Reinforced Concrete Slender Beams Research Articles

Post-Cracking Shear Stiffness Model of Reinforced Concrete Beams

Macro diagonal cracks can significantly reduce the stiffness of slender reinforced concrete (RC) beams, which results in excessive deflection compared with limitations from design specifications. To evaluate the post-cracking stiffness of slender RC beams with diagonal cracks, a shear degradation model that considers shear deformation is proposed. Based on the variable angle truss model, this study deduced the strut angle formula based on the minimum energy principle. Then, the relationship between the stirrup yielding shear stiffness and elastic shear stiffness was modeled. Finally, the calculation procedure was developed by quantifying the stiffness degradation tendency. The comparison between the experimental results of deflection and the proposed analytical method showed good agreement. Additionally, the proposed method can capture the full-range features of shear strain curves.

Prediction of shear strength of RC slender beams based on interpretable machine learning

The purpose of this paper is to explore a prediction model of the shear strength of reinforced concrete (RC) slender beams driven by experimental data and mechanisms. An experimental database containing 774 shear test specimens of RC slender beams with and without stirrups is collected. According to that, six machine learning models are applied and compared, and the interpretability of these models is further explored. Through the comparison of six machine learning models, namely k-nearest neighbor, decision tree, random forests, Adaboost, gradient boosting decision tree, and XGBoost, the XGBoost model performs well in prediction accuracy (R2 = 0.999 and 0.953 in the training set and testing set). The XGBoost model is also significantly better than the mechanism-driven model in terms of prediction accuracy and variance, which is selected for further interpretation analysis. The interpretation analysis consists of three steps: (i) to identify the importance of features, (ii) to analyze feature dependence, (iii) to explore a novel interpretable idea combined the shear mechanism and SHapley Additive exPlanations (SHAP) method. It is the novel interpretable idea that the shear contribution distribution of the RC slender beam obtained by the SHAP value is further discussed. Through the comparison and discussion of the two mechanism models, the results of interpretable analysis indicate that the contribution distribution of the model conforms to the mechanism. Finally, the proposed interpretable approach is feasible and the developed XGBoost model is recommended for predicting the shear strength of RC beams and even similar questions.

Behavioral Evaluation of Strengthened Reinforced Concrete Beams with Ultra-Ductile Fiber-Reinforced Cementitious Composite Layers

In the literature, there is little information available regarding the behavior of composite beams made up of reinforced concrete (RC) and ultra-ductile fiber-reinforced concrete (UDFRC). In this study, UDFRC was examined for its effectiveness in enhancing the strength of RC beams. With a tensile strength of 4.35 MPa and a strain capacity of 2.5%, PVA-based UDFRC was prepared. The performance of 12 medium-sized reinforced concrete (RC) beams was measured under four-point flexural loading. The beams measured 1800 mm long, 150 mm wide, and 200–260 mm deep. The experimental program on beam specimens was divided into two phases. In the first, four 150 × 200 × 1800 mm RC beams with UDFRC layer thicknesses of 0, 30, 60, and 90 mm were tested. Additionally, four concrete and four concrete–UDFRC beams were investigated, measuring 150 × 230 × 1800 mm and 150 × 260 × 1800 mm, respectively. The study focused on medium-sized, slender RC beams under quasi-static loads and room temperature with additional or substituted UDFRC layers. As a result of replacing concrete with UDFRC, the load-carrying capacity at first crack and steel yield significantly increased between 18.4 and 43.1%, but the ultimate load-carrying capacity increased only in the range of 6.3–10.8%. Furthermore, beams with additional UDFRC layers could carry 30–50% more load than their concrete counterparts. An RC-UDFRC beam had a load-carrying capacity 10–15% greater than that of a comparable RC beam. Generally, there is a lower deflection response in UDFRC–concrete composite RC beams than in control concrete beams. The UDFRC layering can potentially improve the load-carrying capacity of RC beams, at least when ductility provisions are considered.

