• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.361-379
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• 2005

Reinforced concrete deep beams have useful applications in tall buildings and foundations. Over the past two decades, numerous design models for deep beams were suggested. However even the latest design manuals still offer little insight into the design of deep beams in particular when complexities exist in the beams like web openings. A method commonly suggested for the design of deep beams with openings is the strut-and-tie model which is primarily used to represent the actual load transfer mechanism in a structural concrete member under ultimate load. In the present study, the development of the strut-and-tie model is transformed to the topology optimization problem of continuum structures. During the optimization process, both the stress and displacement constraints are satisfied and the performance of progressive topologies is evaluated. The influences on the strut-and-tie model in relation to different size, location and number of openings, as well as different loading and support conditions in deep beams are examined in some detail. In all, eleven deep beams with web openings are optimized and compared in nine groups. The optimal strut-and-tie models achieved are also compared with published experimental crack patterns. Numerical results have shown to confirm the experimental observations and to efficiently represent the load transfer mechanism in concrete deep beams with openings under ultimate load.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.269-279
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• 2008

In this study, the ultimate strengths of 229 simply supported reinforced concrete deep beams tested to shear failure were evaluated by the ACI 318-05's strut-tie model approach implemented with the presented indeterminate strut-tie model and its load distribution ratio. The ultimate strengths of the deep beams were also estimated by the experimental shear equations, design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the present strut-tie model and its load distribution ratio was examined through the comparison of the strength analysis results classified according to the prime design variables of the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.449-454
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• 2001

The algorithm and program which implement the bond-slip behavior of pre-tensioned concrete beams to the nonlinear strut-tie model approach, are developed in this study. The validity of the algorithm and program is verified through the strut-tie model evaluation of the strength and behavior of two pre-tensioned concrete deep beams which were failed by bond-slip.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.375-379
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• 2003

In this paper, the linear and nonlinear strut-tie model approaches for the analysis and design of concrete structures are suggested. The validity of the approaches are examined through the strength analysis of four dapped-end beams tested to failure. According to the analysis results, the nonlinear strut-tie model approach which takes the various characteristics of nonlinear behaviors into account in the analysis and design of structural concrete and predicts the strength of structural concrete proven to be an effective method for structural analysis and design.

• Journal of the Korea Concrete Institute
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• v.15 no.2
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• pp.183-196
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• 2003

This paper evaluates the effects of haunches and the characteristic differences of haunch design regulations through design of pier and box structures with/without haunches. The design of the pier and box structures was conducted by using the linear elastic plane stress finite element analysis, the DIN 1045 and ACI 318-99 codes, the suggested experimental design equations, and the strut-tie model approach. To prove the validity of design results obtained by the strut-tie model approach, the ultimate strength of two haunched reinforced concrete beams tested to failure was evaluated by using the approach. According to the comparison and evaluation of the design results, it is concluded that the design results of haunched reinforced concrete structures by using conventional and design codes need to be complemented with those by using the strut-tie model approach that reflected the effects of haunches in design comparatively well through the actions of arch and direct transfer of applied loads.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.411-419
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• 2006

In this study, a new approach employing 3-dimensional strut-tie models for analysis and design of 3-dimensional structural concrete with disturbed regions that are not properly occupied by current design codes is proposed. In addition, a computer graphics program for the practical application of the approach is developed. The approach adopts a grid strut-tie model to exclude the subjectivity in the selection of strut-tie model and evaluates the effective strength of concrete strut by considering the 3-dimensional failure criteria of concrete and the deviation angles between the struts and compressive principal stress trajectories. To verify the appropriateness of the approach, nine pile caps tested to failure are analyzed and a bridge pier is designed. The analysis and design results are compared with those obtained by several different methods.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.403-413
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• 2014

For the reliable design of the structural concrete by the strut-tie model approaches of current design codes, the effective strengths of concrete struts must be determined with sufficient accuracy. Many values and equations for the effective strengths have been suggested until now. As those are for the two-dimensional concrete struts, however, it is inappropriate to employ them in the strut-tie model designs of three-dimensional structural concretes. In this study, an approach, that determines the effective strengths of three-dimensional concrete struts consistently and accurately by reflecting the state of 3-dimensional stresses, the 3-dimensional failure criteria of concrete, the degree of cracks (or tensile strains of reinforcing bars crossing the struts), the strut's longitudinal length, the deviation angle between strut orientation and compressive principal stress flow, compressive strength of concrete, and the degree of concrete confinement by reinforcing bars, is proposed. To examine the validity of the proposed approach, the ultimate strength analyses of 115 reinforced concrete pile caps tested to failure by previous investigators were conducted by the ACI 318-11's strut-tie model approach with the existing and proposed effective strengths of concrete struts.

• 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.5A
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• pp.443-462
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• 2010

The strut-tie model approach has proven to be effective in the ultimate analysis and design of structural concrete with disturbed regions. For the reliable analysis and design by the approach, however, the effective strength of concrete struts must be determined accurately. In this study, the validity of the effective strength of concrete struts, presented by the several design codes and many researchers including the author, was examined through the ultimate strength analysis of 24 reinforced concrete panels, 275 reinforced concrete deep beams, and 218 reinforced concrete corbels by using the conventional linear strut-tie model approach of current codes. The present study shows that the author's approach, resulting in an accurate and consistent evaluation of the ultimate strength of the panels, deep beams, and corbels, may reflect rationally the effects of primary variables including the types of strut-tie model and structural concrete, the conditions of load and geometry, and the strength of concrete in the strut-tie model analysis and design of structural concrete.