Continuous Deep Beams Research Articles

Advances and applications of the strut-and-tie method in reinforced concrete design: A state-of-the-art review

The Strut-and-Tie Method (STM) is a versatile and powerful approach widely used in the design and analysis of reinforced concrete structures, particularly in regions with complex stress distributions and discontinuities. This review article delves into the theoretical foundations, practical applications, and experimental validations of the STM. The article begins by exploring the fundamental principles of the STM and its historical development, with a focus on its application in predicting the capacity of reinforced concrete members. Additionally, the STM efficacy in designing deep beams and comparisons with other analytical methods are thoroughly examined. Notably, the review includes a discussion on the application of STM in concrete beams, highlighting its ability to accurately predict capacity. Several studies investigating the behavior of reinforced concrete deep beams with openings, shear-strengthened deep beams, and continuous deep beams using the STM approach are critically analyzed, providing valuable insights into its reliability and practicality. Furthermore, the review delves into advancements in computational tools and finite element analyses that have been integrated with the STM, offering a more comprehensive and robust approach to design and analysis. The article also evaluates practical applications of STM in engineering scenarios, such as the design of bridge pier caps and complex regions, showcasing its versatility and adaptability. In conclusion, this review underscores the pivotal role of the Strut-and-Tie Method in modern reinforced concrete design and analysis. It serves as a valuable resource for engineers, researchers, and practitioners seeking to apply this method effectively in various structural configurations and challenging scenarios. Ultimately, the article emphasizes the significance of STM as a reliable and efficient tool for optimizing the design and ensuring the safety and performance of reinforced concrete structures.

Synergistic effects of web reinforcement and hybrid fibres on shear performance of continuous deep beams with unsymmetrical web openings

Application of fibre-reinforced concrete or novel web reinforcement detailing could be an effective way to enhance structural behaviour of continuous deep beams with web openings. However, there are very few experimental works studying the synergistic effects of these two methods. Therefore, an experimental programme is introduced in this paper to study synergistic effects of shear reinforcement and hybrid fibres on shear strength of nine double-span deep beams with unsymmetrical web openings (denoted as pierced span). The test specimens were designed to consist of a pierced beam span with a web opening and an adjacent solid beam span. The spans with openings were designed with different shear reinforcement configurations. It was experimentally shown that provision of sufficient web steels above and below web openings has the most important and beneficial effect on ultimate shear strength of the pierced spans. Besides, a tailored steel reinforcing method was also proposed that is capable of improving strut capacity near the web opening. In addition, adoption of hybrid fibre reinforcement led to enhanced crack-opening resistance, ultimate shear strength and shear deformation. Based on the research outcomes, it was recommended to adopt the proposed detailing method or fibre reinforcement dosage for shear strength enhancement of continuous deep beams with web openings. Furthermore, an analytical model was adopted to the shear strength of continuous deep beams accounting for web openings, steel stirrups, and hybrid fibres, which yielded safe predictions.

Experimental and numerical study of high strength reinforced concrete continuous deep beams with circular and rectangular openings

Many modern structures require openings in the reinforced concrete (RC) beams, especially deep beams, to pass utility pipes such as sanitary, electronic, water, communications, and electrical services, especially in low floor heights. Since most of the beams are continuous and use high-strength concrete (HSC), this study investigates the effect of creating two post-construction openings in two-span HSC continuous deep beams. Five two-span HSC beams of 150 (width) × 400 (depth) × 2640 mm were cast, with each span of 1120 mm. The main variables investigated were the shape and location of openings. The circular opening was large of 150 mm diameter and the height and area of the rectangular openings were kept the same. Both openings were located either in one span or one opening in each span having asymmetrical layout. Each opening was located in the critical shear zone at the strut lines, as it is the most critical location in deep beams. The HSC continuous beams were tested till total collapse under two point loads acting at mid of the beam spans. The performance of beams having openings was compared with the reference beam having no opening. The presence of the two openings in the same span caused 38% reduction in failure load irrespective of the shape of opening. For the second opening layout having one opening in each span, the reduction was slightly higher but almost the same for the two shapes of openings (41% for circular and 45% for rectangular opening). To assess the load capacity of HSC continuous deep beams having circular and rectangular openings, 3D numerical models were prepared. The numerical results were compared with the experimental values, which were found to exhibit good agreements.

