Reinforced Concrete Deep Beams Research Articles

STM-based symbolic regression for strength prediction of RC deep beams and corbels

This study uses symbolic regression with a strut-and-tie model to predict the shear strength of reinforced concrete deep beams (RCDBs) and corbels (RCCs). Previous studies have proposed two distinct types of models for estimating shear capacity: explainable models based on theoretical derivations and black-box models derived from machine learning (ML) methods. This study proposes a hybrid model derived from the strut-and-tie model (STM), where the performance of STM is enhanced through the ML approach using genetic programming. This model is based on a comprehensive experimental database of 810 tests for the shear strength of RC deep beams and 371 tests for RC corbels from various research papers. The developed STM-based symbolic regression (SR-STM) integrates two distinct force-transferring mechanisms: the diagonal strut mechanism utilizing concrete strength and the truss mechanism utilizing orthogonal web reinforcement. The SR-STM model is both robust and interpretable, demonstrating high prediction accuracy with mean values of the prediction-to-actual ratios of 0.999 and 1.004 and coefficient of determination values of 0.913 and 0.862 for RCDBs and RCCs, respectively, while providing explainable mathematical expressions that align with the mechanical principles of STM. The developed SR-STM model is benchmarked against several state-of-the-art models and evaluated against the CatBoost ML technique, demonstrating acceptable performance. The results highlight the SR-STM model’s effectiveness in providing reliable predictions and valuable insights for practical engineering applications. Furthermore, a SHAP (Shapley Additive Explanations) analysis was performed, and its results align with the SR-STM model, confirming the model’s effectiveness in accurately capturing the key factors influencing the shear strength of RCDBs and RCCs.

Experimental Analysis of Reinforced Concrete Deep Beams with Circular Openings Strengthened by GFRP and Steel Bars

Experimental Analysis of Reinforced Concrete Deep Beams with Circular Openings Strengthened by GFRP and Steel Bars

The Effect of Construction Joints on the Behavior of Reinforced Concrete Deep Beams

The Effect of Construction Joints on the Behavior of Reinforced Concrete Deep Beams

Experimental behaviour, FE modelling and design of large-scale reinforced concrete deep beams shear-strengthened with embedded fibre reinforced polymer bars

Reinforced concrete (RC) deep beams are widely used in buildings and bridges. However, research on shear strengthening of RC deep beams with embedded fibre reinforced polymer (FRP) bars is limited. This paper presents the first comprehensive study on the experimental behaviour, nonlinear finite element (NLFE) modelling and design of large-scale RC deep beams strengthened in shear with embedded carbon or glass FRP (CFRP or GFRP) bars. An experimental investigation comprising three large-scale RC deep beams was conducted. Subsequently, a three-dimensional NLFE model was developed and validated against the experimental results. The validated NLFE model was used to perform a parametric study, examining the influence of FRP bar type and steel-to-FRP shear reinforcement ratio on shear strength enhancement. The results of the parametric study were utilized to calibrate and validate a novel design model. The results showed that embedded FRP bars can enhance the shear force capacity of large-scale RC deep beams by up to 40 %. The effect of FRP bar type on the shear strength enhancement was insignificant. However, there was 13 % reduction in shear force gain due to the increase in steel-to-FRP shear reinforcement ratio from 0.77 to 10.0. The novel design model reproduced the NLFE results with a mean ratio of 0.921 and a standard deviation of 0.018. Finally, the ability of the design model to capture the effect of the investigated parameters was demonstrated.

Experimental and numerical investigations of the shear performance of reinforced concrete deep beams strengthened with hybrid SHCC-mesh

This paper investigates the shear strengthening of simply supported deep beams using welded wire mesh and glass fiber mesh filled with strain-hardening cementitious composites (SHCC) concrete. Nine reinforced concrete (RC) deep beams were tested in this study to investigate different shear-strengthening techniques including the type of mesh (glass fiber mesh and welded steel wire mesh), number of layers (single and double), and the effects of additional anchor using high-strength bolts on the shear performance of RC deep beams. The results showed the SHCC-mesh jackets increased the ultimate load of the deep beams by up to 82 %, cracking load by up to 73 %, elastic stiffness by up to 457 %, and energy absorption by up to 380 % compared to the unstrengthen control beam. Furthermore, the welded wire mesh provided greater enhancements of strength, stiffness, and energy absorption than the glass fiber mesh. In addition, anchoring the jackets further improved the strengthening efficiency. Advanced nonlinear three-dimensional finite element models were also simulated to capture the structural responses of the RC deep beams strengthened using welded wire mesh and glass fiber mesh. It was found that the numerical models accurately predicted the behavior of the beams upon validation against the experimental results.

