 KCI 등재
대한건축학회지회연합회 대한건축학회연합논문집 제15권 제5호 통권 57호 2013.10 pp.181-188
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4,000원
필로티형 건물의 지진거동을 파악하기 위해 OpenSees프로그램을 이용하여 하부 2개층이 보-기둥 골조로 이루어진 세가지 유형의 필로티형 RC건물에 대한 비선형 정적해석을 수행하였다. 세가지 유형의 건물의 층수는 각각 하부 2개층을 포함하여 5층, 16층, 30층 건물을 선정하였는데,이들 모델은 최근 한국에서 많이 건설되고 있는 공동주택의 대표적인 유형들이다. 5층, 16층, 30층모델의 초과강도는 각각 4.84, 5.60, 12.35로서 KBC 2009에서 제시하는 시스템초과강도계수 3.0을 초과하였다. 또한 상부구조의 과도한 전도거동으로 인해 하부골조에 큰 축력이 변화와 압축력이 발생하였으며, 이는 하부골조기둥의 연성을 저하시키는 요인이 되기도 하였다. 따라서, 설계시 하부기둥에 작용하는 축력에 대한 기둥단면적의 크기의 비율을 어느정도 제한함으로써 하부골조 기둥의 연성을 극대화하는 조치가 필요한 것으로 나타났다.
Three types of piloti-type RC buildings having irregularity in lower two stories were selected and were performed nonlinear static analysis by using OpenSees to analyze the seismic behaviors of piloti-type buildings. The number of stories of three models are 5 stories, 16 stories, and 30 stories. including two stories beam-column frame in lower part of buildings. These models represent structural system of apartment buildings constructed widely in Korea. Overstrength of 5 stories model, 16 stories model and 30 stories model are 4.84, 5.60, and 12.35, respectively, which are larger than 3.0, which is an overstrength factor guided in KBC2009. Overturning behavior of upper part induce to excessive change of axial forces in column, and large compressive forces in columns lead to the reduction of the ductility. Therefore, the ratio of axial capacity and axial force in column has to be limited to provide sufficient ductilities in columns.
Nonlinear Static Analysis of Cable Roof Structures with Unified Kinematic Description
[Kisti 연계] 대한건축학회 Architectural research Vol.18 No.1 2016 pp.39-47
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A finite element analysis technology applicable to the prediction of the static nonlinear response of cable roof structure is presented. The unified kinematic description is employed to formulate the present cable element and different strain definitions such as Green-Lagrange strain, Biot strain and Hencky strain can be adopted. The Newton-Raphson method is used to trace the nonlinear load-displacement path. In the iteration process, the compressive stress of a cable element is not allowed. For the verification of the present cable element, four numerical examples are tackled. Finally, numerical results obtained by using the present cable element are provided as new benchmark test results for cable structures under static loads.
Influences of Column Orientations and Story Levels of the RC Frames under Nonlinear Static Analysis
[Kisti 연계] 대한건축학회 Architectural research Vol.26 No.4 2024 pp.127-138
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Earthquakes present significant challenges to buildings contemporary, and the response of RC frame structures to seismic activity is influ-enced by various characteristics, including column section designs and orientation. The specific designs of column sections directly impact the lateral stiffness of the entire structure. Considering the weak story in an RC frame structure and making changes to column orientations can lead to structural issues in both vertical and lateral stiffness, resulting in weaknesses in the structural plan that increase vulnerability to seismic forces. Therefore, the most crucial aspect of seismic design is creating an efficient structural system that satisfies all seismic per-formance objectives, including considerations for IO (immediate occupancy), LS (life safety), and CP (collapse prevention) under plastic hinge analysis. In evaluating the seismic performance of buildings, nonlinear static pushover analysis has become increasingly prevalent over the past decades. This research concludes that columns with different orientations and stories exhibit different performance attributes when subjected to nonlinear static analysis using both SAP 2000 and ABAQUS. Regarding the structural influences due to different stories, this research summarizes variations in structural performance observed across columns with various orientations and heights, ranging from the first floor to the fifth floor. These findings are expected to provide valuable insights for future analyses examining the performance of column orientations as well as serve as a valuable reference for new construction of RC structures or reinforcement of existing RC structures against seismic activities.
