• 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.

• Advances in concrete construction
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• v.13 no.1
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• pp.1-10
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• 2022

Concrete is a brittle material and weak in tension. Traditionally, web reinforcement in the form of vertical stirrups is used in reinforced concrete (RC) beams to take care of principal stresses that may cause failure when they are subjected to shear stresses. In recent decades, the potential of various types of fibers for improving post-cracking behavior of RC beams and replacing stirrups completely or partially have been studied. It has been shown that the use of steel fibers randomly dispersed and oriented in concrete has a significant potential for enhancing mechanical properties of RC beams. However, the studies on deep steel fiber reinforced concrete (SFRC) beams are limited when compared to those focusing on slender beams. An experimental program consisting of three RC and nine SFRC deep beams without stirrups were conducted in this study. Besides, various models developed for predicting the ultimate shear strength and diagonal cracking strength of SFRC deep beams without stirrups were applied to experimental data obtained from the literature and this study.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.393-396
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• 2004

The objective of this experimental study is to understand the shear behavior of reinforced concrete continuous deep beams. The main variables considered were concrete strength and shear span-to-depth ratio. Specimens of 4 two-span continuous deep beams were tested and compared with the strength of simple span beams. The results show that the influence of concrete strength on the shear strength of continuous deep beams is comparable to that on simple span deep beams. However, the effect of span-to-depth ratio is significantly greater than simple span deep beams.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.189-194
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• 2001

In this study, ultimate strength of concrete deep beams with an opening is predicted by using Strut-and-Tie Model with a new effective compressive strength. First crack occurs around an opening by stress concentration due to geometric discontinuity. This results in decreasing ultimate strength of deep beams with an opening compared with general deep beams. With fundamental notion that ultimate strength of deep beam with an opening decreases as a result of reduction in effective compressive strength of a concrete strut, an equivalent effective compressive strength formula is proposed in order to reflect ultimate strength reduction due to an opening located in a concrete strut. An equivalent effective compressive strength formula which can reflect opening size and position is added to a testified algorithm of predicting ultimate strength of concrete deep beams. Therefore, ultimate strength of concrete deep beam with an opening is predicted by using a simple and rational STM algorithm including an equivalent effective compressive strength formula, not by finite element analysis or a former complex Strut-and-Tie Model

• Smart Structures and Systems
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• v.16 no.3
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• pp.497-519
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• 2015

This study discusses the use of Adaptive-Network-Based-Fuzzy-Inference-System (ANFIS) in predicting the shear strength of reinforced-concrete deep beams. 139 experimental data have been collected from renowned publications on simply supported high strength concrete deep beams. The results show that the ANFIS has strong potential as a feasible tool for predicting the shear strength of deep beams within the range of the considered input parameters. ANFIS's results are highly accurate, precise and therefore, more satisfactory. Based on the Sensitivity analysis, the shear span to depth ratio (a/d) and concrete cylinder strength ($f_c^{\prime}$) have major influence on the shear strength prediction of deep beams. The parametric study confirms the increase in shear strength of deep beams with an equal increase in the concrete strength and decrease in the shear span to-depth-ratio.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.451-456
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• 2003

The behavior of concrete deep beams in shear is substantially influenced by beam size and shape, loading conditions, reinforcement details, and material properties. Therefore, it is not easy to predict the ultimate response of beams correctly and take into account all those factors in practical shear design. In this study, a grid softened strut-tie model approach for determining the shear strengths of various reinforced concrete deep beams is proposed. The validity of the approach is examined through the strength analysis of numerous reinforced concrete deep beams tested to failure. The approach can be further developed to improve the current deep beam design procedures by incorporating the actual shear resisting mechanisms of deep beams.

• Computers and Concrete
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• v.15 no.3
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• pp.357-372
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• 2015

This study reports the test results of twelve reinforced concrete deep beams. The deep beams were tested with loads applied through and supported by columns. The main variables studied were the shear span-to-depth ratios, and the horizontal and vertical stirrups. The shear strengths can be effectively enhanced for deep beams reinforced with both horizontal and vertical stirrups. The test results indicate the shear strengths of deep beams increase with the decrease of the shear span-to-depth ratios. The normalized shear strengths of the deep beams did not increase proportionally with an increase in effective depth. An analytical method for predicting the shear strengths of deep beams is proposed in this study. The shear strengths predicted by the proposed method and the strut-and-tie model of the ACI Code are compared with available test results. The comparison shows the proposed method can predict the shear strengths of reinforced concrete deep beams more accurately than the strut-and-tie model of the ACI Code.

• 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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• 2004.11a
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• pp.385-388
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• 2004

To understand of size effect in high-strength reinforced concrete continuous deep beams, 6 specimens with section overall depth ranging from 400 to 720mm were tested. Test results indicated that the size effect of continuous deep beams is slightly greater than in simply supported deep beams.