• 한국구조물진단유지관리공학회 논문집
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• 제14권1호
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• pp.175-181
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• 2010

평형트러스모델, Mohr적합트러스모델, 그리고 연성트러스모델은 회전각에 기초하기 때문에 회전각모델이라 불리 운다. 이러한 회전각모델들은 콘크리트기여도를 예측할 수 없는 단점이 있다. 콘크리트 기여 성분을 계산할 수 있는 MCFT(Modified Compression Field Theory)나 RA-STM(Rotating Angle-Softening Truss Model) 같은 최근 트러스모델(Modern Truss Model, MTM)은 균열이 발생한 철근콘크리트요소를 연속체 재료로 취급한다. 또한 MTM은 평형조건과 적합조건 그리고 2축 상태에서 콘크리트의 연성 응력-변형률 관계를 이용하여 비선형해석을 수행하고 있다. 본 연구는 전단응력-변형률의 전체 이력 상태를 모두 계산하지 않고, 철근항복과 스트럿 압괴(crushing failure) 파괴기준을 이용하여 해를 찾는 방법으로 수렴속도를 개선한 것이다. 이 알고리즘을 이용하여 Hsu가 실험한 9개의 전단응력-변형률 자료를 분석하였다.

• Interaction and multiscale mechanics
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• 제2권1호
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• pp.69-89
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• 2009

Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.

• Coupled systems mechanics
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• 제11권5호
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• pp.439-458
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• 2022

Over-coating is one of the most popular engineering practices to strengthen Reinforced Concrete (RC) structures, due to the relative quickness and ease of construction. It consists of an external coat bonded to the outer surface of the structural RC element, either by the use of chemical adhesives, mechanical anchor bolts or simply mortar injection. In contrast to these constructive advantages, the numerical estimation of the bearing capacity of the strengthened reinforced concrete element is still complicated, not only for the complexity of modelling a flexible membrane or plate attached to a quasi-rigid solid, but also for the difficulties that raise of simulating any potential delamination between both materials. For these reasons, the standard engineering calculations used in the practice remain very approximated and clumsy. In this work, we propose the formulation of a new 2D solid-layer finite element capable to link a solid body with a flexible thin layer, as it were the "skin" of the body, allowing the potential delamination between both materials. In numerical terms, this "skin" element is intended to work as a transitional region between a solid body (modelled with a classical formulation of a standard quadrilateral four-nodes element) and a flexible coat layer (modelled with cubic beam element), dealing with the incompatibility of Degrees-Of-Freedom between them (two DOF for the solid and three DOF for the beam). The aim of the solid-layer element is to simplify the mesh construction of the strengthened RC element being aware of two aspects: a) to prevent the inappropriate use of very small solid elements to simulate the coat; b) to improve the numerical estimation of the real bearing capacity of the strengthened element when the coat is attached or detached from the solid body.

• Coupled systems mechanics
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• 제12권6호
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• pp.481-501
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• 2023

Over-coating is one of the most popular engineering practices to strengthen Reinforced Concrete (RC) structures, due to the relative quickness and ease of construction. It consists of an external coat bonded to the outer surface of the structural RC element, either by the use of chemical adhesives, mechanical anchor bolts or simply mortar injection. In contrast to these constructive advantages, the numerical estimation of the bearing capacity of the strengthened reinforced concrete element is still complicated, not only for the complexity of modelling a flexible membrane or plate attached to a quasi-rigid solid, but also for the difficulties that raise of simulating any potential delamination between both materials. For these reasons, the standard engineering calculations used in the practice remain very approximated and clumsy. In this work, we propose the formulation of a new 2D solid-layer finite element capable to link a solid body with a flexible thin layer, as it were the "skin" of the body, allowing the potential delamination between both materials. In numerical terms, this "skin" element is intended to work as a transitional region between a solid body (modelled with a classical formulation of a standard quadrilateral four-nodes element) and a flexible coat layer (modelled with cubic beam element), dealing with the incompatibility of Degrees-OfFreedom between them (two DOF for the solid and three DOF for the beam). The aim of the solid-layer element is to simplify the mesh construction of the strengthened RC element being aware of two aspects: a) to prevent the inappropriate use of very small solid elements to simulate the coat; b) to improve the numerical estimation of the real bearing capacity of the strengthened element when the coat is attached or detached from the solid body.