지반특성을 고려한 벨트 트러스 구조물의 비선형 정적해석
대한건축학회지회연합회 대한건축학회지회연합회 학술발표대회논문집 2007년도 추계학술발표대회 2007.12 pp.414-417
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4,000원
The resistance system to the lateral force has developed with high-rise buildings. The tube structure is one of the most effective lateral resisting structure system that behaves like cantilever basically. Setting up belt truss in maximum drift ratio story, seismic performance is better. This study adopts response spectrum analysis and pushover analysis to evaluate the seismic performance of the belt truss structures. To analyze the effect between belt truss structures and soil types, this study performed capacity spectrum method(CSM) under the seismic load. A intersection point of capacity curve and demand curve is performance point. In this paper, after searching for performance point according to return period, performance level is evaluated.
등가단자유도 방법의 영향을 고려한 다경간 교량의 내진성능 평가를 위한 비탄성 정적해석
[Kisti 연계] 대한토목학회 대한토목학회논문집 A Vol.26 No.a3 2006 pp.473-484
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역량스펙트럼 방법은 비선형 거동을 하는 구조물의 최대 변위응답을 간편하게 산정하는데 사용된다. 역량스펙트럼 방법을 사용하여 다경간 교량의 내진성능을 평가하기 위해서는 구조계를 대표하는 하나의 응답을 등가단자유도계 방법을 이용하여 다자유도 응답들로부터 유도하여야 한다. 등가단자유도 방법은 비탄성 정적해석에 의해 산정된 힘-변위 곡선들로부터 역량곡선을 계산하는데 사용된다. 역량스펙트럼 방법에 사용되는 등가단자유도 방법의 정확성을 평가하기 위하여, 몇 개의 등가단 자유도방법과 결합된 역량스펙트럼 방법에 의해 산정된 최대변위응답을 설계지진스펙트럼에 대응되는 인공지진을 사용한 비탄성 시간이력해석의 변위응답과 비교하였다.
The capacity spectrum method (CSM) can be used to simply estimate the maximum displacement response of the nonlinear structures. To evaluate seismic performance of multi-span bridges using the CSM, the representative response for structural system should be derived from the multi-degree-of-freedom (MDOF) responses by using the equivalent single-degree-of-freedom (ESDOF) method. The ESDOF method is used to calculate the capacity curve of the structural system from the pushover curves of all piers or structural members estimated by the pushover analysis. In order to evaluate an accuracy of ESDOF methods used in the CSM, the maximum displacements estimated by the CSM incorporating the several ESDOF methods are compared to those by the inelastic time-history analysis for several artificial earthquakes corresponding to the design spectrum.
해저(海底)파이프라인의 정적(靜的) 비선형(非線形) 해석(解析)
[Kisti 연계] 대한토목학회 대한토목학회논문집 Vol.10 No.1 1990 pp.57-69
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본(本) 연구(硏究)에서는 기하학적(幾何學的) 비선형성(非線形性)을 고려(考慮)하여 해저(海底)파이프라인을 설치(設置)하는 동안의 정적(靜的) 해석방법(解析方法)을 제시(提示)하였다. 해석(解析)방법(方法)으로는 유한요소법(有限要所法)을 사용(使用)하였으며, 기본방정식(基本方程式)은 최소위치(最少位置)에너지의 원리(原理)를 사용(使用)하여 유도(誘導)하였다. 평형방정식(平衡方程式)의 해(解)는 modified Newton-Raphson방법(方法)을 사용(使用)하여 구(求)하였다. 파이프라인요소(要素)의 유한변위(有限變位) 및 회전(回轉)과 축방향력(軸方向力)의 영향(影響)이 고려(考慮)되었고 경계조건(境界條件)은 스프링요소(要素)를 사용(使用)하여 모델화(化)하였다. 해석(解析) 적용례(適用例)에서는 다이아몬드형(形) 프레임, 곡선(曲線)외팔보와 해저(海底)파이프라인을 설치(設置)하는 동안의 정적(靜的) 해석례(解析例)를 다루었으며 다른 방법(方法)에 의(依)한 해석결과(解析結果)와 비교(比較)하여 본(本) 연구(硏究)의 정당성(正當性)을 입증(立證)하였다.
