Shear Design Models Research Articles

Prediction of RC T-Beams Shear Strength Based on Machine Learning

The contribution of shear resisted by flanges of T-beams is usually ignored in the shear design models even though it was proven by many experimental studies that the shear strength of T-beams is higher than that of equivalent rectangular cross-sections. Ignoring such a contribution result in a very conservative and uneconomical design. Therefore, the aim of this research is to investigate the capability of machine learning (ML) techniques to predict the shear capacity of reinforced concrete T-beams (RCTBs) by incorporating the contribution of the flange. Five machine learning (ML) techniques, which are the Decision Tree (DT), Random Forest (RF), Gradient Boosting Regression Tree (GBRT), Light Gradient Boosting Machine (LightGBM), and Extreme Gradient Boosting (XGBoost), are trained and tested using 360 sets of data collected from experimental studies. Among the various machine learning models evaluated, the XGBoost model demonstrated exceptional reliability and precision, achieving an R-squared value of 99.10%. The SHapley Additive exPlanations (SHAP) approach is utilized to identify the most influential input features affecting the predicted shear capacity of RCTBs. The SHAP results indicate that the shear span-to-depth ratio (a/d) has the most significant effect on the shear capacity of RCTBs, followed by the ratio of shear reinforcement multiplied by the yield strength of shear reinforcement (ρvfyv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rho }_{{\ ext{v}}}{f}_{{\ ext{yv}}}$$\\end{document}), flange thickness (hf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${h}_{{\ ext{f}}}$$\\end{document}), and flange width (bf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${b}_{{\ ext{f}}}$$\\end{document}). The accuracy of the XGBoost model in predicting the shear capacity of RCTBs is compared with established codes of practice (ACI 318-19, BS 8110-1:1997, EN 1992-1-2, CSA23.3-04) and existing formulas from researchers. This comparison reinforces the superior reliability and accuracy of the machine learning approach compared to traditional methods. Furthermore, a user-friendly interface platform is developed, effectively simplifying the implementation of the proposed machine-learning model. The reliability analysis is performed to determine the value of the resistance reduction factor (ϕ) that will achieve a target reliability index (βT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\beta }_{T}$$\\end{document}= 3.5).

Limit analysis and design recommendations for fiber‐reinforced concrete subjected to shear

AbstractIt is widely recognized in both research and practice that fibers have great potential to partially, or completely, substitute conventional transverse reinforcement in webs of girders subjected to moderate shear forces. However, despite extensive research in recent years, there is still no consensus in the research community on the mechanically sound modeling of the shear strength of fiber‐reinforced concrete (FRC). Accordingly, current code provisions for the design of FRC to resist shear rely on (semi‐)empirical approaches and are thus justifiably restrictive. This article addresses this knowledge gap by proposing the application of the theory of plasticity to the design of FRC webs. Limit analysis methods for conventionally reinforced concrete are extended to FRC by incorporating the residual crack‐bridging stress offered by the fibers in a consistent manner. This stress, as well as the limits of applicability of the theory of plasticity, are derived through a sensitivity analysis using the recently developed Cracked Membrane Model for FRC considering fixed, interlocking cracks. Based on these investigations, a straightforward and efficient mechanically based shear design model suitable for the design of FRC webs with and without conventional transverse bar reinforcement is proposed. The model is validated against a large database of panel and beam experiments, providing valuable insights into its reliability.

Machine learning and traditional approaches in shear reliability of steel fiber reinforced concrete beams