Prediction and reliability analysis of shear strength of RC deep beams

This study explores machine learning (ML) capabilities for predicting the shear strength of reinforced concrete deep beams (RCDBs). For this purpose, eight typical machine-learning models, i.e., symbolic regression (SR), XGBoost (XGB), CatBoost (CATB), random forest (RF), LightGBM, support vector regression (SVR), artificial neural networks (ANN), and Gaussian process regression (GPR) models, are selected and compared based on a database of 840 samples with 14 input features. The hyperparameter tuning of the introduced ML models is performed using the Bayesian optimization (BO) technique. The comparison results show that the CatBoost model is the most reliable and accurate ML model (R2 = 0.997 and 0.947 in the training and testing sets, respectively). In addition, simple and practical design expressions for RCDBs have been proposed based on the SR model with a physical meaning and acceptable accuracy (an average prediction-to-test ratio of 0.935 and a standard deviation of 0.198). Meanwhile, the shear strength predicted by ML models was then compared with classical mechanics-driven shear models, including two prominent practice codes (i.e., ACI318, EC2) and two previous mechanical models, which indicated that the ML approach is highly reliable and accurate over conventional methods. In addition, a reliability-based design was conducted on two ML models, and their reliability results were compared with those of two code standards. The findings revealed that the ML models demonstrate higher reliability compared to code standards.

Comprehensive Empirical Modeling of Shear Strength Prediction in Reinforced Concrete Deep Beams

This paper presents comprehensive empirical equations to predict the shear strength capacity of reinforced concrete deep beams, with a focus on improving the accuracy of existing codes. Analyzing 198 deep beams imported from 15 existing investigations, this study considers various parameters such as concrete compressive strength (f′c), the shear span-to-effective depth ratio (av/d), and reinforcement ratios (ps, pv, and ph). Introducing a novel predictive empirical equation, this study conducts a rigorous evaluation using statistical metrics and a linear regression analysis (MAE, RMSE, and R2). The proposed model demonstrates a significant reduction in the coefficient of variation (CV) to 27.08%, compared to the existing codes’ limitations. Comparative analyses highlight the accuracy of the empirical equation, revealing an improved convergence of data points and minimal sensitivity to variations in key parameters. The results proved that the proposed empirical equation enhanced the accuracy to predict the shear strength capacity of the reinforced concrete deep beams in various scenarios, making it a valuable tool for structural engineers. This research contributes to advancing the understanding of shear strength capacity in reinforced concrete deep beams, offering a reliable empirical equation with implications for refining design methodologies and enhancing safety with the efficiency of structural systems.

Experimental investigation of the effect of horizontal construction joints on the behavior of deep beams

Abstract Construction joints serve as interruption points in the concrete placement process, which is necessary because it is often not feasible to pour concrete continuously in many structures. The quantity of concrete that can be poured at a single instance depends on the batching and mixing capacity, as well as the strength of the formwork. An effective construction joint must ensure sufficient flexural and shear continuity across the junction. Many studies investigated the construction joints in the reinforced concrete (RC) normal beams, but there are no studies investigating the effect of construction joints on the behavior of the RC deep beams. This study was prepared to show the behavior of deep beams having horizontal construction joints (HCJs) extended through their entire length. The parameter studied in this research was the location of the HCJ within the beam height. Four simply supported RC deep beams were tested under a two-point static load up to failure. One of these beams was without a construction joint and was considered a reference beam. Each one of the other beams has only one horizontal construction. The location of these joints was below, at, or above the beam mid-height. The crack patterns, the strain distributions, the mode of failure, deflection, and failure load are discussed. It was found that the existence of construction joints below, at, or above the beam mid-height results in a decrease in load failure load by 9, 11, and 1% compared with the reference beam. It can be concluded that the best location of the HCJ in the RC deep beam is in the upper part of the beam.

Novel Lower-Bound Solution for Bearing Capacity of Reinforced Concrete Deep Beams

Novel Lower-Bound Solution for Bearing Capacity of Reinforced Concrete Deep Beams

Experimental and Numerical Study on the Behavior of Reinforced Concrete Deep Beams with Normal-Strength and High-Strength Concrete After Being Exposed to Fire

Experimental and Numerical Study on the Behavior of Reinforced Concrete Deep Beams with Normal-Strength and High-Strength Concrete After Being Exposed to Fire

Experimental study on the behavior of pre-loaded reinforced concrete (RC) deep beams with openings strengthened with FRP sheets

