• 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.

• 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.33 no.6
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• pp.2195-2209
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• 2013

The effective strength of concrete struts must be determined accurately for the reliable strut-tie model analysis and design of structural concrete. In this study, the equations of the effective strength, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete deep beams employed in current design codes, are proposed. The effects of shear span-to-effective depth ratio, compressive strength of concrete, and flexural and shear reinforcement ratios are reflected in the development of the proposed equations. To examine the appropriateness of the proposed equations, the strengths of 241 reinforced concrete deep beams, all tested to shear failure, are evaluated by using the three types of strut-tie models with the existing and proposed equations.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.453-458
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• 2001

This paper presents the procedure to find the hysteresis loop of RC member using a modified strut-and-tie model. The forces and displacements at critical points, that are initial yielding point, target displacement point, unloading elastic limit, and reloading point after pinching, are investigated with the strut-and-tie models. Using bond-slip relationship, the elastic behavior of tie element is determined. The plastic flow behavior after flexural yielding is expressed by changing the location of longitudinal strut. Determination of pinching effect completes the initial hysteresis loop, assuming that the behavior of the opposite direction is symmetrical form.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.235-240
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• 2000

Although dapped-end beams are widely used in bridge and building structures, there are not any specific and reasonable design regulations on dapped-end beams. In this study, the validity of the suggested experimental and empirical design methods, conventional strut-tie model approach, and nonlinear strut-tie model approach is evaluated through the analysis of dapped-end beams tested to failure. The nonlinear strut-tie model approach proved to be the most suitable method for dapper-end beam design.

• Structural Engineering and Mechanics
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• v.44 no.2
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• pp.163-178
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• 2012

A strut-and-tie model is introduced in this paper to predict the ultimate shear strength of non-seismically detailed columns. The validity and applicability of the proposed strut-and-tie model are evaluated by comparison with available experimental data. The model was developed based on visible crack patterns observed on the test specimens. The concrete contribution is integrated into the strut-and-tie model through a concept of equivalent transverse reinforcement. To further validate the model a full-scale non-seismically detailed reinforced concrete column was tested to investigate its seismic behavior. The specimen was tested under the combination of a constant axial load, $0.30f_c{^{\prime}}A_g$ and quasi-static cyclic loadings simulating earthquake actions. Quasi-static cyclic loadings simulating earthquake actions were applied to the specimen until it could not sustain the applied axial load. The analytical results reveal that the strut-and-tie method is capable of modeling to a satisfactory accuracy the ultimate shear strength of non-seismically detailed columns subjected to reserved cyclic loadings.

• Structural Engineering and Mechanics
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• v.41 no.4
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• pp.459-477
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• 2012

This paper attempts to determine the inclination of the compression strut within variable angle truss models for RC beams loaded in shear-flexure through a proposed semi-analytical approach. A truss unit is used to analyze a reinforced concrete beam, by the principle of virtual work under the truss analogy. The inclination of the compression strut is then theoretically derived. The concrete contribution is addressed by utilizing the compatibility condition within each truss unit. Comparisons are made between the predicted and published experimental results of the seventy one RC beams with respect to the shear strength and the inclined angle of the compression strut at this state to investigate the adequacy of the proposed semi-analytical approach.

• 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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• 2004.05a
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• pp.244-247
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• 2004

This study proposes the design method of the shear walls with openings using strut-and-tie models. Strut-and-tie models are constructed for opening near the middle of the wall and for opening near a wall boundary. These enables an admissible load path for the horizontal earthquake force. These models consider the size and position of opening effectively. Each model is suitable for the seismic response corresponding with lateral forces in a given direction to be considered. The proposed models are good agreements with nonlinear finite element analysis(DIANA) results.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.209-212
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• 2005

This paper presents, basic concepts on deformation models for D-regions critical to shear. Strut-and-tie models are used to construct for deformation estimation at yielding and ultimate deformation. A generic: strut-and-tie model is proposed to investigate deformation patterns and failure mode identification. Superposition of the basic models enables us to explain deformation limits of arch action and truss action. Displacement at yielding is assessed by consideration of deformation of reinforcing steel only while the ultimate displacement is calculated by limits of ultimate strain of concrete in compression and failure mechanisms.