In the field of structural engineering, the exploration of steel fibre reinforced concrete (SFRC) beams has recently intensified, particularly due to their improved tension and shear performance of structure. This study pioneers a novel reliability analysis of shear capacity predictions for SFRC beams, distinctively classifying the datasets into high-strength (HSFRC) and normal-strength (NSFRC) categories. A comprehensive database of 142 HSFRC and 265 NSFRC beams serves as the foundation for this analysis, which critically examines the standard Gaussian distribution in shear design models and proposes the Lognormal and Weibull distributions as more precise alternatives. Employing advanced First-order (FORM) and Second-order Reliability Methods (SORM), the study covers a broad spectrum of load conditions, including dead, live, snow, wind, and seismic loads, to evaluate various empirical, semi-empirical and machine learning proposed shear capacity prediction formulas. One of the key innovations of this research is the development of differentiated resistance coefficients for various risk levels in the reliability analysis, allowing future structural designers to tailor their designs according to specific risk profiles. This approach significantly enhances the balance between economic efficiency and structural safety based on the evolution of different target reliability indexes. The study reveals that existing design equations for SFRC beams generally lean towards conservatism. This study found that formulas derived from machine learning exhibited superior prediction ability compared to traditional theoretically derived regression formulas. When compared the proposed machine learning formulas, the Tarawneh's formula demonstrated better prediction ability than the Kara's formula when applied to larger datasets. However, high predictive power does not necessarily equate to high reliability. Machine learning formulas prioritise predictive accuracy, often at the expense of insufficient redundancy for ensuring safety. Overall, it introduces Kara's formula for NSFRC beams, which stands out with its superior predictive performance, offering an optimal balance of safety and cost-efficiency. Ashour's formula is also identified as a more effective and safer option for HSFRC beams. Complementing these findings, the extensive sensitivity analysis of the collected data not only confirms the robustness of the conclusions but also prepares for the integration of broader datasets in the future.

Unified two-way shear model for steel and FRP-RC slabs: Evaluation and reliability calibration

This study introduces a unified two-way (punching) shear design model for concrete reinforced with slabs steel- and FRP bars. The unified model modifies the ACI 318-19 punching shear model to account for the axial stiffness of the tension reinforcement by providing a new modification term (ρ Ereft./Ec)0.26, representing the reinforcing ratio multiplied by the elastic modular ratio of longitudinal bars to concrete. The unified punching shear model has been evaluated over two experimental datasets: FRP-RC slabs (145 specimens) and steel-RC slabs (390 specimens). A comparative assessment between the ACI 440.11-22, CSA S806, JSCE, and the proposed models to test their generalization abilities for slabs reinforced with both types of reinforcement. The assessment indicated a similar performance of the proposed model to the CSA S806 and the JSCE models in terms of statistical measures. The ACI 440.11–22 showed a high average strength ratio (Vexp./Vpred.) of 1.83. However, the ACI and the CSA models showed reduction in the conservatism at high reinforcement axial stiffness. In addition, reliability analysis using Monte Carlo simulation indicated that the unified punching shear model provides a satisfactory safety level with a reliability index between 3.5 and 4.0 for both steel and FRP-RC slabs.

Modified Shear Design Model for Steel- and Fiber- Reinforced Polymer-Reinforced Concrete Beams

Modified Shear Design Model for Steel- and Fiber- Reinforced Polymer-Reinforced Concrete Beams

Proposing a one-way shear design model for FRP-RC members: Evaluation and reliability calibration

Existing shear design models for reinforced concrete are based on semi-empirical approaches and were calibrated with different experimental databases. The existing FRP-RC shear design models vary significantly in accuracy and conservatism. In particular, various studies indicated that the ACI 440-15 model is less accurate and highly conservative compared to other design models. The recently published ACI 440.11-22 adopts a similar procedure to ACI 440.1R-15 but incorporates the size effect and minimum shear strength. This study presents a detailed evaluation of different design codes based on a worldwide surveyed database spanning 344 beams. A modified shear design model consistent with the current ACI 318-19 model is proposed. This newly proposed model, which accounts for FRP axial stiffness, has demonstrated higher accuracy and hence was calibrated to achieve a reliability index of 4.0 to balance safety and conservatism. The calibrated proposed model for concrete resistance is)Vc = 0.4 (nc ρfl)1/3 λs √f’c bw d(, where nc is the elastic modular ratio of longitudinal FRP bars to concrete. Finally, the applicability of generalizing and extending the proposed model to steel-RC concrete beams has been tested on a published evaluation shear database. The proposed model outperformed the ACI 318-19 model in different statistical measures.

