• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.821-826
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• 2001

This paper presents four types of strut-tie model design approaches of structural concrete through the anchorage zone design of a post-tensioned concrete I-beam. The differences and distinctive feature of each approach in terms of structural type of selected strut-tie model, external force acting on strut-tie model, effective strength of concrete strut, and strut-tie model design procedure are analyzed and compared. The outcomes of present study enable structural designers to understand the merits and demerits of each strut-tie model design approach, and thus to conduct reasonable and accurate design of structural concrete.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.241-246
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• 2000

In the strut-tie model design of structural concrete, the importance of the effective strength of concrete strut has been overlooked by many practitioners. The authors believe that the effective strength of concrete strut is an important factor not only in determining steel tie forces but also in verifying the nodal zone strength and geometric compatibility condition of a selected strut-tie model. This study evaluate the effect of the effective strength of concrete strut on structural concrete design by applying the different effective strut strengths to the strut-tie model design of a post-tensioned anchorage zone and a continuous concrete deep beam.

• Computers and Concrete
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• v.2 no.4
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• pp.267-291
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• 2005

To date, many studies have been conducted for the analysis and design of reinforced concrete members with disturbed regions. However, prestressed concrete deep beams have not been the subject of many investigations. This paper presents an evaluation of the behavior and strength of three pre-tensioned concrete deep beams failed by shear and bond slip of prestressing strands using a nonlinear strut-tie model approach. In this approach, effective prestressing forces represented by equivalent external loads are gradually introduced along strand's transfer length in the nearest strut-tie model joints, the friction at the interface of main diagonal shear cracks is modeled by the aggregate interlock struts along the direction of the cracks in strut-tie model, and an algorithm considering the effect of bond slip of prestressing strands in the strut-tie model analysis and design of pre-tensioned concrete members is implemented. Through the strut-tie model analysis of pre-tensioned concrete deep beams, the nonlinear strut-tie model approach proved to present effective solutions for predicting the essential aspects of the behavior and strength of pre-tensioned concrete deep beams. The nonlinear strut-tie model approach is capable of predicting the strength and failure modes of pre-tensioned concrete deep beams including the anchorage failure of prestressing strands and, accordingly, can be employed in the practical and precise design of pre-tensioned concrete deep beams.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.595-599
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• 2003

For implementation of the strut-tie model approach to the practical analysis and design of structural concrete, the effective strengths of concrete struts in a strut-tie model, which have a crucial effect on the determination of strut and tie forces and the validity verification of strut-tie model's geometric compatibility condition, have to be determined accurately. In this study, the validity of the methods for determining the effective strengths of concrete struts was evaluated by conducting the strut-tie model analyses of the three reinforced concrete deep beams tested to failure with the effective strengths of concrete struts obtained from the suggested determination methods.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.265-268
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• 2006

Recently, many design standards recommend the use of a strut-tie model approach for design of structural concrete with D-region(s). However, since the design standards of the conventional strut-tie model approaches are suggested on the assumption of using a determinate strut-tie model, it is difficult to apply an indeterminate strut-tie model in the design of continuous deep beams. In this study, an indeterminate strut-tie model for continuous deep beams is proposed to resolve the problem, and the ultimate strengths of 35 continuous deep beams tested to failure are evaluated for the validity check of the proposed indeterminate strut-tie model. The analytical results by the proposed model are compared with those by the conventional approaches of ACI 318-99 and ACI 318-05.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.961-966
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• 2003

