• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.259-267
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• 2008

The ultimate strengths of reinforced concrete deep beams are governed by the capacity of the shear resistance mechanism composed of concrete and shear reinforcing bars, and the structural behaviors of the beams are mainly controlled by the mechanical relationships according to the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strengths and complicated structural behaviors is presented for the design of simply supported reinforced concrete deep beams. In addition, a load distribution ratio, defined as a magnitude of load transferred by a vertical truss mechanism, is proposed to help structural designers perform the design of simply supported reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of a load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the prime design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete influencing the ultimate strength and behavior are reflected upon based on various and numerous numerical analysis results. In the companion paper, the validity of presented model and load distribution ratio was examined by employing them to the evaluation of the ultimate strengths of various simply supported reinforced concrete deep beams tested to failure.

• Computers and Concrete
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• v.5 no.2
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• pp.117-134
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• 2008

An experimental and numerical research was conducted to gain a deeper insight on the structural behaviour of deep-beams with indirect supports and to assess the size effects in the ultimate state behaviour. The experimental campaign focused on the influence of the reinforcement tie distribution height on the compression check of the support region and on the benefits of using unbonded prestressing steel. Three reduced scale specimens were tested and used to validate the results obtained with a nonlinear finite element model. As a good agreement could be found between the numerical and the experimental results, the numerical model was then further used to perform simulations in large scale deep-beams, with dimensions similar to the ones to be adopted in a practical case. Two sources of size effects were identified from the simulation results. Both sources are related to the concrete quasi-brittle behaviour and are responsible for increasing failure brittleness with increasing structural size. While in the laboratory models failure occurred both in the experimental tests as well as in the numerical simulations after reinforcement yielding, the numerically analysed large scale models exhibited shear failures with reinforcement still operating in the elastic range.

• Steel and Composite Structures
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• v.42 no.3
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• pp.299-313
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• 2022

Steel-concrete-steel composite structures with bidirectional webs (SCSBWs) are used in large-scale projects and exhibit good mechanical performances and constructional efficiency. The shear behaviors of SCSBW deep beam members in key joints or in locations subjected to concentrated forces are of concern in design. To address this issue, experimental program is investigated to examine the deep-beam shear behaviors of SCSBWs, in which the cracking process and force transfer mechanism are revealed. Compared with the previously proposed truss model, it is found that a strut-and-tie model is more suitable for describing the shear mechanism of SCSBW deep beams with a short span and sparse transverse webs. According to the experimental analyses, a new model is proposed to predict the shear capacities of SCSBW deep beams. This model uses strut-and-tie concept and introduces web shear and dowel action to consider the coupled multi mechanisms. A stress decomposition method is used to distinguish the contributions of different shear-transferring paths. Based on case studies, a simplified model is further developed, and the explicit solution is derived for design efficiency. The proposed models are verified using experimental data, which are proven to have good accuracy and efficiency and to be suitable for practical application.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.40-46
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• 1996

Three procedures are currently used for the design of deep beams, which are Empirical design method, Nonlinear analysis, and Truss models. The engineering logic and decisions inherent in these design procedures are dependent on the acquired knowledge and experience of the structural engineer. Knowledge-based system is useful to solve problems which require human experties. Therefore, this study presents an application of Knowledge-Based System for design of reinforced concrete deep beams with web openings.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.3-12
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• 2011

The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for 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 is introduced to ensure a 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 concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.

• Journal of the Korea Concrete Institute
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• v.19 no.2
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• pp.171-178
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• 2007

Twelve reinforced concrete continuous deep beams having web openings within interior shear spans were tested to failure. All beams tested had the same geometrical dimensions. The main variables investigated were the opening size and amount of inclined reinforcement around openings. An effective inclined reinforcement factor combining the influence of the opening size and amount of inclined reinforcement on the structural behavior of the beams tested is proposed. It was observed that the load distribution, diagonal crack width, and load capacity of beams tested were greatly dependent on the effective inclined reinforcement factor which ranged from 0 to 0.171 for the test specimens. The higher this factor, the smaller the diagonal crack width and its development rate. A higher load capacity also developed in beams having effective inclined reinforcement factor above 0.077 than in the corresponding solid deep beams. A numerical technique based on the upper bound analysis of the plasticity theory is proposed to evaluate the load capacity of continuous deep beams having openings within interior shear spans. Predictions obtained from the proposed formulas are in good agreement with test results.

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• Steel and Composite Structures
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• v.43 no.1
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

• Journal of the Korea Concrete Institute
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• v.15 no.5
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• pp.689-696
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• 2003

Recently, Appendix A of ACI 318∼02 Code introduced the Strut-and-Tie Model(STM) procedure in shear design of deep flexural members. The STM procedure is widely used in the design of concrete regions where the distribution of longitudinal strains is significantly nonlinear, such as deep beams, beams with large openings, corbels, and dapped-end beams. Experimental study included five high-strength reinforced concrete deep beams with different detailing schemes for the horizontal and vertical reinforcement. The specimens were designed as simply supported beams subjected to concentrated loads on the top face and supported on the bottom face. At failure, all specimen exhibited primary diagonal crack running from the support region to the point load. Specimens which had mechanical anchorages(terminators) gives better representation of the load-carrying mechanism than the specimen had standard 90-degree anchorage at failure in deep flexural members. Based on the test results, shear design procedures contained in the ACI 318-99 Code, Appendix A of the ACI 318-02 Code, CSA A23.3-94 Code and CIRIA Guide-2 were evaluated. The Shear design of ACI 318-99 Code, Appendix A of the ACI 318-02 Code and CIRIA Guide-2 shown to be conservative predictions from 10% to 36% in the shear strength of the single-span deep beam which was tested. ACI 318-99 Code was the lowest standard deviation.