• Steel and Composite Structures
• /
• v.16 no.5
• /
• pp.481-489
• /
• 2014

The function of carbon fibre reinforced polymer (CFRP) reinforcement in increasing the ductility of reinforced concrete (RC) deep beam is important in such shear-sensitive RC member. This paper aims to investigate the effect of CFRP-strengthening on the energy absorption of RC deep beams. Six ordinary RC deep beams and six CFRP-strengthened RC deep beams with shear span to the effective depth ratio of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 were tested till failure in this research. An empirical relationship was established to obtain the energy absorption of CFRP-strengthened RC deep beams. The shear span to the effective depth ratio and growth of energy absorption of CFRP-strengthened deep beam were the significant factors to establish this relationship.

• Structural Engineering and Mechanics
• /
• v.77 no.2
• /
• pp.273-291
• /
• 2021

The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of disturbed regions ('D' regions) of reinforced concrete members such as in corbels and deep beams, where traditional flexure theory does not apply. This paper evaluates the applicability of the equilibrium based STM in strength predictions of deep beams (with rectangular and circular cross-section) and corbels using the available experiments in literature. STM is found to give fairly good results for corbel and deep beams. The failure modes of these deep members are also studied, and an optimum amount of distribution reinforcement is suggested to eliminate the premature diagonal splitting failure. A comparison with existing empirical and semi empirical methods also show that STM gives more reliable results. The nonlinear finite element analysis (NLFEA) of 50 deep beams and 20 corbels could capture the complete behaviour of deep members including crack pattern, failure load and failure load accurately.

• Computers and Concrete
• /
• v.16 no.3
• /
• pp.357-380
• /
• 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
• /
• 2001.05a
• /
• pp.189-194
• /
• 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

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

• Proceedings of the Korea Concrete Institute Conference
• /
• 2004.11a
• /
• pp.385-388
• /
• 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.

• Computers and Concrete
• /
• v.15 no.1
• /
• pp.21-35
• /
• 2015

The objective of this study is to examine the effect of carbon fiber reinforced polymer (CFRP) on the shear strengths of deep beams with web openings. A total of 18 high-strength concrete deep beams with web openings were tested. Twelve were externally wrapped with four layers of CFRP, six of them strengthened in the horizontal direction and the others in the vertical direction. The parameters of the configuration of CFRP, the sizes of the openings and the locations of the openings were covered in this study. The test results indicates the shear strengths of deep beams with openings sized $60{\times}40mm$ were about 16% higher than that with openings sized $68{\times}68mm$. For deep beams with openings sized $60{\times}40mm$, the lower the locations of openings the higher the shear strengths were. The test results also indicate the shear strengths of deep beams with web openings strengthened by CFRP wrapped in the vertical direction can be enhanced by about 10%. However, the shear strengths of deep beams with web openings strengthened by CFRP wrapped in the horizontal direction can only be enhanced by about 6%. The shear strengths of deep beam, with different size and location of web openings and strengthened by different configuration of CFRP can be reasonably predicted by the empirical formulas of Kong and Sharp.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.6
• /
• pp.699-708
• /
• 2007

Reinforced concrete deep beams are general structural members used as transfer-girder, pile cap, foundation wall and so on. They have a complex stess formation. Generally, failure mechanisms differ from either continuous deep beams or simple supported deep beams. In continuous deep beams, a negative moment is occurred over intermediate support and the location of maximum moment coincide with high shear force. Therefore, failure usually occurs at this region. While on the other hand, in simple supported deep beam, the region of high shear coincides with the region of low moment. The web opening of deep beams for accepting a facility makes shear behaviors of deep beams more complex and gives rise to an expansion of crack around the opening and a decline of shear capacity of deep beams. Therefore, Engineers must determine a delicate reinforcement method to control a crack and increase a shear capacity. The purpose of this report is a computation of an effective reinforcement method through non-linear finite element method by means of adopting various reinforcement method as variables and a computation of shear capacity formula taking an effectiveness of reinforcement into consideration.

• Computers and Concrete
• /
• v.13 no.1
• /
• pp.135-147
• /
• 2014

Strut-and-tie model (STM) has been recommended by many codes and standards as a rational model for discontinuity regions in structural members. STM has been adopted in ACI building code for analysis of reinforced concrete (RC) deep beams since 2002. However, STM recommended by ACI 318-11 is only applicable for analysis of ordinary RC deep beams. This paper aims to develop the STM for CFRP strengthened RC deep beams through the strut effectiveness factor recommended by ACI 318-11. Two sets of RC deep beams were cast and tested in this research. Each set consisted of six simply-supported specimens loaded in four-point bending. The first set had no CFRP strengthening while the second was strengthened by means of CFRP sheets using two-side wet lay-up system. Each set consisted of six RC deep beams with shear span to effective depth ratio of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00.The value of strut effectiveness factor recommended by ACI 318-11 is modified using a proposed empirical relationship in this research. The empirical relationship is established based on shear span to effective depth ratio.

• Architectural research
• /
• v.7 no.2
• /
• pp.55-60
• /
• 2005

Based on an experimental study, this study provides an equation to describe the shear strength of high-strength concrete deep beams with rectangular openings and without web reinforcements. Twenty-four concrete deep beams were tested with the variables of concrete strength, size of web opening, and shear span-to-depth ratio. The proposed equation is expressed as the sum of the shear strength provided by longitudinal bars and concrete. It is illustrated that the proposed equation predicts the load-carrying capacity of the deep beams more properly than the experimental equations proposed by other researchers.