In recent, the design of diaphragm which is representative disturbed region in PSC box girder bridge have been performed according to the empirical method or beam theory. But, these methods couldn't be described the behavior of the end diaphragm, and placed reinforcements accurately. As the compressive stress transferred by the web concentrated on the lower parts of diaphragm, it was demonstrated that the basic assumption of 2-D strut-and-tie model for the diaphragm that the compressive stress acts on the upper parts of the diaphragm is wrong. Meanwhile, in this research, after analyzing the variables of end diaphragm, the 2-D strut-and-tie models appropriate to each cases are proposed. And, the problems of 2-D strut-and-tie model were analyzed, so 3-D strut-and-tie model is proposed as well. There is no codes which include the demonstration of safety of 3-D strut-and-tie model. Hence, for nodes, the stresses at the elements which included the singular node in strut-and-tie model were investigated using the finite element analysis. And, the stress states of strut has one direction, so effective stresses were considered at the stage, dimensioning of the model. From the results, 3-D strut-and-tie model could predict the behavior of end diaphragm accurately, and design of reinforcement could be performed economically.

• Computers and Concrete
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• v.16 no.3
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• pp.357-380
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• 2015

In this study, a simple indeterminate strut-tie model which reflects complicated characteristics of the ultimate structural behavior of continuous reinforced concrete deep beams was proposed. In addition, the load distribution ratio, defined as the fraction of applied load transferred by a vertical tie of truss load transfer mechanism, was proposed to help structural designers perform the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie was introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete were reflected upon. To verify the appropriateness of the present study, the ultimate strength of 58 continuous reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-11's strut-tie model approach associated with the presented indeterminate strut-tie model and load distribution ratio. The ultimate strength of the continuous deep beams was also estimated by the experimental shear equations, conventional design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the proposed strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of the continuous deep beams fairly well compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of the continuous deep beams consistently and reasonably. The present study may provide an opportunity to help structural designers conduct the rational and practical strut-tie model design of continuous deep beams.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.04a
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• pp.392-397
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• 1997

In this paper, design and analysis of anchorage zone in prestressed concrete structure using nonlinear strut and tie model is presented. Nonlinear strut and tie model is an analysis and design model which constructs strut and tie model based on nonlinear analysis considering the nonlinear behavior of concrete. Based on the nonlinear strut and tie model, the analysis and design are performed for the anchorage zone having singular concentric tendons, singular eccentric tendons and multiple tendons, respectively. For verification of the model, comparisons are made with experimental results as well as results by linear strut and tie models. from the comparisons, it is shown that the design of the anchorage zone by the nonlinear model is still economical without loosing the degree of safety and the prediction of the ultimate load by the nonlinear model gives better accuracy than by the linear one.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.271-274
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• 2005

Existing strut-and-tie model cannot be applied to analysis of slender beams without shear reinforcement because shear transfer mechanism is not formed. In the present study, a new strut-and-tie model with rigid joint was developed. Basically, concrete strut is modeled as a frame element which can transfer shear force (or moment) as well as axial force. Employing Rankine failure criterion, failure strength due to shear-tension and shear-compression developed in compressive concrete strut was defined. For verification, various test specimens were analyzed and the results were compared with tests. The proposed strut-and-tie model predicted shear strength and failure displacement with reasonable precision, addressing the design parameters such as shear reinforcement, concrete compressive strength, and shear span ratio.

• Computers and Concrete
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• v.14 no.1
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• pp.19-40
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• 2014

Reinforced concrete deep beams are structural beams with low shear span-to-depth ratio, and hence in which the strain distribution is significantly nonlinear and the conventional beam theory is not applicable. A strut-and-tie model is considered one of the most rational and simplest methods available for shear strength prediction and design of deep beams. The strut-and-tie model approach describes the shear failure of a deep beam using diagonal strut and truss mechanism: The diagonal strut mechanism represents compression stress fields that develop in the concrete web between diagonal cracks of the concrete while the truss mechanism accounts for the contributions of the horizontal and vertical web reinforcements. Based on a database of 406 experimental observations, this paper proposes a new strut-and-tie-model for accurate prediction of shear strength of reinforced concrete deep beams, and further improves the model by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. Seven existing deterministic models from design codes and the literature are compared with the proposed method. Finally, a limit-state design formula and the corresponding reduction factor are developed for the proposed strut-andtie model.