Innovative Reinforced Concrete Deep Beam Analysis Using Improved Strut-and-Tie Method

Deep beams are common elements in concrete structures such as bridges, water tanks, etc. Deep beams were designed by using the strut-and-tie model (STM) method without any web reinforcement using ACI 318-14 with a shear span to depth ratio (a/d =1). RC deep beams show brittle failure by crushing of struts under applied load. Fiber reinforced concrete (FRC) is a better alternative for the reinforced concrete beam without web reinforcement as it contains fibers such as a ramid, steel, etc. The fibers used were steel fibers of 1% volume, and aspect ratio of 60. The use of carbon fiberreinforced polymer (CFRP) for strengthening the deep beams is utilized and a comparison between reinforced concrete(RC) and fiber-reinforced concrete (FRC) deep beams with and without CFRP strengthening is carried out using (Analysis of Systems) ANSYS 18.1. The mid-span deflections were significantly decreased and improved shear strength was observed in CFRP strengthened deep beams and FRC deep beam in comparison of RC deep beam. The ultimate loads for a maximum deflection value were compared in all the deep beams and RC frame with embedded carbonfiber reinforced polymer (RC-CFRP), fiber reinforced concrete carbon-fiber reinforced polymer(FRC-CFRP) and FRC deep beams showed 29.4%, 42.47% and 32.05% improvement, respectively, when compared with the RC deep beam. A total of 43.4% decrease in deflection and 74% decrease in shear stress was observed in FRC deep beam. The deflection and stress values in strengthened beams were comparatively lesser. In this study, deflection was observed to decrease by 74.4% and 82%, and shear stress decreased by 92% and 93.5% in the strengthened RC and FRC deep beam, respectively, compared to the deep beam RC model. It is suggested that strengthened FRC is a better alternative to RC deep beams.

Reinforced Concrete (RC) deep beams are commonly used in structural design to transfer vertical loads when there is a vertical discontinuity in the load path. Due to their deep geometry, the force distribution within the RC deep beams is very different than the RC shallow beams. There are some strut and tie model (STM) already been developed for RC deep beams. However, most of these models are developed for RC deep beams with the simply supported boundary condition, which do not apply for RC deep beams with the fix-ended condition. In this paper, five fixed-end RC deep beams have been tested experimentally which were subjected to monotonic and cyclic loads. Also, a simple STM was proposed to simulate the load capacity and failure mode of fix-ended RC deep beams. The proposed STM has the main strut and sub struts to simulate the force distribution within the RC deep beams. This STM were verified using five fixed-end RC deep beams subjected to monotonic and cyclic loads and compared to the response of 31 additional independent experimental tests. The result shows the newly proposed STM can simulate the load capacity and failure mode of fix-ended RC deep beams very well.

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.

<p>Reinforced concrete (RC) deep beams are used as a structural member having a shear span to effective depth ratio of not exceeding 1.0 as well as for the application to frame structures, caisson foundations, and corbels. There is, however, a peculiar problem in the analysis of RC deep beams; the variety of supporting condition for RC deep beams induces various failure modes. The goal of this research is to identify the shear-resistant mechanism as well as the shear-load capacity of RC deep beams. To tackle with this objective, the research has focused on internal strain distributions of the RC deep beams under external loading. Based on experimental results, this paper concluded the failure mode and the load capacity of RC deep beams associated with supports condition and the specimen design.</p>

For the analysis and design of reinforced concrete (RC) deep beams, the strut-and-tie model is typically employed to simulate the flow of stresses. A bottle-shaped strut develops between the loading point and support, in which compressive stress spreads laterally and induces tensile strain in the transverse direction, which reduces the compressive strength of the strut significantly. Web reinforcements are provided in deep RC beams to prevent splitting of the diagonal strut due to the presence of these transverse strains. In this article, a simplified design procedure based on the strut-and-tie model (STM) is proposed for the evaluation of the shear capacity of deep beams with web reinforcement. The suggested model is based on modified compression field theory and considers the impact of shear reinforcement ratio, transverse tensile strain, post-cracking strength of concrete, and the actual dispersion of compressive stress based on strut geometry (aspect ratio) for strength prediction of bottle-shaped struts. The experimental results of RC panels and deep RC beams reported in the literature are used to validate the results of the suggested model. The findings demonstrate that the proposed STM evaluates the shear capacity of deep RC beams more precisely than capacities estimated by ACI 318-19, AASHTO LRDF, and Eurocode 2 (EC2). In addition, a comprehensive parametric study has been carried out to investigate the effect of various design parameters on the shear capacity of deep RC beams.

