• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.369-374
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• 2007

For a stability design of steel frames, AISC-LRFD specification recommend to use Alignment Chart and story-based methods in order to determine an effective budding length. Recently, elastic buckling analysis, which is the method that calculate the effective length of members using eigenvalue of the overall structure, has been widely used in practical design of steel frames because this method can be performed effectively and automatically by computers. However, it can in some cases lead to unexpectedly large effective length in column having small axial forces. Therefore, this paper propose a method using elastic buckling analysis, which estimate a proper effective buckling length for all members having a small axial force. For verification of proposed method, it is compared with system based approach and stiffness distribution factor method. As a result, proposed method can rationally solve a problem in some case of column having small axial force. Also, adoption range for proposed method is established.

• Structural Engineering and Mechanics
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• 제85권6호
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• pp.825-835
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• 2023

The effective buckling length factor is an important parameter in the elastic buckling analysis of steel structures. The present article aims at developing a new method that allows the determination of the buckling factor values for frames. The novelty of the method is that it considers the interaction between the bracing and the elastic supports for asymmetrical frames in particular. The approach consists in isolating a critical column within the frame and evaluating the rotational and translational stiffness of its restraints to obtain the critical buckling load. This can be achieved by introducing, through a dimensionless parameter 𝜙_i, the effects of coupling between the axial loading and bending stiffness of the columns, on the classical stability functions. Subsequently, comparative, and parametric studies conducted on several frames are presented for assessing the influence of geometry, loading, bracing, and support conditions of the frame columns on the value of the effective buckling length factor K. The results show that the formulas recommended by different approaches can give rather inaccurate values of K, especially in the case of asymmetric frames. The expressions used refer solely to local stiffness distributions, and not to the overall behavior of the structure.

• 한국공간구조학회논문집
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• 제13권1호
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• pp.87-96
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• 2013

This study investigated characteristics of buckling load and effective buckling length by member rigidity of dome-typed space frame which was sensitive to initial conditions. A critical point and a buckling load were computed by analyzing the eigenvalues and determinants of the tangential stiffness matrix. The hexagonal pyramid model and star dome were selected for the case study in order to examine the nodal buckling and member buckling in accordance with member rigidity. From the numerical results, an effective buckling length factor of adopted models was bigger than that of Euler buckling for the case of fixed boundary. These numerical models indicated that the influence of nodal buckling was greater than that of member buckling as member rigidity was higher. Besides, there was a tendency that the bifurcation appeared on the equilibrium path before limit point in the member buckling model.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.293-296
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• 2007

This study investigated the out-of-plane elastic buckling load and effective length factor of X-bracing system. The members of X-bracing system which are studied in this paper are rigidly attached to the structure at their end connections, and are pinned or rigidly connected at their point of intersection. The effective length factors are derived for the general case where the tension and compression brace have different material and geometrical properties.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.605-638
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• 2015

It is intended to perform buckling analysis of steel gabled frames with tapered members and flexible connections. The method is based on the exact solutions of the governing differential equations for stability of a gabled frame with I-section elements. Corresponding buckling load and subsequently effective length factor are obtained for practical use. For several popular frames, the influences of the shape factor, taper ratio, span ratio, flexibility of connections and elastic rotational and translational restraints on the critical load, and corresponding equivalent effective length coefficient are studied. Some of the outcomes are compared against available solutions, demonstrating the accuracy, efficiency and capabilities of the presented approach.

• 한국강구조학회 논문집
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• 제15권2호
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• pp.159-165
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• 2003

단부에 관통 가셋트판이 부착된 강관부재의 좌굴거동은 단부의 형상 및 상태에 따라 구속정도가 상이하게되며 단부요소는 세 장비에 따라 탄성 및 비탄성 거동 특성을 보임에 따라 이론적 좌굴내력을 도출하는 것은 사실상 불가능하다. 본 연구에서는 탄성좌굴의 이론적 접근을 바탕으로 세장비($\lambda$), 강성비($\beta$), 지지길이비(G), 강관크기, 부재의 초기변형 등을 고려하여 비탄성 유한요소 해석을 수행하여 각각의 영향요소가 좌굴하중에 미치는 영향을 살펴보았다. 또한 유한요소 모델링시 세장비($\lambda$), 강성비($\beta$), 지지길이비(G), 강관크기 등의 매개변수 분석을 통하여 강도식을 도출하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.185-192
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• 2004