Experimental and Statistical Capacity of Rubberized Continuous Deep Beams under Monotonic and Repeated Load

Continuous Deep Beams (CDBs) are highly exposed to repeated loads especially at the bridges during vehicle loads and adding rubber into it support the ductility to overcome concrete brittleness. Six Beams were designed in considering the strut tie method (STM) and tested under monotonic and repeated loads. Mathematical model for such problem has been investigated. It can be concluded that, the CDBs lose some of its ultimate capacity due to the dropping of concrete compressive strength after aggregate-rubber replacement, while an increment in the deflection could be seen due to the higher deformability of the rubcrete mix i.e., the concrete gained some flexibility after replacing. Also, the ultimate strength of the beams decreases when comparing with the static loads by 14%, 8% and 9% for conventional beam, gravel and sand replacement beams respectively. Fuzzy regression system offers a polynomial from the third degree to represent the Fuzzy data of the CDBs.

Experimental and Numerical Study of UHPFRC Continuous Deep Beams with Openings

To study the performance of UHPFRC continuous deep beams with openings, experimental and numerical investigations have been carried out. The test program included seven continuous deep beams with openings, in addition to one similar solid beam. The variables were the ratio of transverse reinforcement and the position, height, and width of the opening. The results showed that the failure mode of UHPFRC two-span continuous deep beams depends mainly on the position and size of the opening in the shear span. The shear failure occurs in the diagonal strut between the support and the applied force through the opening edges. The maximum spacing between stirrups (sv,max) of ACI 318-2019 was not suitable for UHPFRC. Providing stirrups with spacing 129% greater than sv,max of ACI 318-2019 had a slight effect on the failure load. Web openings of 20% of beam height reduced the failure load by 31.6% to 43.0% compared with a similar solid beam. For specimens with the same opening height and position, increasing the width of the opening by about 75% more than that of a similar beam reduced the failure load by about 27.8%. The proposed 3-D numerical model successfully predicted the failure load and performance of UHPFRC continuous deep beams.

Shear behavior of two-span continuous concrete deep beams reinforced with GFRP bars

To investigate the shear behavior of reinforced concrete (RC) continuous deep beams with glass fiber reinforced polymer (GFRP) bars, four large-scale beams with a constant shear span-to-overall depth ratio of 1.2 and different GFRP shear reinforcement ratios were tested. Digital image correlation technology was used to track the kinematics of diagonal shear cracks in the shear span. It was found that the moment redistribution in the deep beams was very limited. A tie-arch action was confirmed in the tested deep beams with the crack propagation and the strains developed in longitudinal reinforcements. For the beams without GFRP stirrups, the aggregate interlock contribution constituted 46.3% of the total shear resistance. For the beams with GFRP stirrups, however, the shear contribution of aggregate interlock was less significant. As the GFRP shear reinforcement ratio increased from 0% to 0.47%, the failure mode changed from shear compression failure to compression strut failure. As the shear GFRP reinforcement ratio increased from 0.24% to 0.32% and 0.47%, the load-carrying capacity increased by 35.5% and 73.5%, respectively. The minimum required GFRP shear reinforcement in ACI 440.1R-15 was ineffective for the tested GFRP-RC continuous deep beams in terms of shear capacity enhancement and shear crack control. Finally, a database of shear tests on continuous GFRP-RC beams was collected to assess the ability of strut-and-tie methods in three code guidelines.

Shear strength evaluation of RC D-Regions based on Single-Panel Strut-and-Tie model

In existing shear test databases of reinforced concrete D-regions (discontinuity or disturbance regions), most data points are concentrated in parameter ranges of high main reinforcement ratio, small overall dimensions, or low concrete strength. Based on regression analysis of these databases, large model errors in effective coefficients of strut compressive strength (hereafter referred to as strut coefficients) for strut-and-tie models (STMs) have been obtained. In this study, a uniformly distributed (or unbiased) large-scale shear database is generated through a mechanics-based cracking strut-and-tie model (CSTM), which has been validated against extensive test results. Then a strut coefficient with a simple form and comprehensive consideration of various design parameters is proposed through regression analysis. On the other hand, the traditional STM presents a tedious design procedure and uncertainty in structural reliability caused by the subjectivity in geometric modeling. In order to simplify the design procedure and eliminate the uncertainty, a unified shear design equation based on the strut coefficient is proposed for D-regions that the single-panel STM can well simulate. The accuracy of the unified equation is verified by an extensive shear test database consisting of simple and continuous deep beams, corbels, squat shear walls, and short coupling beams.