Shear Design of Strain-Hardening Fiber-Reinforced Concrete Beams

Strain-hardening fiber-reinforced concrete (SH-FRC), such as ultrahigh-performance concrete (UHPC), offers sustained tensile capacities up to high values of postcracking strains and, consequently, delivers shear resistance through different mechanisms than conventional concrete. Existing shear design methods for conventional concrete beams include empirical approximations of the tensile resistance offered by the cracked concrete that do not apply to SH-FRC materials. This article presents a design formulation that predicts the shear capacity of SH-FRC beams in support of ongoing efforts to develop UHPC structural design guidance in the United States. The proposed model leverages foundational concepts from engineering mechanics, similar to the modified compression-field theory (MCFT) for conventional reinforced and prestressed concrete, while integrating relationships that address behaviors specific to SH-FRC. The model predicts shear stress versus shear strain behavior of a cracked SH-FRC membrane element, which is then used to model the web of a beam. Verified against experimental shear test results of I-shaped prestressed and non-prestressed beams with different material properties, beam geometries, axial strains, and transverse reinforcement ratios, the proposed shear design model is demonstrated to conservatively predict the shear capacity of SH-FRC beams. As such, this work constitutes a fundamental step in developing mechanics-based SH-FRC shear design guidance.

Experimental shear testing of corrugated web girders with compression tubular flanges used in conventional buildings

Steel corrugated web girders (SCWGs) have been extensively investigated and applied in bridges and buildings worldwide, due to their excellent out-of-plane stiffness of their webs and their high shear strengths. This paper proposes a new type of SCWGs based on previous literature, namely the girder including a hollow tubular compression flange, a corrugated web, and a flat lower flange. Small-scale specimens suiting building applications are designed and tested experimentally to examine their failure modes and bearing capacities under shear. Based on the test results, FE models are generated and validated accurately through the comparisons of the ultimate loads, load–deflection relationships and failure modes. Then, parametric studies are performed to increase the pool of available results of the current girders, from which the effects of tubular flange, web thickness, web height, web slenderness ratio and tube depth-to-width ratio are evaluated. It is found that the tube depth-to-width ratio has a great effect on the shear behaviour of SCWGs with the upper tubular flange. In the tests, the ratio of the shear force at the upper tubular flange to the shear of the corresponding cross-section is about 12%–18% for the flat folds, while the ratio is 9%–13% for the inclined folds. A minimum tube depth for the new kind of girder is suggested that yields higher strength compared with SCWGs with plate flange of the same area. Moreover, the results show that the post-buckling strength is improved by using the new kind of girders compared to conventional SCWGs with plate flanges. At the end, available shear design methods, originally suggested for SCWGs with plate flanges, are applied to the current girders to check their accuracy. The comparisons illustrate that these methods yield conservative predictions for SCWGs with tubular flanges for many cases but unconservative for few cases, highlighting the importance of proposing a new shear design model that takes into account the effect of the upper tubular flange in the near future.

Shear Strength Prediction of Slender Steel Fiber Reinforced Concrete Beams Using a Gradient Boosting Regression Tree Method

For the design or assessment of concrete structures that incorporate steel fiber in their elements, the accurate prediction of the shear strength of steel fiber reinforced concrete (SFRC) beams is critical. Unfortunately, traditional empirical methods are based on a small and limited dataset, and their abilities to accurately estimate the shear strength of SFRC beams are arguable. This drawback can be reduced by developing an accurate machine learning based model. The problem with using a high accuracy machine learning (ML) model is its interpretation since it works as a black-box model that is highly sophisticated for humans to comprehend directly. For this reason, Shapley additive explanations (SHAP), one of the methods used to open a black-box machine learning model, is combined with highly accurate machine learning techniques to build an explainable ML model to predict the shear strength of SFRC slender beams. For this, a database of 330 beams with varying design attributes and geometries was developed. The new gradient boosting regression tree (GBRT) machine learning model was compared statistically to experimental data and current shear design models to evaluate its performance. The proposed GBRT model gives predictions that are very similar to the experimentally observed shear strength and has a better and unbiased predictive performance in comparison to other existing developed models. The SHAP approach shows that the beam width and effective depth are the most important factors, followed by the concrete strength and the longitudinal reinforcement ratio. In addition, the outputs are also affected by the steel fiber factor and the shear-span to effective depth ratio. The fiber tensile strength and the aggregate size have the lowest effect, with only about 1% on average to change the predicted value of the shear strength. By building an accurate ML model and by opening its black-box, future researchers can focus on some attributes rather than others.

