• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.596-601
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• 2008

This paper presents how to develop visual design tools for construction of strut-and-tie models(S (STM). STMs have shown internal force flows for dimensioning and proportioning of D-regions of reinforced concrete structures. In order to select an appropriate strut-and-tie model some interactive graphic tools are necessary to help designers compare alternatives by changing the geometry of initial STM. This study proposes to use force polygons representing the equilibrium state of STM. The change of STM dynamically shows change of force magnitudes by force polygon. Once the geometry of STM is determined the detailing design process is required in the next procedure.

• Journal of the Korea institute for structural maintenance and inspection
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• v.4 no.2
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• pp.113-129
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• 2000

This study evaluates the behavior and strength of an anchorage zone of the prestressed concrete box girder bridge on the Kyungboo highway railroad using the 2D SUB-3D STM approach and a linear elastic finite element analysis. The 2D SUB-3D STM approach utilizes several two-dimensional sub strut-tie models that represent the compressive and tensile stress flows of each projected plane of the three-dimensional structural concrete in the selection of a three dimensional strut-tie model, evaluation of the effective strengths of the concrete struts, and verification of the geometric compatibility condition and bearing capacity of the critical nodal zones in the selected three-dimensional strut-tie model. The finite element analysis uses an 8-node brick element and the longitudinal prestressing force is considered as the equivalent nodal force. Analysis results show that the 2D SUB-3D STM approach and linear elastic finite element method can be effectively applied to the analysis and design of three-dimensional structural concrete including a prestressed concrete box girder anchorage zone.

• Computers and Concrete
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• v.15 no.5
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• pp.807-831
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• 2015

In the previous analytical studies on 2D reinforced concrete (RC) beam-column joints, the modified compression field theory (MCFT) and the strut-and-tie method (STM) are usually employed. In this paper, the limitations of these analytical models for RC joint applications are reviewed. Essentially for predictions of RC joint shear behaviour, the MCFT is not applicable, while the STM can only predict the ultimate shear strength. To eliminate these limitations, an improved STM is derived and applied to some commonly encountered 2D joints, viz., interior and exterior joints, subjected to monotonic loading. Compared with the other STMs, the most attracting novelty of the proposed improved STM is that all critical stages of the shear stress-strain relationships for RC joints can be predicted, which cover the stages characterized by concrete cracking, transverse reinforcement yielding and concrete strut crushing. For validation and demonstration of superiority, the shear stress-strain relationships of interior and exterior RC beam-column joints from published experimental studies are employed and compared with the predictions by the proposed improved STM and other widely-used analytical models, such as the MCFT and STM.

• Computers and Concrete
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• v.28 no.6
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• pp.621-634
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• 2021

For the reliable strut-and-tie model (STM) design of disturbed regions of concrete members, structural designers must accurately determine the strength of concrete struts to check the strength conditions of a selected STM el and the anchorage of reinforcing bars in nodal zones. In this study, the author proposed a consistent numerical method for strut strength, applicable to all two-dimensional STMs. The proposed method includes the effects of a biaxial stress state associated with tensile strains in reinforcing bars crossing a strut, deviation angle between strut orientation and compressive principal stress flow, and degree of confinement provided by reinforcement. The author examined the method's validity through the STM prediction of the ultimate strengths of 517 reinforced concrete (RC) deep beams, 24 RC panels, and 258 RC corbels, all tested to failure.

• Computers and Concrete
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• v.20 no.3
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• pp.329-338
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• 2017

A new simple and practical strut-and-tie model (STM) for predicting the shear strength of RC pile caps is proposed in this paper. Two approaches are adopted to take into account the concrete softening effect. In the first approach, a concrete efficiency factor based on compression field theory is employed to determine the effective strength of a concrete strut, assumed to control the shear strength of the whole member. The second adopted Kupfer and Gerstle's biaxial failure criterion of concrete to derive the simple nominal shear strength of pile caps containing the interaction between strut and tie capacity. The validation of these two methods is investigated using 110 RC pile cap test results and other STMs available in the literature. It was found that the failure criterion approach appears to provide more accurate and consistent predictions, and hence is chosen to be the proposed STM. Finally, the predictions of the proposed STM are also compared with those obtained by using seven other STMs from codes of practice and the literature, and were found to give better accuracy and consistency.

• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.221-239
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• 2013

This paper focuses on a development of strut-and-tie model (STM) to predict the capacity of an improved longitudinal joint for decked bulb-tee bridge systems. Nine reinforced concrete beam/slab specimens anchored by spliced headed bars with different details were tested. Test results were evaluated and compared with an anticipation of the validated STM. The proposed STM provides a lower bound of the ultimate capacity of the joint zone. It shows that the lap length of headed bars has a significant effect on structural behaviors of the improved joint. To develop a full strength joint, the range of the lap length can be determined by the strength and compatibility requirement. Design recommendations to spliced headed bars, concrete strength, as well as lacer bars in the joint zone are proposed for developing a full strength joint.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.415-420
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• 1998

In this paper, 2D SUB-3D STM approach for analysis and design of 3D structural concrete is presented. In the approach several 2D sub strut-tie models which are representations of compressive and tensile stress flows of each projected plane of 3D structural concrete are utilized in the sketch of a 3D strut-tie model, in the evaluation of effective strengths of compressive concrete struts, and in the verification of geometric compatibility and bearing capacity of critical nodal zones of 3D strut-tie model. To prove the validity and rationality of the suggested approach, the behavior and strength of a prestressed box girder diaphragm tested to failure are evaluated.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.617-622
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• 2000

In this study, effective compressive strength and nodal zone of Strut-and-Tie Model are studied to propose a new design method for RC T-type pier coping for prevention of sudden brittle failure. The coping which transmits loads of bridge to pier should be properly designed to retain ductile behavior. In order to carry out this proper design using STM, tie must yield before concrete fails, and a stress at strut should not exceed a certain effective stress. Therefore, reasonable determination of the effective compressive strength of strut by considering stress states at the nodal zone exactly is very important. Since conventional STM is applied under assumption that all nodes are under hydrostatic stress state, actual non-hydrostatic stress state in nodal zone caused by geometrical characteristics, loading conditions, support conditions of structures can not be considered properly. In order to apply STM for design of RC T-type pier coping, the non-hydrostatic stress state of nodal zone is considered and effective compressive strength is proposed. Then, a new design method of RC T-type pier coping which applies the principle of superposition to obtain optimum ductile behavior is rationally designed.

• Structural Engineering and Mechanics
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• v.77 no.2
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• pp.273-291
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• 2021

The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of disturbed regions ('D' regions) of reinforced concrete members such as in corbels and deep beams, where traditional flexure theory does not apply. This paper evaluates the applicability of the equilibrium based STM in strength predictions of deep beams (with rectangular and circular cross-section) and corbels using the available experiments in literature. STM is found to give fairly good results for corbel and deep beams. The failure modes of these deep members are also studied, and an optimum amount of distribution reinforcement is suggested to eliminate the premature diagonal splitting failure. A comparison with existing empirical and semi empirical methods also show that STM gives more reliable results. The nonlinear finite element analysis (NLFEA) of 50 deep beams and 20 corbels could capture the complete behaviour of deep members including crack pattern, failure load and failure load accurately.

• 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.