Diagonal Tension Cracking Strength and Risk of RC Deep Beams

This study focuses on the shear serviceability of simple and continuous reinforced concrete deep beams. The test results of 81 simple deep beams (i.e., simply supported single-span deep beams) and 29 continuous deep beams, for which their diagonal tension cracking loads were reported, were collected from existing studies. On this basis, the diagonal tension cracking mechanism is discussed, and four existing models for diagonal tension cracking are evaluated. The evaluation results show the existing models fail to accurately reflect the influences of the main design parameters (including the shear span-to-effective depth ratio and main tensile reinforcement ratio) on the diagonal tension cracking strength. Therefore, a new equation for the diagonal tension cracking strength for simple and continuous deep beams is proposed. The proposed equation is verified to be superior to the existing models, showing an average value and a coefficient of variation for tested-to-predicted diagonal tension cracking strength ratios of 1.02 and 0.21, respectively. On the other hand, a probabilistic analysis is conducted to evaluate the diagonal tension cracking risk under service load, showing that 35% of deep beams exhibited a diagonal tension cracking load that is less than the service load, which indicated that diagonal cracks easily occur in RC deep beams under service loads.

Response of Rubcrete Continuous Deep Beams under Sinusoidal Loads

Continuous deep beams (CDBs) are the most used members in constructions with highly exposing to different types of dynamic loads. It is well known that; the concrete is a brittle material and has a weak resistance to energy absorption. Using scrapped tire rubber enhances the concrete energy absorption for sustainability purposes. Timoshenko beam theory has been used to solve CDBs subjected to sinusoidal load and has been adopted for verification of numerical results of ANSYS APDL V.15.0. Seven concrete mixes have been simulated with different types and amounts of aggregate – rubber replacements. Several parameters have been studied like replacing type, percentages, shear span of beam to depth ratio (a/h) and load intensity. It was found that Timoshenko beam theory can be used for harmonic loading CDBs. Furthermore, replacement in general provided more ductility due to rubber elasticity property. Gravel replacement by 45% has the larger displacement values among the other types. Also, it has been noted that, the sensitive of concrete deep beams towards a/h ratio stills considerable for harmonic loads, i.e. minimizing the ratio leads to decrementing the deflection wave amplitudes.

Continuous Deep Beams Behavior Under Static Loads: A Review Study

Few studies discussed the continuous deep beams CDB behaviour in spite of its great importance in building constructions due to the usual use in bridges and tall buildings as a load distributer. The behaviour of CDB shows a different behaviour when comparing with the simply supported one, so the expected behaviour of SDB does not match with the CDB. So, this paper deals with reviewing the behaviour of CDB in the past researches. It has been concluded that, the CDB resist the applied loads by flexural and shear together, the flexural behaviour appears at the first loading stage then the beam start to resist by shear capacity. The amount of resistance of beam by flexural depends on a/h ratio, main and web steel reinforcement and concrete compressive strength. Flexural behaviour may not appear for very small a/h ratio or over main reinforcement. Also, main steel reinforcement at both top and bottom of beam does not reach to yielding point expected one case, which is, the main steel ratio is less than 0.6%, thereby, tie failure will governs.

An Experimental and Numerical Study on Continuous RC Deep Beams Strengthened with CFRP Strips

An Experimental and Numerical Study on Continuous RC Deep Beams Strengthened with CFRP Strips

Numerical Study on Nonlinear Behavior of RC Continuous Deep Beams

The aim of the study is to demonstrate the extent of the effect that occurs to continuous reinforced deep beams when performing a parametric study in terms of support settlement and different support conditions for dual span continuous deep beams (CDBs), in terms of failure load and failure mode, using the ANSYS 2020 nonlinear finite element program. As the parametric study relied on the laboratory study conducted by Yang et al. [8]. Six samples were taken from continuous reinforced concrete beams with two spans with the extension of the shear to the depth ratios (0.5, 1). This was done to ensure that the form was handled appropriately. The pre-owned model to research the behavior of deep RC girders under static support conditions with different beam heights. Whereas, it was observed that there is a marked variation in the value of the failure load under the influence of different support conditions and the support settlement that occurs in them. This inspection is characterized by real, conceivable results of support conditions and support settlement in presenting two span continuous reinforced concrete deep beams.