Shear strength degradation mechanism dependent on size increase in RC slender beams by using 3D Rigid-Body-Spring-Method

This study aims to clarify the mechanism of the size effect on the shear behavior for reinforced concrete (RC) slender beams. Three Dimensional Rigid-Body-Spring-Method (3D RBSM), a basic analytical tool applied in this paper, was first demonstrated to be capable of reproducing the shear behavior of large scaled RC slender beams without and with stirrup. Furthermore, the size effect on the shear behavior of three groups of geometrically similar RC slender beams with shear span-depth ratio a/d of 3.51 classified by different levels of stirrup ratio were quantitatively evaluated, and the mechanism of size effect was explained by investigating on beam and arch actions and localized information such as compressive stress in concrete and crack pattern. The analytical results indicated that the RC beams without stirrup showed evident size effect on the shear strength while the arrangement of stirrups along shear span inhibited the size effect to a great extent. More importantly, it was revealed that the size effect on the shear strength of beams without stirrup was dominant by the size dependence of arch action which resulted from the overall decrease in the level of nominal compressive resultant with increasing effective depth. On the other side, for the beams with stirrup, it was clarified that although the size effect on arch action still existed, it was caused by the change in the slope of arm length for arch action, which was induced by the transformation of diagonal crack pattern with increasing effective depth. However, this transformation of diagonal crack pattern contributed to the increase in nominal beam action. As a result, the decrease in nominal arch action was offset by the increase in nominal beam action in terms of combined size effect.

A knowledge transfer enhanced ensemble approach to predict the shear capacity of reinforced concrete deep beams without stirrups

AbstractThis paper proposes a novel learning algorithm, the transfer ensemble neural network (TENN) model, to increase the performance of shear capacity predictions on small datasets, illuminating the usefulness of advanced machine learning techniques in general. By incorporating ensemble learning and transfer learning, the TENN model is designed to control the high variability inherent in machine learning models trained on small amounts of data. The novel TENN model is validated to predict the shear capacity of deep reinforced concrete (RC) beams without stirrups across varying data availability levels. Knowledge acquired through pretraining a model on slender RC beams is utilized for training a model to better predict the shear capacity of deep RC beams without stirrups. To evaluate the performance of the TENN model, three baseline models are developed and examined across multiple data availability levels. The novel TENN model outperforms the baseline models, particularly when trained on a very limited dataset. Furthermore, the proposed algorithm achieves a higher accuracy than the currently accepted design standards in accurately predicting deep RC beams' shear capacity and demonstrates the capabilities of the TENN model to extrapolate in other domains where large‐scale or physical testing is cost‐prohibitive.

Shear Strength Models for Reinforced Concrete Slender Beams: Comparative Analysis and Parametric Evaluation

Shear failure of reinforced concrete (RC) members belongs to brittle failure and has always been concerned. In this paper, 16 existing shear strength models of RC slender beams have been selected and comprehensively compared based on a set of 781 experimental test results. These formulas from eight national codes and eight published papers are mainly the semi-empirical models or the analytical models. These experimental test results were collected from 66 published papers, and the range of key parameters is relatively wide. The accuracy of these shear strength models is evaluated from overall prediction level and the effect of key parameters. These key parameters mainly contain concrete compressive strength, shear-span-to-depth ratio, effective depth, and stirrup ratio. According to the results of overall prediction and evaluation of key parameters, the prediction results of Zsutty’s, Gunawan’s, and Bazant–Kim’s models are more accurate than others for both beams with stirrups and without stirrups. The models of ACI and JSCE exhibit higher prediction accuracy and safety margin, and their average values are between 1.19 and 1.28. The results of this study may provide reference for the selection and/or improvement of the shear strength model for RC slender beams.