Purpose Recently, the repairing of reinforced concrete (RC) structures attracted great research attentions, but the research interests were mainly concentrated on common repairing types. To this end, in this paper, a repairing of pre-loaded RC beams strengthened by aramid reinforcement polymers (AFRP) is presented. Furthermore, the purpose of this paper is to study the behavior of pre-loaded RC Deep beams under sustained load. The AFRP has many advantages such as controlling stresses distribution around the openings, controlling failure modes, and enhancing the structural capacity of pre-cracked RC beams. Design/methodology/approach Four specimens were experimentally tested: one specimen without strengthening, which is considered as control specimen, one strengthened specimen using AFRP without pre-cracking and two specimens subjected to pre-cracking load before prior to AFRP application. Furthermore, after validation of experimental data by using ANSYS software, a parametric study was conducted to investigate the effect of pre-damage level on shear capacity of RC beams. For pre-cracked beams, loading was first applied until the cracking stage, followed by specimen repairing with epoxy injection, and then the specimens were loaded again until failure point. Findings The result showed that pre-damage level and AFRP strengthening have great influence on the ultimate strength and failure mode. In addition, the results obtained from experimental tests were compared with those from numerical validation with ANSYS and showed good agreement. Originality/value Based on ACI guidelines, an analytical equation for calculating the shear strength of strengthened RC beams with openings subjected to pre-damage was then proposed, and the calculated results were compared with those from the tests, with differences not exceeding 10%.

Review on NSM-CFRP Method for Enhancing Shear Capacity in Reinforced Concrete Deep Beams

The demand for improved strengthening techniques for current concrete structures is on the rise. Many structures that will still be in use two decades from now have already been constructed. A portion of these structures must undergo enhancements or be replaced, as they are deteriorating not only from natural processes but also from mistakes made during their design and construction. Near-surface mounted (NSM) utilizing Fiber-Reinforced Polymer (FRP) bars has proven to be a successful method in enhancing the flexural and shear performance of both existing and new Reinforced Concrete (RC) elements. This technique is considered innovative and rapidly developing, attracting significant attention from researchers. Therefore, this study aims to analyze previous and current research on the shear strengthening of RC deep beams using NSM-CFRP bars. The research findings were gathered from four prominent databases: ASCE, EBSCO, SCOPUS, and Science Direct. A thorough literature review was conducted, focusing specifically on NSM-CFRP for shear strengthening. A total of 56 articles were categorized into three main groups. Group 1 consisted of studies examining the use of NSM for shear strengthening, while Group 2 focused on articles related to the structural behavior of RC members in shear. Group 3 included articles discussing the theoretical aspects of NSM-FRP in enhancing shear strength, aiming to develop a new method for calculating shear effects provided by NSM-FRP. In conclusion, this study highlights three fundamental aspects of this field: (1) the rationale behind utilizing NSM-FRP bars for shear reinforcement and their practical applications, (2) existing challenges and barriers to widespread adoption, and (3) recommendations for enhancing the acceptance and utilization of NSM-FRP bars.

Evaluation of Shear Strength Prediction on Steel Reinforced Concrete Deep Beams Using Simple Strut-and-Tie Model

Evaluation of Shear Strength Prediction on Steel Reinforced Concrete Deep Beams Using Simple Strut-and-Tie Model

The Experimental and Theoretical Effect of Fire on the Structural Behavior of Laced Reinforced Concrete Deep Beams

A Laced Reinforced Concrete (LRC) structural element comprises continuously inclined shear reinforcement in the form of lacing that connects the longitudinal reinforcements on both faces of the structural element. This study conducted a theoretical investigation of LRC deep beams to predict their behavior after exposure to fire and high temperatures. Four simply supported reinforced concrete beams of 1500 mm, 200 mm, and 240 mm length, width, and depth, respectively, were considered. The specimens were identical in terms of compressive strength ( 40 MPa) and steel reinforcement details. The same laced steel reinforcement ratio of 0.0035 was used. Three specimens were burned at variable durations and steady-state temperatures (one hour at 500 °C and 600 °C, and two hours at 500 °C). The flexural behavior of the simply supported deep beams, subjected to the two concentric loads in the middle third of the beam, was investigated with ABAQUS software. The results showed that the laced reinforcement with an inclination of 45˚ improved the structural behavior of the deep beams, and the lacing resisted failure and extended the life of the model. The optimal structural response was observed for the specimens. The laced reinforcement improved the failure mode and converted it from shear to flexure-shear failure. The parametric study showed that the lacing bars remarkably improved the strength of the deep beams and they were not affected more by the steady-state temperature and duration. Furthermore, a greater increase in load-carrying capacity was associated with an increase in the flexural diameter of approximately 12 and 16 mm by approximately 24.77% and 87.61%, respectively, compared to the reference LRC deep beams.