Utilising PET Bottle Fibers in the production of Concrete

This study attempts to apply the concept of sustainability by reducing the environmental pollution of plastic waste, especially Polyethylene Terephthalate (PET) that are used in production soft drinks bottles. The plastic bottles were collected, roughened) Roughen the surface by using a metal clip after exposing it to heat, and then place it on smooth surfaces) and shredded into fibres of specific size and shape with an aspect ratio (L/D) of 34.5. Various proportions of PET (i.e. 0.5, 1.0, and 1.5%) have been used in the production of ordinary concrete. The influence of PET fibers on the properties of concrete was studied, such as workability, compressive and splitting tensile strengths. Furthermore, the shear characteristics of continuous reinforced concrete deep beams with dimensions of (150×300×2000) mm produced from such concrete were also investigated. For all percentage of replacements, The fresh property, compressive strength, and tensile strength of PET fibre encapsulated cement concrete were investigated. With the addition of plastic fibre, compressive strength increased marginally, but tensile strength measurements showed a substantial improvement over the control specimen. it has been found that there was an apparent impact of waste plastic fibers on the structural behavior of the investigated beams in terms of its brittleness. The increase in the ultimate load capacity With the increase in the percentage of fiber until a percentage(1%), then it begins to decrease after this percentage of continuous deep beams refers to the use of waste plastic fibers to improve the tensile properties of concrete and to limit the spread and width of cracks within the structure.

Structural Behavior of Retrofitted Reinforced SCC Continuous Deep Beam With CFRP and Hybrid Techniques

In this research, the results of experimental test of seven reinforced SCC continuous deep beams after being retrofitting by CFRP with different techniques. The main objective of the current research is to investigate the structural behavior in the shear performance and failure modes. The first beam tested up to failure and assumed as reference beam, while remaining six beams firstly loaded with 65% of ultimate load capacity then retrofitted by three systems namely: externally bonded reinforcing (EBR) by CFRP strips, near surface mounted technique (NSM) CFRP rods and the third system was hybrid technique by composite between EBR CFRP strips and NSM CFRP rods. The experimental results show that applying the EBR CFRP strips in a vertical direction improved the loading capacity in comparison with the horizontal direction. On the other hand, the NSM CFRP rods applied in horizontal direction presented higher values in both ultimate loading capacity and final deflection, where the increasing in ultimate load capacity about 43.48%, and the increasing in deflection about 33.5% compared with control beam. Therefore, it can be concluded that applying the hybrid technique is more efficient when the EBR strips and NSM bars applied in the vertical, and the horizontal directions, respectively.

Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips.

To accommodate utilities in buildings, different sizes of openings are provided in the web of reinforced concrete deep beams, which cause reductions in the beam strength and stiffness. This paper aims to investigate experimentally and numerically the effectiveness of using carbon fiber reinforced polymer (CFRP) strips, as a strengthening technique, to externally strengthen reinforced concrete continuous deep beams (RCCDBs) with large openings. The experimental work included testing three RCCDBs under five-point bending. A reference specimen was prepared without openings to explore the reductions in strength and stiffness after providing large openings. Openings were created symmetrically at the center of spans of the other specimens to represent 40% of the overall beam depth. Moreover, finite elements (FE) analysis was validated using the experimental results to conduct a parametric study on RCCDBs strengthened with CFRP strips. The results confirmed reductions in the ultimate load by 21% and 7% for the un-strengthened and strengthened specimens, respectively, due to the large openings. Although the large openings caused reductions in capacities, the CFRP strips limited the deterioration by enhancing the specimen capacity by 17% relative to the un-strengthened one.