Machine Learning-Based Model for Predicting the Shear Strength of Slender Reinforced Concrete Beams without Stirrups

The influence of concrete mix properties on the shear strength of slender structured concrete beams without stirrups (SRCB-WS) is a widespread point of contention. Over the past six decades, the shear strength of SRCB-WS has been studied extensively in both experimental and theoretical contexts. The most recent version of the ACI 318-19 building code requirements updated the shear strength equation for SRCB-WS by factoring in the macroeconomic factors and the contribution of the longitudinal steel structural ratio. However, the updated equation still does not consider the effect of the shear span ratio (a/d) and the yield stress of longitudinal steel rebars (Fy). Therefore, this study investigates the importance of the most significant potential variables on the shear strength of SRCB-WS to help develop a gene expression-based model to estimate the shear strength of SRCB-WS. A database of 784 specimens was used from the literature for training and testing the proposed gene expression algorithm for forecasting the shear strength of SRCB-WS. The collected datasets are comprehensive, wherein all considered concrete properties were considered over the previous 68 years. The performance of the suggested algorithm versus the ACI 318-19 equation was statistically evaluated using various measures, such as root mean square error, mean absolute error, mean absolute percentage error, and the coefficient of determination. The evaluation results revealed the superior performance of the proposed model over the current ACI 318-19 equation. In addition, the proposed model is more comprehensive and considers additional variables, including the effect of the shear span ratio and the yield stress of longitudinal steel rebars. The developed model reflects the power of employing gene expression algorithms to design reinforced concrete elements with high accuracy.

Residual shear strength of reinforced concrete slender beams without transverse reinforcement after elevated temperatures

Forty-eight reinforced concrete (RC) beams without transverse reinforcement were tested at ambient and after exposure to high temperatures. Beams were heated to high steady-state temperatures of 350 °C, 550 °C, and 750 °C in a programmable closed electric furnace and loaded to failure after cooling down. In addition to exposure temperature, tension reinforcement percentage (ρ) and shear-span-to-depth ratio (a/d) were kept as the variables. In the beams tested at ambient and after the elevated temperature of 350 °C, beam action was dominant, and diagonal tension failure was the observed mode of failure. When beams were exposed to 550 °C and 750 °C, beam action almost vanished, and the beams failed due to the failure of a compression strut joining the loading point and the support. After exposure to high temperatures, shear strength loss observed in beams with a lower tension reinforcement ratio was found to be more significant. Whereas, change in a/d ratio had an insignificant influence on the shear strength loss of the beams. An increase in temperature resulted in the decrease of the beams stiffness and increased the deflection corresponding to the ultimate load. An empirical model was also developed from the data of the present study for the prediction of shear strength of RC slender beams exposed to high temperatures.

Shear Strength Evaluation of Directly and Indirectly Loaded Rectangular Recycled Self-Compacted Reinforced Concrete Slender Beams Using Experimental and Finite Element Analysis

This study presents an experimental and numerical evaluation of the shear behavior of recycled aggregate concrete beams without transversal reinforcement. These beams were manufactured as self-compacted concrete with the use of both natural aggregate and recycled aggregate. The beams were subjected to direct and indirect loading conditions. The mechanical properties of four mixes were characterized in terms of compressive strength, splitting tensile strength, and elastic modulus. The experimental results showed that the shear capacity of recycled aggregate concrete is lower than those made with natural aggregate. The experimental shear capacities of the tested beams were compared with ACI318M-14 and relevant research studies in the literature. The ratio of experimental shear stress divided by the root square of concrete compressive strength , which indicates the ability of diagonally cracked concrete to transmit tension and shear. was remained for all configurations greater than 0.17, which is the minimum value recommended by the ACI318-14. Results from nonlinear finite element models were compared with the experimental data, and good agreement was achieved

Shear behavior of RC slender beams without stirrups by using precast U-shaped ECC permanent formwork

ECC characterized by its strain-hardening behavior in tension, high tensile and compressive strain and cracking control capacity is an ideal material for permanent formwork of reinforced concrete (RC) beams. This study investigated the shear behavior of RC slender beams without shear reinforcements by using precast U-shaped ECC permanent formwork. A total of 10 beams, including 1 RC beam for reference and 9 beams using U-shaped permanent formwork with different thicknesses and interfacial properties were fabricated and tested. ECC permanent formwork with three different thickness, namely 15, 20 and 25 mm, respectively were precast. At each thickness of permanent formwork, three different interfacial properties, namely smooth interface, anchored interface and rugged interface, respectively were prepared to investigate the effects of interfacial properties. All beams were tested by four-point loading tests to investigate the shear behavior and failure mechanism. The experimental results revealed that the shear carrying and deformation capacities of RC slender beams without stirrups could be enhanced significantly by using U-shaped ECC permanent formwork. The predictive equations for shear carrying capacities of RC beams without stirrups by using precast U-shaped ECC formwork were also proposed based on modified truss model and it agreed well with experimental result.