Effect of stirrups on shear performance of geometrically-similar reinforced concrete deep beams: An experimental study

In practical engineering, reinforced concrete (RC) beams with stirrups are the predominant form of RC beams. The geometric dimensions of RC beams are large, and the brittle shear failure of them maybe show the characteristics of size effect. However, current research primarily focuses on the size effect of shear failure in RC beams without stirrups, with less emphasis placed on those with stirrups. Furthermore, when the minimum stirrup ratio is exceeded, there is no consensus regarding on whether the size effect still exists. Therefore, the objective of the present work is to discover the influence of the stirrup ratio on the size effect in RC deep beams. In this work, the shear failure experiment of RC deep beams considering the structural size (maximum beam height of 900 mm) and stirrup ratio (0%∼0.942%) is designed and completed. The experiment results indicate that: 1) for the beams without stirrups, clearly, the corresponding size effect on the shear strength is the most obvious, with beam depth increases from 300 mm to 900 mm, the nominal shear strength decreases approximately by 41%; 2) as the stirrup ratio increases from 0 to 0.942%, the size effect is weakened with the presence of stirrups; 3) however, size effect cannot be completely eliminated even when the stirrup ratio reaches as high as 0.942%; (4) generally, for the stirrup ratio of 0.3%, there is a decrease in nominal shear strength by 20%, indicating that consideration of size effects should be taken seriously in practical concrete structure design; (5) moreover, Jin et al.’s size effect law is also compared and validated by the present test data.

Response to discussion on “A Knowledge Transfer Enhanced Ensemble Approach to Predict the Shear Capacity of Reinforced Concrete Deep Beams without Stirrups,” Computer‐Aided Civil and Infrastructure Engineering, 38:11, 1520–1535

Response to discussion on “A Knowledge Transfer Enhanced Ensemble Approach to Predict the Shear Capacity of Reinforced Concrete Deep Beams without Stirrups,” Computer‐Aided Civil and Infrastructure Engineering, 38:11, 1520–1535

Experimental Study of Pre-Cast Reinforced Concrete Deep Beams (Hallow Core section) Retrofitting with Carbon Fiber Reinforced Polymer (CFRP)

Experimental programs based test results has been used as a means to find out the response of individual elements of structure. In the present study involves investigated behavior of five reinforced concrete deep beams of dimension (length 1200 x height 300 x width150mm) under two points concentrated load with shear span to depth ratio of (1.52), four of these beams with hallow core andretrofit with carbon fiber reinforced polymer CFRP (with single or double or sides Strips). Two shapes of hallow are investigated (circle and square section) to evaluated the response of beams in case experimental behavior. Test on simply supported beam was performed in the laboratory & loaddeflection, strain of concrete data and crack pattern of those five reinforced concrete beams was recorded. Parametric studies are also conducted in this study includes the effect of hallow opening (shapes and materials), and CFRP ratio (single, double strips and side horizontal stirrups). Comparisons of test results from experimental data are based on load capacity, deflection, crack pattern and strain of concrete for all beams. From this comparison it was found that hallow effect on strength capacity i.e. decrease by about (13%) and increased in deflection and strain by about (18%, 24%) respectively compared with solid section. Also find that CFRP give more enhancements in loading capacity by about(33 to 66%) and decreased deflection for same applied load by about (26%). Test results that show when sides of beams retrofit with CFRP strip against horizontal shear increased strength by about by (20%). Finally the using double CFRP strips for hallow section gives equivalent or more than strength capacity of solid section.

The nonlinear analysis of reactive powder concrete effectiveness in shear for reinforced concrete deep beams

Abstract The aim of this article is to investigate the effect of using reactive powder concrete (RPC) for reinforcement concrete deep beams (CDBs) to study the shear effect by the numerical analysis. The method of finite element analysis model simulations using a program was used. The characteristics of RPC and the deep beam of reinforced concrete were obtained from previous scientific research. Non-linear analysis for two models of deep beams, one with RPC and the other without using it, was conducted to compare with experimental results from recent tests of deep concrete beams with RPC and loaded until failure. The data obtained from the specimens have many factors related to the effect of the strength and action of reinforcement CDBs such as shear load deflection, crack pattern, mode failure, and concrete strength. On the other hand, the mesh changing was investigated in terms of the maximum concrete strength and the running time by changing the mesh size to 50, 25, and 15. Models were simulated with a two-point load using a shear span-to-depth with an av/d ratio of 0.77. The difference in percentage deflection between the numerical and experimental models’ data was observed at 2.60 and 5.9% for concrete deep beam and RPC deep beam, respectively, and the maximum shear load was 2.27 and 5.40%. The importance of the outputs of this article lies in bridging the research gap of this new topic and identifying the shear behavior of deep beams reinforced with RPC due to the lack of research related to this topic. It was noted that the obtained data for finite element analysis are very consistent with the previous laboratory scientific research, while the error rate did not exceed 10%.

A Strut and Tie Model for Steel Fiber Reinforced Concrete Deep Beams

A Strut and Tie Model for Steel Fiber Reinforced Concrete Deep Beams

A Comprehensive Formula to Predict the Shear Contribution of FRP Sheets in Strengthened Reinforced Concrete Deep Beams

A Comprehensive Formula to Predict the Shear Contribution of FRP Sheets in Strengthened Reinforced Concrete Deep Beams