Punching Shear Strength of FRP-Reinforced Concrete Slabs without Shear Reinforcements: A Reliability Assessment.

The recent failure of buildings because of punching shear has alerted researchers to assess the reliability of the punching shear design models. However, most of the current research studies focus on model uncertainty compared to experimentally measured strength, while very limited studies consider the variability of the basic variables included in the model and the experimental measurements. This paper discusses the reliability of FRP-reinforced concrete slabs’ existing punching shear models. First, more than 180 specimens were gathered. Second, available design codes and simplified models were selected and used in the calculation. Third, several reliability methods were conducted; therefore, three methods were implemented, including the mean-value first-order second moment (MVFOSM) method, the first-order second moment (FOSM) method, and the second-order reliability method (SORM). A comparison between the three methods showed that the reliability index calculated using the FOSM is quite similar to that using SORM. However, FOSM is simpler than SORM. Finally, the reliability and sensitivity of the existing strength models were assessed. At the same design point, the reliability index varied significantly. For example, the most reliable was the JSCE, with a reliability index value of 4.78, while the Elgendy-a was the least reliable, with a reliability index of 1.03. The model accuracy is the most significant parameter compared to other parameters, where the sensitivity factor varied between 67% and 80%. On the other hand, the column dimension and flexure reinforcement are the least significant parameters compared to other parameters where the sensitivity factor was 0.4% and 0.3%, respectively.

Shear Behavior of Post-Tensioned Concrete Beams with Draped FRP Tendons and without Transverse Reinforcement

To investigate the shear behavior of post-tensioned concrete beams with fiber-reinforced polymer (FRP) reinforcements, six large-scale post-tensioned beams without transverse reinforcement and with a shear span-to-effective depth ratio of approximately 3.0 were tested to failure. All beams were longitudinally reinforced with draped prestressed carbon FRP tendons and non-prestressed glass FRP bars. The test variables included the amount of flexural reinforcement and the prestressing level. With the aid of full-field measurement on the beam surface using digital image correlation, the kinematics of the critical shear crack of each beam were tracked. Two shear failure modes, including shear compression and shear tension, were observed in the tested beams. Generally, when the amount of flexural reinforcement increased, there was a corresponding increase in the maximum shear force. When the total prestressing force was increased from 360 to 440 kN, the shear cracking strength and the maximum shear strength increased by 6.9% and 10.0%, respectively. It was demonstrated that an arch mechanism formed in the tested FRP post-tensioned beams, although the contribution of aggregate interlock to the shear capacity was negligible. The predictions of the shear capacity calculated from various shear design models showed that the American and Japanese recommendations were highly conservative, whereas the Canadian recommendations were more consistent with the experimental results.

Shear in sand-lightweight and conventional high strength concrete through the push-off test

abstract: Shear design models in reinforced concrete structures depend on stress transfer through cracks. Such mechanism is influenced by the displacement and roughness of the opposite faces generated during cracking. Shear is reduced when an aggregate particle is fractured leading to a smoother crack as found in lightweight and high strength concrete. This study evaluated the ultimate shear strength of sand-lightweight and conventional high strength concrete as well as the differences in their behavior. Results from Pereira and Soares with 29 push-off test specimens were used. Transverse clamping stress ranged from 4.79 to 12.71 MPa while fcm was 30 and 50 MPa. The experimental results showed significant differences in the concrete studied. A tri-linear model was proposed to calculate the ultimate shear strength. An overall mean value of τu, exp/τu, cal was 0.96.