Overstrength requirements to avoid brittle shear failure in RC slender beams with stirrups

In this paper, an analytical expression was derived for the prediction of shear strength of slender reinforced concrete (RC) beams with stirrups. Failure occurring in B and D regions of the beam was considered. An expression derived for the shear strength of the B region was based on a modified constant angle truss model. The analytical expression derived consisted of three terms. The first one was related to the concrete contribution expressed through the square root of cylindrical compressive strength, geometrical ratio of longitudinal bars, and depth to width ratio. The second one was relating to the shear force induced by yielding of stirrups to the inclination of the main crack occurring at failure; its value depends on the geometrical ratio of longitudinal bars, transverse stirrups, and modulus of elasticity of concrete and steel. Finally, the third term was related to the shear force induced by the flexure of steel bars in the space s, which depends on the number and diameter of longitudinal bars and the yielding stress of longitudinal bars. Failure of the D regions was related to the concrete crushing of loaded joint under the effect of shear force and compressive force, including also the confinement effect due to the presence of stirrups. The original contribution of the paper was the determination of the maximum mechanical ratio of longitudinal and transverse steel to ensure over strength in shear respecting the strength hierarchy.Expressions derived and some of those available in the codes were verified against three different data banks of experimental researches available in the literature. The data banks utilized considered a very wide range of the geometrical ratio of longitudinal bars and transverse stirrups, including, for the latter, very high value producing brittle failure due to concrete crushing.

Prediction of Shear Capacity of Slender Reinforced Concrete Beams with Steel Fiber

Prediction of Shear Capacity of Slender Reinforced Concrete Beams with Steel Fiber

Alternative Approaches to Predict Shear Strength of Slender RC Beams Strengthened with Externally Bonded Fiber-Reinforced Polymer Laminates

AbstractThe method provided in ACI 440.2R for predicting the shear strength of reinforced concrete (RC) beams strengthened with externally bonded reinforcement (EBR) gives conservative estimates of...

Cyclic Response of Steel Fiber Reinforced Concrete Slender Beams; an Experimental Study.

Reinforced concrete (RC) beams under cyclic loading usually suffer from reduced aggregate interlock and eventually weakened concrete compression zone due to severe cracking and the brittle nature of compressive failure. On the other hand, the addition of steel fibers can reduce and delay cracking and increase the flexural/shear capacity and the ductility of RC beams. The influence of steel fibers on the response of RC beams with conventional steel reinforcements subjected to reversal loading by a four-point bending scheme was experimentally investigated. Three slender beams, each 2.5 m long with a rectangular cross-section, were constructed and tested for the purposes of this investigation; two beams using steel fibrous reinforced concrete and one with plain reinforced concrete as the reference specimen. Hook-ended steel fibers, each with a length-to-diameter ratio equal to 44 and two different volumetric proportions (1% and 3%), were added to the steel fiber reinforced concrete (SFRC) beams. Accompanying, compression, and splitting tests were also carried out to evaluate the compressive and tensile splitting strength of the used fibrous concrete mixtures. Test results concerning the hysteretic response based on the energy dissipation capabilities (also in terms of equivalent viscous damping), the damage indices, the cracking performance, and the failure of the examined beams were presented and discussed. Test results indicated that the SFRC beam demonstrated improved overall hysteretic response, increased absorbed energy capacities, enhanced cracking patterns, and altered failure character from concrete crushing to a ductile flexural one compared to the RC beam. The non-fibrous reference specimen demonstrated shear diagonal cracking failing in a brittle manner, whereas the SFRC beam with 1% steel fibers failed after concrete spalling with satisfactory ductility. The SFRC beam with 3% steel fibers exhibited an improved cyclic response, achieving a pronounced flexural behavior with significant ductility due to the ability of the fibers to transfer the developed tensile stresses across crack surfaces, preventing inclined shear cracks or concrete spalling. A report of an experimental database consisting of 39 beam specimens tested under cyclic loading was also presented in order to establish the effectiveness of steel fibers, examine the fiber content efficiency and clarify their role on the hysteretic response and the failure mode of RC structural members.

