• 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.

• Journal of the Korea Concrete Institute
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• v.20 no.3
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• pp.345-356
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• 2008

In the previous study, direct inelastic strut-and-tie model (DISTM) was developed to perform inelastic design of reinforced concrete members by using linear analysis for their secant stiffness. In the present study, for convenience in design practice, the DISTM was further simplified so that inelastic design of reinforced concrete members can be performed by a run of linear analysis, without using iterative calculations. In the simplified direct inelastic strut-and-tie model (S-DISTM), a reinforced concrete member is idealized with compression strut of concrete and tension tie of reinforcing bars. For the strut and tie elements, elastic stiffness or secant stiffness is used according to the design strategy intended by engineer. To define the failure criteria of the strut and tie elements, concrete crushing and reinforcing bar fracture were considered. The proposed method was applied to inelastic design of various reinforced concrete members including deep beam, coupling beam, and shear wall. The design results were compared with the properties and the deformation capacities of the test specimens.

• Proceedings of the Korea Concrete Institute Conference
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• 1994.04a
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• pp.53-58
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• 1994

Beam-column joints of the skeleton structure can be classified as geometrical D-region, where the assumption of Bernoulli is not applicable. For the detailing of D-region in concrete structure, "Strut-and-Tie' Model is a very powerful tool, which has been widely used by practical engineers. This paper shows how the methodology of Strut-and-Tie Model can be applied for the various cases of beam-column joints. We can find this mechanical model does not give only an appropriate answer to the given problem but also a better insight to the structral behavior of beam-column joints.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.295-302
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• 2002

This paper introduces a method to determine strut-tie models in reinforced concrete (RC) structures using the evolutionary structural optimization (ESO). Even though strut-tie models are broadly adapted in design of reinforced concrete members subjected to shear and torsion, conventional methods can hardly give correct models in RC members subjected to complex loadings and geometry conditions. In this paper, the basic idea of the ESO method is used to determine more rational strut-tie models. Since an optimum topology of structures, finally obtained by the ESO method, usually represents a truss-like structure, the ESO method can effectively be used in finding the best strut-tie model in RC structures. Several example structures are provided to demonstrate the capability of the proposed method in finding the best strut-tie model of each RC structure and to verify its efficiency in application to real design problems.

• 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.36 no.4
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• pp.605-615
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• 2016

It is difficult to form a rational strut-tie model that represents a true load transfer mechanism of structural concrete with disturbed stressed region(s). To overcome the difficulty and handle numerous load cases with just one strut-tie model, a two-dimensional grid strut-tie model method was proposed previously. However, the validity of the method was not fully examined, although the incorporated basic concepts and new methods regarding the effective strength of concrete strut, load carrying capacity of struts and ties, and geometrical compatibility of grid strut-tie model were explained in detail. In this study, for accurate strength analysis and reliable design of reinforced concrete deep beams, the appropriateness of the two-dimensional grid strut-tie model method is verified. For this, the failure strength of 237 reinforced concrete deep beams, tested to shear failure, is predicted by the two-dimensional grid strut-tie model method, and the results are compared with those obtained by the sectional shear design methods and conventional strut-tie model methods of current design codes.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05a
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• pp.183-186
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• 2005

The Current design procedures of ACI 318-02 and CEB-FIP for the exterior beam-column joints do not provide engineers with a clear understanding of the physical behavior of the beam-column joints. In this paper, the failure strengths of the exterior beam-column joint specimens tested to failure were evaluated using the approach implementing 3-dimensional strut-tie models, design criteria of ACI 318-02, ACI-ASCE committee 352 and Park and paulay, and softened strut-tie model approach. The analysis results obtained from the 3-dimensional strut-tie models were compared with those obtained from the other approaches, and the validity of the approach implementing 3-dimensional strut-tie models were examined.

• 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 Earthquake Engineering Society of Korea Conference
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• 2005.03a
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• pp.145-152
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• 2005

This paper presents a deformable strut-and-tie model of determining the shear strengths and ultimate deformations of the shear-dominant reinforced concrete members. The proposed model originates from the strut-and-tie model concept and satisfies equilibrium, compatibility, constitutive laws, and the geometric conditions of shear deformation. This study attempts to apply deformation patterns to strut-and-tie models. The yielding of flexural reinforcements determines yielding states and the ultimate states of reinforced concrete coupling beam are defined as the ultimate compressive strain of struts and the degradation of compressive strength due to principal tensile strain of struts. The validity and accuracy of the proposed model is then tested against available experimental data. The parameters reviewed include the ratios of truss action and arch action, the reinforcement ratios, and the shear span-depth ratio. It is expected that this model can be applied to displacement-based design methods.