Shear capacity prediction of slender reinforced concrete structures with steel fibers using machine learning

Shear failure in reinforced concrete beams poses a critical safety issue since it may occur without any prior signs of damage in some cases. Many of the existing shear design equations for steel fiber reinforced concrete (SFRC) beams include significant uncertainty due to failure in reflecting the phenomenology of shear resistance accurately. Given these, adequate reliability evaluation of shear design provisions for SFRC beam is of high significance, and increased accuracy and minimisation of variability in the predictive model is essential. This contribution proposes machine learning (ML) based methods - Gaussian Process regression (GPR) and the Random Forest (RF) techniques - to predict the ultimate shear resistance of SFRC slender beams without stirrups. The models were developed using a database of 326 experimental SFRC slender beams obtained from previous studies, utilising 75% for model training and the remainder for testing. The performance of the proposed models was assessed by statistical comparison to experimental results and to that of the state-of-practice existing shear design models (fib Model Code 2010, German guideline, Bernat et al. model). The proposed ML-based models are in close alignment with the experimentally observed shear strength and the existing predictive models, but provide more accurate and unbiased predictions. Furthermore, the model uncertainty of the various resistance models was characterised and investigated. The ML-based models displayed the lowest bias and variability, with no significant trend with input parameters. The inconsistencies observed in the predictions by the existing shear design formulations at the variation of shear span to effective depth ratio is a major cause for concern; reliability analysis is required. Finally, partial resistance safety factors were proposed for the model uncertainty associated with the existing shear design equations.

Assessment of Punching Shear Design Models for FRP-RC Slab–Column Connections

Several empirical models have been introduced during the last two decades to estimate the punching capacity of two-way slabs reinforced with fiber-reinforced polymer (FRP) reinforcement. In this study, the applicability of these models on FRP-reinforced concrete (RC) slab-column interior and edge connections subjected to gravity loads is assessed. The models are also calibrated against experiments conducted previously by the authors on FRP-RC edge connections subjected to reversed-cyclic lateral loads. Test results of 68 interior and 25 edge specimens, 6 of which were tested under reversed-cyclic lateral loads, were used to evaluate the available models. Based on the analysis, a universal model capable of accurately predicting the capacity of both interior and edge specimens subjected to gravity or cyclic loads is proposed. The proposed model provided a mean test-to-predicted strength of 1.01 ± 0.14 and 1.01 ± 0.09 for interior and edge specimens, respectively. Furthermore, a design model is proposed to estimate gravity shear limits for FRP-RC connections without shear reinforcement and subjected to cyclic load.

Shear strength of prestressed FRP reinforced concrete beams with shear reinforcement

To avoid brittle shear failures, the shear strength of reinforced concrete beams has to be verified at ultimate limit state. For this purpose, simple but accurate shear design provisions or shear resistance models are required. In current design provisions the influence of prestressing is either neglected or insufficiently considered in the design equations leading to rather conservative results due to the lack of investigations concerning the shear strength of FRP prestressed beams. To overcome this drawback, shear tests on concrete beams with textile shear reinforcement and pre-tensioned CFRP tendons were conducted and the results are presented in this paper. Besides the investigation of the influence of the level of prestressing and of the shear span-depth ratio on the shear strength, special attention was paid to the formation and the inclination of the shear cracks as well as the crack pattern to investigate the failure mechanism more in detail. Furthermore, theoretical investigations were conducted in order to derive a simple shear design model for prestressed concrete beams with FRP shear reinforcement. For this purpose, an existing shear resistance model based on a truss model with variable strut inclination is extended considering the beneficial effects of prestressing on shear strength.