The static nonlinear analysis of offshore pipeline is carried out by the finite element method. The governing equilibrium equation are derived by the principle of minimum potential energy and the modified Newton-Raphson procedure is used to solve the system of nonlinear algebraic equation. Geometrically nonlinear beam elements and spring elements are utilized to model the pipeline, stinger, pipe supports and seabed simultaneously. The beam element developed can be used to model redundant structures. It provides for both the torsional deformation and elongation of pipeline, and permits the use of different physical properties in each principal direction. The validity of this method is investigated by comparing the results with these obtained by other methods.
Nonlinear static analysis of smart beams under transverse loads and thermal-electrical environments
[Kisti 연계] 테크노프레스 Advances in computational design Vol.7 No.2 2022 pp.99-112
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This research has been devoted to examine nonlinear static bending analysis of smart beams with nano dimension exposed to thermal environment. The beam elastic properties are corresponding to piezo-magnetic material of different compositions. The large deflection analysis of the beam has been performed assuming that the beam is exposed to transverse uniform pressure. Based on the rule of Hamilton, the governing equations have been derived for a nonlocal thin beam and solved using differential quadrature method. Temperature variation effect on nonlinear deflection of the smart beams has been studied. Also, the beam deflection is shown to be affected by electric voltage, magnetic intensity and material composition.
Nonlinear static analysis of functionally graded porous beams under thermal effect
[Kisti 연계] 테크노프레스 Coupled systems mechanics Vol.6 No.4 2017 pp.399-415
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This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.
[Kisti 연계] 테크노프레스 Advances in nano research Vol.16 No.5 2024 pp.509-519
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In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.
[Kisti 연계] 테크노프레스 Structural engineering and mechanics : An international journal Vol.59 No.3 2016 pp.431-454
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In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.
[Kisti 연계] 한국지진공학회 한국지진공학회 학술대회논문집 2006 pp.225-232
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Three building structures haying piloti frames in the lower two stories were selected as prototypes and were analyzed using nonlinear static analysis to investigate the seismic capacity of these buildings. The first one has a symmetrical moment resisting frame (Model 1), the second has an infilled shear wall in the central frame (Model 2), and the third has an infilled shear wall only in one of exterior frames (Model 3), The analytical results were compared with those of shaking table tests with regards to the overstrength and ductility of the irregular buildings. Infilled shear wall in Model 2 and Model 3 induced large overstrength factors, 6.8 and 6.0, respectively, which are about two times larger than that of Model 1, 3.5. The displacement ductility ratio in Model 2 was only 2.5, due to the shear failure of wall in the piloti stories, whereas those of Model 1 and Model 3 reached 3.2.
[Kisti 연계] 한국전산구조공학회 전산구조공학 Vol.27 No.2 2014 pp.15-19
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[Kisti 연계] 한국전산구조공학회 한국전산구조공학회 학술대회논문집 2000 pp.257-264
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Nonlinear dynamic time history analysis of a structure with energy dissipation devices is complicated and time consuming. In this regard the nonlinear static analysis is a practical alternative for evaluating the earthquake resisting capacity of a structure. In this study the nonlinear static response of a structure was obtained first, and the equivalent viscous modal damping ratio required to satisfy the performance objective was computed in the capacity spectrum format. Then proper amount of viscous dampers were installed to provide the required damping. Parametric study has been performed for the period of the structure, yield strength, and the stiffness after the first yield. According to the earthquake time history analysis results, the maximum displacement of the model structure with viscous dampers designed in accordance with the proposed method corresponds well with the target displacements that was used in the beginning of the design process.
