• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.353-360
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• 2002

The objective of this study is to develop a technique that analyzes the global behavior of frame structures with local cracks. The technique is based on frame analysis and uses the stiffness matrix of cracked frame element. An algorithm proposed here analyzes a frame structure with local transverseedge cracks, considering the effects of crack length and location. Stress intensity factors are employed to calculate additional local compliance due to the cracks based on linear elastic fracture mechanics theory, and then this local compliance is utilized to derive the stiffness matrix of the cracked frame element. In order to verify the accuracy and reliability of the proposed approach, numerical results are compared with those of Finite Element Method for the cracked frame element, and the effects of single crack on the behavior of truss structure are also examined.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.826-831
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• 2005

In this paper the effect of moving mass on dynamic behavior of cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The crack is assumed to be in the first mode of fracture. As the depth of the crack is increased, the tip displacement of the cantilever beam is increased. When the crack depth is constant the frequency of a cracked beam is proportional to the spring stiffness.

• 한국소음진동공학회논문집
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• 제15권10호
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• pp.1195-1201
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• 2005

In this paper, the effect of a moving mass on dynamic behavior of the cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory The crack is assumed to be in the first mode of fracture. As the depth of crack is increased, the tip displacement of the cantilever beam is Increased. When the depth of crack is constant, the frequency of a cracked beam is proportional to the spring stiffness.

• 한국구조물진단유지관리공학회 논문집
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• 제20권5호
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• pp.93-101
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• 2016

본 연구에서는 비국지 탄성이론과 미분변환법을 이용하여 탄성매질속 다중 크랙을 가진 비균질 나노빔의 지배방정식을 유도하고, 유도된 지배방정식과 경계조건에 미분변환법을 적용하여 나노빔의 축방향의 진동해석을 하며, 나노빔의 첫단과 끝단의 경계조건이 각각 고정단(Clamped end)과 자유단(Free end)의 경우에 대하여 수치해석을 수행하였다. 수치해석 결과를 기존 연구결과와 비교하여 타당성을 입증한 후, 비국지 작은 척도효과 (Nonlocal small scale effect), 탄성매질의 강성, 크랙의 위치, 크랙의 강성 그리고 비국지 탄성이론의 나노빔에 대한 진동해석 결과를 고찰하였다.

• 콘크리트학회논문집
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• 제11권5호
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• pp.79-88
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• 1999

The purpose of this paper is to develop a mathematical expression for computing crack angles based on reinforcement volumes in the longitudinal and transverse directions, member end-fixity and length-to-width aspect ratio. For this a reinforced concrete beam-column element is assumed to possess a series of potential crack planes represented by a number of differential truss elements. Depending on the boundary condition, a constant angle truss or a variable angle truss is employed to model the cracked structural concrete member. The truss models are then analyzed using the virtual work method of analysis to relate forces and deformations. Rigorous and simplified solution schemes are presented. An equation to estimate the theoretical crack angle is derived by considering the energy minimization on the virtual work done over both the shear and flexural components the energy minimization on the virtual work done over both the shear and flexural components of truss models. The crack angle in this study is defined as the steepest one among fan-shaped angles measured from the longitudinal axis of the member to the diagonal crack. The theoretical crack angle predictions are validated against experimentally observed crack angle reported by previous researchers in the literature. Good agreement between theory and experiment is obtained.

• Structural Engineering and Mechanics
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• 제22권2호
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• pp.169-184
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• 2006

A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity $(e/h)_c$, from limit-point buckling to fracture failure, was proposed and the critical values of $(e/h)_c$ were numerically determined for various eccentricities, crack depths and slenderness.

• 한국전산구조공학회논문집
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• 제23권1호
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• pp.73-80
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• 2010