Variable strut inclination model for shear design of FRP reinforced concrete members with shear reinforcement

To avoid brittle shear failures, the shear strength of reinforced concrete beams has to be verified at ultimate limit state. For this purpose, simple but accurate shear design provisions or shear resistance models are required. In this paper, the derivation of a simple shear design model for beams with FRP shear reinforcement is presented. At first, the suitability of existing code provisions and shear resistance models is evaluated using a large databank on shear tests on members with FRP shear reinforcement. Based on the results, a shear resistance model is developed based on a truss model with variable strut inclination, which is also the basis of the shear design of members with steel shear reinforcement according to current Eurocode 2. An important aspect regarding the derivation of the model is the definition of an appropriate method to determine the angle of the compression strut. For this purpose, a compression field model originally developed for steel reinforced concrete beams is adopted. The proposed resistance model is validated by means of a databank evaluation. Moreover, an equation to determine the minimum shear reinforcement ratio of FRP reinforced concrete members is derived based on the shear design provisions according to Eurocode 2.

A shear design model for RC beams strengthened with fabric reinforced cementitious matrix

The shear behavior of fabric reinforced cementitious matrix (FRCM) strengthened beams requires more research efforts to be fully understood. A detailed investigation into the shear capacity of FRCM shear-strengthened beams has generally been limited. Therefore, the development of an accurate and reliable mechanics-based design model is required for broader applications of the FRCM system. This research contribution proposes a shear model based on the simplified modified compression field theory (SMCFT). The accuracy of the proposed model was assessed and compared against an experimental database of FRCM shear-strengthened beams available in the literature. The database is representative of various beam geometries, concrete strengths, and internal reinforcement. Moreover, the FRCM strengthening system comprises of different fiber types including carbon, glass, basalt, and polyparaphenylene benzobisoxazole (PBO) applied using different bond schemes. The proposed analytical procedure provides accurate and safe predictions for the shear capacity of the strengthened beams with an average theoretical to experimental shear capacity (Vth/Vex) ratio of 0.96 with a standard deviation of 0.14. Moreover, the prediction capability of the proposed model was compared with other models available in the literature and resulted in a better prediction capability in terms of safety, accuracy, and economic aspects.

Shear strength model of reinforced concrete beams without stirrup used in the CIS countries

ABSTRACTSNiP code is widely used in the so-called Post-Soviet Union or Commonwealth of Independent States (CIS) countries for the structural designs of reinforced concrete (RC) structures. The existing shear strength estimation model specified in SNiP code was initially developed about 90 years ago based on a semi-empirical approach, which means its accuracy and safety level significantly depends on the shear test results available at that time. In this study, a rational modification factor is derived to improve the accuracy of the shear design equation in SNiP code using a current up-to-date large shear database, and the key influencing factors of the shear resistance of RC beams, such as the size effect and tensile strength of concrete, were addressed. To verify the accuracy and safety level of the proposed models, detailed verifications are introduced with comparisons to the six different shear design models used in the international building codes, in which ACI-DAfStb shear database consisting of a total of 784 test results was utilized. According to verification results, the SNiP code model with the new modification factor provided a comparable analytical accuracy and reasonable safety level compared to the current international building code models.

ANALYSIS OF SHEAR DESIGN RECOMMENDATIONS FOR FRP REINFORCED CONCRETE BEAMS

Research shows that most shear design models for concrete beams reinforced with FRP reinforcement provide conservative results that leads to excessive amounts of reinforcement and increased overall cost of such construction. This paper presents comparative analysis of current shear design models for concrete beams reinforced with longitudinal FRP reinforcement and FRP stirrups. New analytical shear design model, developed by Valivonis et al., has been included in the analysis. A database with 88 specimens reinforced with FRP reinforcement was compiled in order to verify the accuracy of the proposed model by Valivonis et al. It is shown that proposed shear design model yields quite accurate and consistent results as an average of Vexp / Vpred values is 0.98 and coefficient of variation is 26.0% for this model.

Comparison of Shear Design Models for Reinforced Concrete Beams Strengthened with Inorganic Matrix Composite Materials

Comparison of Shear Design Models for Reinforced Concrete Beams Strengthened with Inorganic Matrix Composite Materials