[Kisti 연계] 한국지진공학회 한국지진공학회논문집 Vol.30 No.1 2026 pp.29-37
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To ensure structural safety, seismic performance must be evaluated under ground motions applied in the principal direction that produces the maximum seismic response. However, in irregular buildings, additional torsional behavior may cause this principal direction to deviate from the analysis axes. Determining the principal direction requires identifying the orientation that yields the maximum base shear among all possible directions, which makes the procedure highly cumbersome. In practice, the 100:30 combination rule specified in current seismic design provisions is commonly used to evaluate seismic responses while conservatively accounting for multi-directional excitation effects. This study examines the validity of this rule for irregular buildings. After identifying the principal direction of the irregular building, nonlinear static analyses were performed by applying seismic loads along either the principal direction or the analysis axes. The analysis results showed that the 100:30 combination rule produced non-conservative outcomes even for regular buildings, and this tendency became more pronounced in irregular buildings due to torsional effects. To address this issue, the 100:40 combination rule was also examined; however, no significant improvement was observed. In addition, this study proposed a simplified mode-shape-based method for identifying the principal direction, which yielded results comparable to those obtained with the more rigorous base-shear-based approach.
전단벽 모형화 방법에 따른 구조해석 신뢰성에 대한 고찰
[Kisti 연계] 한국산학기술학회 한국산학기술학회논문지 Vol.18 No.3 2017 pp.718-723
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구조설계 실무 현장에서의 구조해석 모델링 방법을 조사해 보면, 대부분의 경우, 삼차원 구조해석을 위해 슬래브를 판요소를 이용한 메쉬의 형태로 모형화 하고, 전단벽을 쉘요소 또는 벽요소를 사용하여 모형화 하고 있다. 여기서 주목할 점은 해석모형 작성의 편의성을 위하여 전단벽을 층과 층 및 기둥선과 기둥선 사이에 존재하는 한 개의 요소로 모형화 한다는 것이다. 이와 같은 모형화 방법은 사용되는 컴퓨터 프로그램에 따라 해석 오류를 발생시킬 수 있으며, 이러한 오류는 해석 결과의 신뢰성을 저하시키게 된다. 따라서 구조해석의 신뢰성을 확보하기 위해서는 이러한 오류가 발생하는 원인을 조사하고 합리적인 모형화 방법을 찾기 위한 연구가 필요하다. 원인 분석을 위한 비교 대상 해석 프로그램은 MIDAS와 SAP2000 및 neoMAX등과 같은 상용프로그램과 요소의 강성을 추측하기 위해 연구용인 sNs를 사용하였다. 본 연구에서는, 구조해석 실무현장에서 사용하고 있는 전단벽 모형화 방법에 따른 해석오류의 원인들을 분석해 보고자 한다. 또한 이러한 분석 결과를 바탕으로 전단벽 모형화를 위한 몇 가지 고려사항들을 제시하고자 한다.
When structural analysis modelling methods of practical fields are investigated, a slab is generally modeled by a finite element mesh using plate elements and a shear wall is modeled using a shell element or wall element for 3-D structural analysis. The point worthy of notice in this practice is that a shear wall is modelled using only one wall or shell element divided by floors and column lines to produce structural models. The modeling method like this can cause analysis errors according to the type of computer programs in use, and these errors reduce the reliability of the analysis results. Therefore, to secure the reliability of structural analysis, studies of the causes of errors and finding reasonable modeling methods are necessary. In this study, the causes of analysis errors according to the modelling methods of a shear wall, which are used in practical fields, were investigated and some considering matters for modelling a shear wall are presented to reduce the analysis errors on these analysis results.
이선형 재료모델의 비선형 정적해석을 위한 강성추정 알고리즘 개발
[Kisti 연계] 한국산학기술학회 한국산학기술학회논문지 Vol.17 No.2 2016 pp.620-626
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구조물의 비선형 지진응답을 평가하는 것은 내진공학에 있어서 중요한 요소로 인식되고 있다. 비선형 정적해석은 이를 위한 대표적인 방법론의 하나이며, 특정 해석단계에서의 구조물 강성추정을 위한 다양한 수치해석적 방법론들이 제시, 적용되고 있다. 하지만, 이러한 방법론들은 상당한 해석시간을 요하거나 부정확한 간편법에 그치고 있어 실무적용에 많은 어려움이 존재한다. 이러한 이유로 본 연구에서는 비선형 정적해석 시 정확하고 효과적인 구조물 강성추정 방법론을 제시하고자 한다. 이를 위하여, 기존의 단계해석법에 대한 이론적 연구를 수행하였으며, 이를 바탕으로 이선형 재료모델 특성을 가진 구조물의 강성구성 알고리즘을 제시하였다. 최종적으로, 제시된 알고리즘을 적용한 컴퓨터 프로그램 sNs를 개발하였다.
