• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.847-852
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• 2000

This paper presents an evaluation of the behavior and strength of two pre-tensioned concrete deep beams tested to failure with using the nonlinear strut-tie model approach. In the approach, the effective prestressing forces represented be equivalent external loads are gradually introduced along its transfer length in the nearest strut-tie model joints, the friction at the interface of main diagonal shear cracks is modeled by diagonal struts along the direction of the cracks in strut tie-model, and additional positioning of concrete ties a the place of steel ties is incorporated. Through the analysis of pre-tensioned concrete deep beams, the nonlinear strut-tie model approach proved to present effective solutions for prediction the essential aspects of the behavior and strength of pre-tensioned concrete deep beams.

• Computers and Concrete
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• v.4 no.4
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• pp.259-272
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• 2007

A method based on the lower-bound theorem of limit analysis is presented for the capacity assessment of nodal zones in strut-and-tie models. The idealized geometry of the nodal zones is formed by the intersection of effective widths of the framing struts and ties. The stress distribution is estimated by dividing the nodal zones into constant stress triangles separated by lines of stress discontinuity. The strength adequacy is verified by comparing the biaxial stress field in each triangle with the corresponding failure criteria. The approach has been implemented in a computer-based strut-and-tie tool called CAST (Computer-Aided Strut-and-Tie). An application example is also presented to illustrate the approach.

• Structural Engineering and Mechanics
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• v.43 no.6
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• pp.711-724
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• 2012

The goal of this study is to conceptually orientate optimized layouts of outrigger belt trusses which are in widespread use today in the design of tall buildings by strut-and-tie truss models utilizing a topology optimization method. In this study unknown strut-and-tie models are realized by using a typical SIMP method of topology optimization methods. In tradition strut-and-tie model designs find the appropriate strut-and-tie trusses along force paths with respect to elastic stress distribution, and then engineers or designers determine the most proper truss models by experience and intuition. It is linked to a trial-and-error procedure based on heuristic strategies. The presented strut-and tie model design by using SIMP provides that belt truss models are automatically and robustly produced by optimal layout information of struts-and-ties conforming to force paths without any trial-and-error. Numerical applications are studied to verify that outrigger belt trusses for tall buildings are optimally chosen by the proposed method for both static and dynamic responses.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.04a
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• pp.430-435
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• 1997

This paper represents the investigation of the shear fatigue behavior and damage procedure of reinforced concrete beams subject to repeated loading using the strut-tie model. Damage Index is defined as the ratio of deflection at each cycle to the ultimate deflection of inelastic region. Two types of strut-tie model are designed according to the inclined angles of concrete-struts and the consideration of concrete-ties. In one model, aggregate interlock and resistance of uncracked concrete are regarded as the main sheat resisting mechanism and in the other, stirrup is. The results show that the strut-tie model combined with damage index can describe the shear fatigue behavior of RC beams subject to repeated loading effectively.

• Journal of the Korea Concrete Institute
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• v.17 no.2 s.86
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• pp.201-212
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• 2005

A new strut-tie model using secant stiffness, Direct Inelastic Strut-Tie Model, was developed. Since basically the proposed design method uses linear analysis, it is convenient and stable in numerical analysis. At the same time, the proposed design method can accurately estimate the inelastic strength and ductility demands of struts and ties because it can analyzes the inelastic behavior of structure using iterative calculations for secant stiffness. In the present study, the procedure of the proposed design method was established, and a computer program incorporating the proposed method was developed. Design examples using the proposed method were presented, and its advantages were highlighted by the comparison with the traditional strut-tie model. The Direct Inelastic Strut-Tie Model, as an integrated analysis/design method, can directly address the design strategy intended by the engineer to prevent development of macro-cracks and brittle failure of struts. Since the proposed model can analyze the inelastic deformation, indeterminate strut-tie model can be used. Also, since the proposed model controls the local deformations of struts and ties, it can be used as a performance-based design method for various design criteria.