• 한국공간구조학회논문집
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• 제3권1호
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• pp.77-85
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• 2003

This paper presents a truss model that can predict the shear behavior of reinforced concrete (RC) beams subjected to the combined actions of shear and flexure. Unlike other truss models, the proposed truss model, TATM, takes into account the effect of the flexural moment on the shear strength of RC beams with different shear span-to-depth ratios. To check the successfulness of the proposed model experimentally obtained stress shear strain curves were compared to the predicted ones using the proposed truss model. Furthermore, the shear strengths of 170 RC test beams with variable shear span-to-depth ratios were compared to the shear strengths as given by the truss model reported in this paper.

• Structural Engineering and Mechanics
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• 제7권1호
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• pp.35-52
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• 1999

Realistic steel-concrete bond/slip relationships proposed in the literature are usually uniaxial. They are based on phenomenological theories of deformation and degradation mechanisms, and various pull-out tests. These relationships are usually implemented using different analytical methods for solving the differential equations of bond along the anchored portion, for particular situations. This paper justifies the concepts, and points out the assumptions underlying the construction and use of uniaxial bond laws. A finite element implementation is proposed using 2-D membrane elements. An application example on an interior beam-column joint illustrates the possibilities of this approach.

• Computers and Concrete
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• 제8권6호
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• pp.735-755
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• 2011

The capability of a multi-directional fixed smeared crack constitutive model to simulate the flexural/punching failure modes of fiber reinforced concrete (FRC) laminar structures is discussed. The constitutive model is implemented in a computer program based on the finite element method, where the FRC laminar structures were simulated according to the Reissner-Mindlin shell theory. The shell is discretized into layers for the simulation of the membrane, bending and out-of-plane shear nonlinear behavior. A stress-strain softening diagram is proposed to reproduce, after crack initiation, the evolution of the normal crack component. The in-plane shear crack component is obtained using the concept of shear retention factor, defined by a crack-strain dependent law. To capture the punching failure mode, a softening diagram is proposed to simulate the decrease of the out-of-plane shear stress components with the increase of the corresponding shear strain components, after crack initiation. With this relatively simple approach, accurate predictions of the behavior of FRC structures failing in bending and in shear can be obtained. To assess the predictive performance of the model, a punching experimental test of a module of a façade panel fabricated with steel fiber reinforced self-compacting concrete is numerically simulated. The influence of some parameters defining the softening diagrams is discussed.

• 대한토목학회논문집
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• 제8권3호
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• pp.11-20
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• 1988

사하중과 단조 활하중을 받고 있는 철근콘크리트판에 대한 일반적인 유한요소 해석방법을 개발하였다. 이 방법을 통하여 탄성, 비탄성 및 극한범위에서 하중-변형 응답과 균열전파를 추적할 수 있었고 또한 응답 경로를 통하여 콘크리트와 철근의 내부응력을 결정할 수 있었다. 면내응력과 휨응력간의 상호작용을 고려하는 층분할된 8 절점 등매개변수 요소를 개발하였다. 수치해를 구하는 방법은 접선증분 강성도법을 이용하였다. 본 해법에 대한 유효성을 검토하기 위하여 다른 해석결과들과 비교하였다.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표논문집(II)
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• pp.405-411
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• 1998

An iterative numerical computational algorithm is presented to design a plate of shell element subjected to membrane and flexural forces. Based on equilibrium consideration, equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. The amount of reinforcement is determined locally, i. e., for each sampling point, from the equilibrium between applied and internal forces. One case of design is performed for a hyperbolic paraboloid saddle shell (originally used by Lin and Scordelis) to check the design strength against a consistent design load, therefore, to verify the adequacy of design practice for reinforced concrete shells. Based on nonlinear analyses performed, the analytically calculated ultimate load exceeded the design ultimate load from 14-43% for an analysis with relatively low to high tension stiffening, ${\gamma}$ =5~20 cases. For these cases, the design method gives a lower bound on the ultimate load with respect to Lower bound theorem. This shows the adequacy of the current practice at least for this saddle shell case studied. To generalize the conclusion many more designs-analyses are performed with different shell configurations.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2000년도 봄 학술발표회 논문집
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• pp.501-506
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• 2000

An iterative numerical computational algorithm is presented to design a plate or shell element subjected to membrane and flexural forces. Based on equilibrium consideration, equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. The amount of reinforcement is determined locally, i.e., for each sampling point, from the equilibrium between applied and internal forces. Based on nonlinear analyses performed in a hyperbolic cooling tower, the analytically calculated ultimate load exceeded the design ultimate load from 50% to 55% for an analysis with relatively low to high tension stiffening, cases $\gamma$=10 and 15. For these cases, the design method gives a lower bound on the ultimate load with respect to Lower bound theorem, This shows the adequacy of th current practice at least for this cooling tower shell case studied. To generalize the conclusion more designs - analyses should be reformed with different shell configurations.