Estimating the nonlinear seismic response of structure in earthquake engineering is important. Nonlinear static analysis is a typical method, and a variety of methods and techniques for estimating the stiffness of structural system at a certain analysis stage have been introduced and used in numerical structural analysis. On the other hand, such methods have many difficulties in practical usage because they use time-consuming iterative methods or simplified algorithms for calculating the structural stiffness at specific points in the time of nonlinear static analysis. For this reason, this study suggests an accurate and effective method for estimating the stiffness of a structure in nonlinear static analysis. For this goal, existing theories of an incremental step-by-step solution was investigated first. Subsequently, an algorithm available for calculating the precise stiffness of a structural system, each element of which has a bilinear material model, was developed based on the investigated methods. Finally, a computer program, sNs, was developed with the algorithm used.
[Kisti 연계] 한국콘크리트학회 한국콘크리트학회 학술대회논문집 2000 pp.63-68
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Concrete is popular as a building material, however it is inherently brittle and performs poorly during earthquakes if nor reinforced properly. Traditional retrofit design techniques assume that buildings respond elastically to earthquakes. This assumption simplifies the analysis procedure but can lead to an erroneous conclusion. The complete nonlinear time history analysis is considered overly complex and impractical for general use. Simplified nonlinear analysis methods, referred to as nonlinear static analysis procedures, include the capacity spectrum method(CSM) developed in detail at ATC-40 and the displacement coefficient method(DCM) utilized at FEMA-273. In this study wall APT system. The results were compared and analyzed. The program used was neaMAX-3D to express nonlinear material.
비선형 정적해석을 이용한 철근 콘크리트 구조물 성능평가기법
[Kisti 연계] 한국콘크리트학회 한국콘크리트학회 학술대회논문집 2006 pp.373-376
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There are representative two performance evaluation methods for performance-based design(PBD) of reinforced concrete structures by the nonlinear static analysis, one method includes the capacity spectrum method(CSM) suggested in ATC-40(996) and the other is the displacement coefficient method(DCM) in FEMA-273(1997). The objective of this paper is to compare and verify two methods and suggest the displacement-based design for new performance evaluation of reinforced concrete structures.
비선형 정적해석을 이용한 필로티형 저층 RC 집합주택의 내진성능평가
[Kisti 연계] 한국콘크리트학회 한국콘크리트학회 학술대회논문집 2008 pp.237-240
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1층에 필로티를 가지는 저층 RC 집합주택의 표준대상구조물을 선정하여 비선형 정적해석에 의해 우리나라 내진 기준에 정하는 최대 지진과 설계 지진에 대하여 내진성능을 평가하는 것이 본 연구의 목적이다. 이를 위하여 FEMA356 (혹은 ASCE/SEI-41) 보고서에 의해 목표 변위를 산정한 후 이 목표 변위에 대한 주요 부재(기둥, 벽체)의 상태를 검토하였다. 이 결과 (1) 기둥은 생명안전수준(LS)과 붕괴 방지 수준(CP)의 요구 조건을 전부 만족하고 있지만 (2) 벽체의 경우 단변 방향은 LS는 만족하였지만, CP는 만족하지 못하였고, 장변 방향의 경우 LS와 CP 공히 만족하지 못하는 것으로 나타났다.
The objective of this study is to evaluate the seismic performance of the low-rise RC apartment buildings having piloties at ground level by using nonlinear static analysis with regards to the maximum considered and design earthquakes in Korea. To do this, the target displacement at roof was estimated according to FEMA356 (or ASCE/SEI-41), and the deformations of the critical members were compared with the failure criteria of Life Safety(LS) and Collapse Prevention(CP) given in FEMA356. The conclusions are as follows: (1) columns satisfy criteria of LS and CP, but (2) the shear wall in the longitudinal direction failed to satisfy those of both LS and CP while those in the transverse direction satisfy that of LS, but failed that of CP.
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