Reinforced Concrete (RC) deep beams perform better structurally when steel fibers are added, as this reduces the need for web steel reinforcements, boosts shear strength, and helps to bridge cracks. The current ACI 318-19 code does not include predicting shear strength models to account for the added steel fibers in Steel Fibers Reinforced Concrete (SFRC) deep beams without stirrups; therefore, structural engineers are less motivated to use them. To fill this gap, the databases of 281 RC and 172 SFRC deep beams were compiled, and the preliminary investigation of the collected databases revealed that (1) Longitudinal steel reinforcement significantly increases the shear strength of SFRC specimens, as the steel fibers make deep beams better at carrying loads by assisting them in bridging cracks; and (2) Although shear stress and span-to-depth ratio are inversely related, SFRC deep beams encounter larger shear loads than RC deep beams because when the span-to-depth ratio of beams increases, the failure mode switches from crushing struts to diagonal shear failure. To help structural engineers adopt SFRC deep beams, a nonlinear regression-based model was developed to estimate the shear strength of SFRC deep beams using the experimental database of SFRC beams. Three factors—feature selection, data preprocessing, and model development—were considered. Additionally, the model’s effectiveness was evaluated and compared with other models found in the literature. The proposed shear strength model of SFRC performed better than the other models in the literature, providing the lowest Root Mean Square Error (RMSE) of 1.58 MPa. The results of this study give practitioners a strong platform for establishing precise and useful estimations of shear strength in SFRC deep beams without stirrups.

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.

Experimentally studying and development of curved STM to predict the load capacity and failure mode of fixed-ended RC deep beams

Strut-and-tie model for externally bonded CFRP-strengthened reinforced concrete deep beams based on particle swarm optimization algorithm: CFRP debonding and rupture

This paper comprehensively studies the effects of linear and nonlinear creep and shrinkage on shear strength and deformation of reinforced concrete (RC) deep beams through a time‐dependent reliability analysis framework. The three‐dimensional finite element‐based program of ABAQUS was used to model RC deep beams. A viscoelastic approach was adopted to model linear creep and shrinkage by a user‐defined material model developed and implemented in user subroutines UMAT and UEXPAN. The software was initially examined using two experimental results for short/long‐term behavior of shallow and deep concrete beams. In the nonlinear range, creep was taken into account by the affinity hypothesis theorem to consider the effect of high‐level sustained loading. Due to the complicated and time‐consuming nature of the finite element method (FEM), adaptive neuro‐fuzzy inference system (ANFIS) and Monte Carlo simulation (MCS) replaced these complex analyses. Finally, based on the numerical results obtained from the analyses of case study samples, it was concluded that, in a serviceability limit state, for RC deep beams, the probability of failure was reduced to less than one‐fifth that for the shallow beams. On the contrary, in a strength limit state, a safety factor of about 1.7∼1.8 could be considered for the effect of sustained high‐level loading on the shear strength of RC deep beams.

Shear strengthening of RC deep beams using glass chopped strand mat (GCSM) composite

Deep beams are commonly used in tall buildings, offshore structures, and foundations. According to many codes and standards, strut-and-tie model (STM) is recommended as a rational approach for deep beam analyses. This research focuses on the STM recommended by ACI 318-11 and AASHTO LRFD and uses experimental results to modify the strut effectiveness factor in STM for reinforced concrete (RC) deep beams. This study aims to refine STM through the strut effectiveness factor and increase result accuracy. Six RC deep beams with different shear span to effective-depth ratios (a/d) of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 were experimentally tested under a four-point bending set-up. The ultimate shear strength of deep beams obtained from non-linear finite element modeling and STM recommended by ACI 318-11 as well as AASHTO LRFD (2012) were compared with the experimental results. An empirical equation was proposed to modify the principal tensile strain value in the bottle-shaped strut of deep beams. The equation of the strut effectiveness factor from AASHTTO LRFD was then modified through the aforementioned empirical equation. An investigation on the failure mode and crack propagation in RC deep beams subjected to load was also conducted.

This research aims to study the effects of the size and location of openings on deep beams. The analysis of deep beams with openings presents a rather complex problem for engineers, as there are currently no guidelines within the design codes for this problem. Using the strut and tie model is a feasible solution, but also gives some uncertainties due to the various models that can be used. This paper proposes using a strut and tie model for the deep beams with openings where reinforcement is laid out in the form of embedded struts and ties. The study is divided into an experimental and a numerical part. The experimental study was conducted on eight reinforced concrete deep beams under vertical loads. Seven of the beams had web openings of different sizes and locations, while the eighth specimen was a reference beam without any openings. The beams had the same concrete dimensions with the size of the openings in the web taken as 150 150 mm and 300 300 mm, and the location of the opening in the horizontal direction was varied between 0.11 to 0.4 the span. The experimental results were analyzed in terms of cracking pattern, mode of failure, and load-deflection behavior and then compared to numerical analysis conducted using a finite element program. A parametric study followed to investigate the influence of reinforcement arrangement and reinforcement around the openings on the behavior of deep beams. The results showed that large web openings that directly interrupted the compression strut had the most reduction in beam capacity and that the location of the opening did not significantly affect the strength of the beam in the case of small openings. Doi: 10.28991/CEJ-SP2021-07-011 Full Text: PDF

Investigation on shear behavior of reinforced concrete deep beams without shear reinforcement strengthened with fiber reinforced polymers

Shear strength of reinforced concrete deep beams – A review with improved model by genetic algorithm and reliability analysis