The goal of this paper is to determine the accurate effective length factor(K factor) for buckling design of plane frames and to point out the practical limitations of the alignment chart which provides the approximate effective length factor. At present, the most general method to obtain K factors is to use the alignment chart which is given in the form of nomograph in LRFD-AISC specification commentaries. However it should be realized that various simplifications and assumptions were used in obtaining the alignment chart. Therefore, a simple but effective method to obtain accurate K-factors through the stability analysis of plane frames is developed in this study. To demonstrate the accuracy and effectiveness of the present scheme, K-factors by system buckling analysis of frames are calculated and compared with those calculated by the alignment chart.

• 한국강구조학회 논문집
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• 제19권1호
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• pp.129-137
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• 2007

본 연구에서는 X-브레이싱 접합부의 경계조건에 따른 탄성 면외 좌굴하중 및 유효 좌굴길이 계수에 관한 연구를 수행하였다. X-브레이싱의 접합부는 연결방법에 따라 강접합 혹은 단순 연결로 가정할 수 있으며, 이러한 접합부의 경계 조건은 X-브레이싱의 좌굴하중에 영향을 미친다. 본 연구에서는 접합부의 경계 조건에 따른 X-브레이싱의 면외 유효 좌굴길이 계수들을 유도 하였으며, 면외 유효 좌굴계수들은 압축부재와 인장부재의 길이비 $L_P$/$L_T$, 인장력과 압축력의 비 T/P, 및 인장부재와 압축부재의 Euler 좌굴하중의 비 $P_{ET}$/$P_{EP}$의 함수로 나타났다. 이러한 연구결과는 기존 연구자들 및 유한요소해석결과와 비교 분석하여 그 타당성과 적용성을 검증하였다. 마지막으로 유도된 면외 유효 좌굴길이 계수들을 비교하여 접합부의 경계 조건이 X-브레이싱의 면외 좌굴하중에 미치는 영향을 분석하였다.

• 한국안전학회지
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• 제16권1호
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• pp.59-64
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• 2001

Even though there is a guideline for the required strength of pipe support in inspection, it does not mean the nominal strength which can be used for the form work design. And, Concrete Specification defines that the pipe support should be designed according to the steel design guidelines but the design details are not provided, such as buckling length and the sectional modulus, etc. For the better prediction of strength of pipe support, the slenderness ratio of support which reflects the boundary condition should be considered. In this paper, the elastic buckling formula based on the slenderness is derived. The formula contains the strength reduction factor that consider the strength deduction caused by initial lateral deformation and is 0.65 consistently regardless of boundary conditions. And the coefficient of effective buckling length is calculated from the experiment.

• Steel and Composite Structures
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• 제5권2_3호
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• pp.181-192
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• 2005

The effective length method for flexural (column) buckling has been used for many decades but its use is somewhat limited in various contemporary design codes to moderately slender structures with elastic critical load factor (${\lambda}_{cr}$) less than 3 to 5. In pace with the use of higher grade steel in recent years, the influence of buckling in axial buckling resistance of a column becomes more important and the over-simplified assumption of effective length factor can lead to an unsafe, an uneconomical or a both unsafe and uneconomical solution when some members are over-designed while key elements are under-designed. Effective length should not normally be taken as the distance between nodes multiplied by an arbitrary factor like 0.85, 1.0, 2.0 etc. Further, the classification of non-sway and sway-sensitive frames makes the conventional design procedure tedious to use and, more importantly, limited to simple regular frames. This paper describes the practical use of second-order analysis with section capacity check allowing for $P-{\delta}$ and $P-{\Delta}$ effects together with member and system imperfections. Most commercial software considers only the $P-{\Delta}$ effect, but not member and frame imperfections nor $P-{\delta}$ effect, and engineers must be very careful in their uses. A verification problem is also given for validation of software for this type of powerful second-order analysis and design. It is a trend for popular and advanced national design codes in using the second-order analysis as a norm for analysis and design of steel structures while linear analysis may only be used in very simple structures.