• Structural Engineering and Mechanics
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• v.10 no.6
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• pp.589-601
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• 2000

A simplified analysis procedure utilizing the strut-tie modeling technique is developed to take a close look into the post-elastic deformation capacity of beam-column connections in ductile reinforced concrete frame structures. Particular emphasis is given to the effect of concrete strength decay and quantity and arrangement of joint shear steel. For this a fan-shaped crack pattern is postulated through the joints. A series of hypothetical rigid nodes are assumed through which struts, ties and boundaries are connected to each other. The equilibrium consideration enables all forces in struts, ties and boundaries to be related through the nodes. The boundary condition surrounding the joints is obtained by the mechanism analysis of the frame structures. In order to avoid a complexity from the indeterminacy of the truss model, it is assumed that all shear steel yielded. It is noted from the previous research that the capacity of struts is limited by the principal tensile strain of the joint panel for which the strain of the transverse diagonal is taken. The post-yield deformation of joint steel is taken to be the only source of the joint shear deformation beyond the elastic range. Both deformations are related by the energy consideration. The analysis is then performed by iteration for a given shear strain. The analysis results indicate that concentrating most of the joint steel near the center of the joint along with higher strength concrete may enhance the post-elastic joint performance.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.621-637
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• 2006

Although the approaches implementing strut-tie models are the valuable tools for designing discontinuity regions of structural concrete, the approaches of the current design codes have to be improved for the design of structural concrete subjected to complex loading and geometrical conditions because of the uncertainties in the selection of strut-tie model, in the use of an indeterminate strut-tie model, and in the effective strengths of struts and nodal zones. To improve the uncertainties, a grid struttie model approach is proposed in this study. The proposed approach, allowing to perform a consistent and effective design of structural concrete, employs an initial grid strut-tie model in which various load combinations can be considered. In addition, the approach performs an automatic selection of an optimal strut-tie model by evaluating the capacities of struts and ties using a simple optimization algorithm. The validity and effectiveness of the proposed approach is verified by conducting the analysis of the four reinforced concrete deep beams tested to failure and the design of shearwalls with two openings.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.425-436
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• 2014

Although the strut-tie model approaches of current design codes are regarded as the valuable methods for designs of structural concretes with D-regions, the approaches have to be improved because of the uncertainties in terms of the concepts and provisions for designs of 3-dimensional structural concretes. To improve the uncertainties, a new strut-tie model approach is proposed in this study. In the proposed approach, the concepts of employing a 3-dimensional grid element allowing load transfers in all directions at a node to construct a strut-tie model, a numerical analysis approach to determine the effective strengths of concrete struts and nodal zones by reflecting the effects of reinforcing bars and 3-dimensional stress state, and maximum areas of struts and ties to examine their load carrying capacities are integrated into the strut-tie model approaches of current design codes.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.979-984
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• 2008

This paper discusses how to use basic strut-and-tie models(STM) for practical application. Construction of STM starts with drawing of load paths with equilibrium conditions. Understanding of structural systems including form active systems, vector active systems, and section active systems help us select appropriate systems for possible STM. Simple circular fans can be employed for load paths from concentrated forces to distributed forces. Strength of struts depends on configuration of their nodal zones which meet tension ties and effective compressive strength. The effective compressive strength of struts are assumed to be mainly influenced by transverse strain.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.143-152
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• 2020

Deep coupling beams are more prone to suffer brittle shear failure. The addition of steel fibers to seismic members such as coupling beams can improve their shear performance and ductility. Based on the test results of steel fiber reinforced concrete(SFRC) coupling beams with span-to-depth ratio between 1.5 and 2.5 under lateral reverse cyclic load, the shear mechanism were analyzed by using strut-and-tie model theory, and the effects of the span-to-depth ratio, compressive strength and volume fraction of steel fiber on shear strengths were also discussed. A simplified calculation method to predict the shear capacity of SFRC deep coupling beams was proposed. The results show that the shear force is mainly transmitted by a strut-and-tie mechanism composed of three types of inclined concrete struts, vertical reinforcement ties and nodes. The influence of span-to-depth ratio on shear capacity is mainly due to the change of inclination angle of main inclined struts. The increasing of concrete compressive strength or volume fraction of steel fiber can improve the shear capacity of SFRC deep coupling beams mainly by enhancing the bearing capacity of compressive struts or tensile strength of the vertical tie. The proposed calculation method is verified using experimental data, and comparative results show that the prediction values agree well with the test ones.