Shear Capacity of Glass Fiber-Reinforced Polymer- Reinforced Concrete Continuous Deep Beams without Web Reinforcement

Shear Capacity of Glass Fiber-Reinforced Polymer- Reinforced Concrete Continuous Deep Beams without Web Reinforcement

Reinforcing struts and ties in concrete continuous deep beams

This work proposed reinforced concrete two-span continuous deep beams by replacing the well-known conventional reinforcement by reinforcing struts and ties only and omitting the concrete where the struts and ties do not pass through. The strut and tie modelling recommended by ACI 318M-14 was adopted herein. The struts and ties were reinforced as compressive and tensile members, respectively. Twelve specimens, which were divided into four groups, were cast and tested. In every group, the first specimen was a conventionally reinforced reference beam, the second specimen was a specimen in which only the stress paths of the struts and ties were reinforced, and the third specimen was the proposed frame. The strut-tie angle, specimen width and loading type were taken into consideration as main parameters. Generally, the proposals gave less load capacity than the reference specimens, but they remained higher than the design load. In addition, the proposed specimens significantly reduced the weight.

Loading Capacity Prediction of Rubberized Reinforced Concrete Continuous Deep Beams

Results of fourteen two-span continuous concrete deep beams were presented and discussed in this research. One sample was designed as a reference to be an ordinary reinforced concrete beam (ORC) while thirteen samples were made of rubberized concrete (RRC). The investigated parameters were the shear span/overall depth ratio (a/h) and the rubber replacement ratio with the fine and coarse aggregate. The volumetric replacement ratios were 0, 5%, 10%, 15%, and 20% of the fine aggregate while the coarse aggregate content was kept constant. The same replacement ratios were used for the coarse aggregate. Two shear span/overall depth ratios were used of 1.66 and 1.33.All beams showed the main crack formatted diagonally between the intermediate support and the applied load, indicating a shear failure. The excluded results were compared with those calculated by the strut and tie methods (STM) of the American and Euro codes. It was found that the predicted results of the American and European standards were conservative with mean values of experimental/calculated results of 1.29 and 1.24, respectively. Additionally, the effectiveness factors of the STM suggested by different researchers have been examined. It was found that those approaches were incapable to reflect the effects of the size and amount of rubber used in this study. Therefore, another effective factor was recommended to meet the requirements investigated in the current study. A respectable convergence between the predicted and the experimental results was found in which the mean and coefficient of variation values were 1.004 and 1.158%, respectively.

Theoretical and Experimental Studies of Two‐Span Reinforced Concrete Deep Beams and Comparisons with Strut‐and‐Tie Method

Regarding the complicated behavior of continuous deep beams, a research program including three parts was conducted. First part: three continuous concrete deep beams with different shear span‐to‐depth ratios (a/h) were tested. The effects of varying a/h ratio on ultimate strength and failure modes were investigated. Second part: the nonlinear finite element (FE) analyses were performed to simulate the experimental specimens and 21 large‐scale continuous deep beams. The main parameters investigated were a/h ratio from 0.33 to 2 and considered 40 MPa, 60 MPa, and 80 MPa. Third part: the strut‐and‐tie modeling of different design codes and indeterminate strut‐tie method were studied for continuous deep beams. Regardless of the a/h ratio, all beam specimens failed in shear mode with main diagonal cracks. Although EC2 load prediction was conservative for all beam models, the ACI and CSA predictions for concrete deep beams with high compressive strength were unsafe. The indeterminate truss model showed closer results to FE analysis in comparison with ACI, EC2, and CSA strut‐and‐tie method.

Effect of Large Openings on the Behavior of Reinforced Concrete Continuous Deep Beams under Static and Repeated Load

This paper aims to investigate the behavior of the existence of large openings on reinforced concrete continuous deep beams (RCCDBs) under static and limited cycles of repeated load. The experimental work included testing seven RCCDBs. One of these beams was solid subjected to static load, while the other beams having external shear spans, internal shear spans, and mid-span openings subjected to static and fifteen cycles of repeated loading. The range of the repeated loading was varied between a lower level and an upper level, equal to 30 and 70 percent, respectively, of the ultimate load of the beam subjected to static load. All test specimens were tested under five-point bending. For beams with large openings, 160×160 mm (which represents 40% of the overall depth of the section) openings were created symmetrically at various locations. Experimental results showed that the maximum ultimate loads of beams with large openings were decreased by about 36% for beams with large openings locating at interior shear spans compared to a solid beam. However, the maximum reduction in ultimate load of the beam with a large opening subjected to repeated load was about 6%.