Shear Strength Models for Reinforced Concrete Slender Beams: A Comparative Study

Shear strength is one of the most widely investigated parameter in reinforced concrete (RC) beams. Numerous papers are published in last 66 years which investigate experimentally and theoretically the shear strength of RC beams without shear reinforcement. In this paper a database on shear strength of 719 RC beams without transverse reinforcement is generated from experimental results published between 1952 and 2018. Well-known shear strength models proposed in the literature are summarized and evaluated through comparison with the experimental results of generated database. It was found that models proposed by Niwa et al. (1986) and Zararis and Papadakis (2001) predicts shear strength of RC beams more accurately than the other models. The former model gives an average strength ratio of 1.05 with a coefficient of variation of 29% while the latter yielded an average strength ratio of 1.10 with a coefficient of variation of 29%. A detailed evaluation in various ranges of parameters revealed that both the models gives unconservative results of shear strength for beams with concrete compressive strength >90 MPa. Parametric study of the two models within the individual test series showed that model of Niwa et al. does not capture the size effect in RC beams very effectively while the model of Zararis and Papadakis yields uniform results over the whole range of experimental data.

Shear Creep Failures of Reinforced Concrete Slender Beams without Shear Reinforcement

Shear Creep Failures of Reinforced Concrete Slender Beams without Shear Reinforcement

Energy absorption evaluation of reinforced concrete beams under various loading rates based on particle swarm optimization technique

ABSTRACTThis study proposes an energy absorption model for predicting the effect of loading rates, concrete compressive strength, shear span-to-depth ratio, and longitudinal and transverse reinforcement ratio of reinforced concrete (RC) beams using the particle swarm optimization (PSO) technique. This technique avoids the exhaustive traditional trial-and-error procedure for obtaining the coefficient of the proposed model. Fifty-six RC slender and deep beams are collected from the literature and used to build the proposed model. Three performance measures, namely, mean absolute error, mean absolute percentage error and root mean square error, are investigated in the proposed model to increase its accuracy. The design procedure and accuracy of the proposed model are illustrated and analysed via simulation tests in a MATLAB/Simulink environment. The results indicate the minimal effect of swarm size on the convergence of the PSO algorithm, as well as the ability of PSO to search for an optimum set of coefficients from within the solution space.

Influence of Stirrup Corrosion on Shear Strength of Reinforced Concrete Slender Beams

Influence of Stirrup Corrosion on Shear Strength of Reinforced Concrete Slender Beams

Formulation of shear strength of slender RC beams using gene expression programming, part II: With shear reinforcement

Abstract In this study, a new variant of genetic programming, namely gene expression programming (GEP) is utilized to predict the shear strength of reinforced concrete (RC) beams with stirrups. The derived model relates the shear strength to mechanical and geometrical properties. The model is developed using a database containing 466 experimental test results gathered from the literature. Sensitivity and parametric analyses are performed for further verification of the model. The comparative study proves the superior performance of the GEP model compared to the expressions developed in several codes of practice.

Closure to “Simplified Shear Design of Slender Reinforced Concrete Beams with Stirrups” by Zhi-Qi He, Zhao Liu, and Zhongguo John Ma

Closure to “Simplified Shear Design of Slender Reinforced Concrete Beams with Stirrups” by Zhi-Qi He, Zhao Liu, and Zhongguo John Ma