건축물의 풍진동은 건축물의 사용성평가에 중요한 구조설계 요인 중 하나이다. 신뢰성있는 풍하중 및 풍진동을 구하기 위해서는 정확한 고유주기의 예측이 필요하며 이러한 고유주기에 오차가 있을 경우 하중을 과대 또는 과소평가하게 되는 문제를 유발한다. 본 논문에서는 최근 본격적으로 증가하고 있는 초고층 무량판 구조시스템의 건축물에 대하여 계측을 통한 횡강성 산정식의 유효성을 검정하였다. 이를 위하여 최근 건설된 초고층 무량판 구조시스템이 적용된 3개의 건물에 대하여 계측 결과와 해석 모델의 고유주기를 비교 분석하였다. 이때, 무량판 구조물의 횡강성에 영향을 미치는 요인들에 대하여 각 케이스별로 해석을 수행하였으며, 특히 일반적으로 사용되고 있는 콘크리트의 할선탄성계수와 동탄성계수가 적용 되었을 때의 구조물의 고유주기 변화를 비교하였다. 그 결과 풍진동에 의한 건물의 변형률은 매우 적기 때문에 할선탄성계수의 적용보다는 동탄성계수의 적용이 보다 정확한 해석의 결과를 가져올 것으로 판단된다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1991년도 가을 학술발표회 논문집
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• pp.133-138
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• 1991

The aim of the present paper is to develop a computer program predicting ultimate fracture strength of initially cracked structure under monotonically increasing external loads. For this purpose, two kinds of 3-D isoparametric solid elements, one 6-node wedge element and another 8-node brick element are formulated along the small deformation theory. Plasticity in the element is checked using von Mises' yield criterion. Elasto-plastic stiffness matrix of the element is calculated taking account of strain hardening effect. If the principal strain at crack tip which is one nodal point exceeds the critical strain dependin on the material property, crack tip is supposed to be opened and the crack tip node which was previously constrained in the direction perpendicular to the crack line is released. After that, the crack lay be propagated to the adjacent node. Once a crack tip node is fractured, the energy of the newly fractured node should be released which is to be absorbed by the remaining part. The accumulated reaction force which was carried by the newly fractured node so far is then applied in the opposite direction. During the action of crack tip relief force, since unloading may be occured in the plastic element, unloading check should be made. If a plastic element unloads, elastic stress-strain equation is used in the calculation of the stiffness matrix of the element, while for a loading element, elasto-plastic stress-strain equation is continuously used. Verification of the computer program is made comparing with the experimental results for center cracked panel subjected to uniform tensile load. Also some factors affecting ultimate fracture strength of initially cracked plate are investigated. It is concluded that the computer program developed here gives an accurate solution and becomes useful tool for predicting ultimate fracture load of initially cracked structural system under monotonically increasing external loads.

• Computers and Concrete
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• 제12권1호
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• pp.19-36
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• 2013

In the finite element analysis of reinforced concrete structures, discrete representation of the steel reinforcing bars is considered advantageous over smeared representation because of the more realistic modelling of their bond-slip behaviour. However, there is up to now limited research on how to simulate the dowel action of discrete reinforcing bars, which is an important component of shear transfer in cracked concrete structures. Herein, a numerical model for the dowel action of discrete reinforcing bars is developed. It features derivation of the dowel stiffness based on the beam-on-elastic-foundation theory and direct assemblage of the dowel stiffness matrix into the stiffness matrices of adjoining concrete elements. The dowel action model is incorporated in a nonlinear finite element program based on secant stiffness formulation and application to deep beams tested by others demonstrates that the incorporation of dowel action can improve the accuracy of the finite element analysis.

• Structural Engineering and Mechanics
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• 제39권4호
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• pp.465-498
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• 2011

Concrete structures are generally cracked in flexural tension at working loads. Concrete beams with asymmetric section details and crack patterns exhibit different flexural rigidity depending upon the sense of the applied flexural moment. In this paper, three different models, having the same natural period, of such SDOF bilinear dynamical systems have been proposed. The Model-I and Model-II have constant damping coefficient, but the latter is characterized by two stiffness coefficients depending upon the sense of vibration amplitude. The Model-III, additionally, has two damping coefficients as well. In this paper, the dynamical response of Model-III to sinusoidal loading has been investigated and compared with that of Model-II studied earlier. It has been found that Model-III exhibits regular and irregular sub-harmonics, jump phenomena and strong sensitivity to initial conditions, forcing frequency, system period as well as the sense of peak sinusoidal force. The constant sustained load has been found to affect the natural period of the dynamical system. The predictions of Model-I have been compared with those of the approximate linear model adopted in present practice. The behaviour exhibited by different models of the SDOF cracked elastic concrete structures under working loads and the theoretical and practical implications of the approach followed have been critically evaluated.