Shear Strength Of Beams Research Articles

Shear Strength of RC Beams without and with Stirrups: Analytical Expressions and Comparison with Experimental Data

Shear Strength of RC Beams without and with Stirrups: Analytical Expressions and Comparison with Experimental Data

Hygrothermal aging behavior of C/GFRP hybrid rod with bundle‐by‐bundle dispersion

AbstractFiber hybrid with bundle‐by‐bundle dispersion can achieve the high performance of composites, fully understand the hybrothermal resistance of hybrid composites is the key to prove the applications in engineering structures. In the present paper, the hygrothermal resistance performances of new type carbon and glass fiber reinforced epoxy based hybrid rod with bundle‐by‐bundle dispersion produced by pultrusion technology is investigated experimentally. The tests of water absorption and desorption, thermal and mechanical performances are performed to obtain the evolution rules of hygrothermal aging. As a result, the water absorption of hybrid rod confirms to the Fick's diffusion behavior, the serious relaxation of resin matrix and the interfacial debonding of fiber‐resin exposed at high temperature provide more diffusion space for water molecules. Long‐term hydrothermal aging results in the recoverable plasticization of resin matrix and irrecoverable interfacial debonding of fiber‐resin, which brings about the degradation of 6.7%–15.0% for short beam shear strength (SBSS) retention. In addition, the plasticization effect reduces the cross‐linking density of resin matrix, which leads to the degradation of 3.3%–15.6% for glass transition temperature (Tg) retention. The life prediction results show that degradation rate of SBSS is gradually slow down and reached to a stable retention of 85.5%.Highlights Relaxation of resin matrix and interfacial debonding accelerate the diffusion of water molecules. Plasticization and interfacial debonding lead to the degradation of short beam shear strength retention and glass transition temperature. Long‐term life prediction shows that short beam shear strength e retention is 85.5%.

Shear Performance of RC Beams Strengthened with High-Performance Fibre-Reinforced Concrete (HPFRC) Under Static and Fatigue Loading

This study experimentally assessed the shear performance of reinforced concrete (RC) beams strengthened with U-shaped High-Performance Fibre-Reinforced Concrete (HPFRC) under static and fatigue loading. Key parameters included HPFRC jacket thickness and beam shear span–depth (a/d) ratio. Five beams were tested under static loads to determine ultimate shear strengths, followed by fatigue tests on identical beams at 30–70% of ultimate shear strengths at 4 Hz. In static loading experiments, all the HPFRC jacketing proved effective, increasing the shear strength of RC beams by 95% to 130%. Although the strengthening system did not change the failure mode of the beams, the strengthened beams exhibited pseudo-ductile behaviour. As the a/d increased, the shear enhancement capability of the HPFRC jackets decreased. In fatigue loading experiments, all the HPFRC systems improved the fatigue life of RC beams. Specifically, in beams with an a/d ratio of 2.0, the fatigue life was extended from 75 cycles to a maximum of 951 cycles, while in beams with an a/d ratio of 3.5, it increased from 12,525 cycles to 48,786 cycles. In addition, a predictive model has been developed for the fatigue life of HPFRC/UHPFRC shear-strengthened beams, utilising the maximum fatigue load and the design’s ultimate shear strength under static loading conditions.

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

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

A deformability-based mechanical model for predicting shear strength of FRP-strengthened RC beams failed in concrete cover separation

Concrete cover separation (CCS) is frequently happened prior to the yielding of steel stirrups in FRP-strengthened RC beams. However, the debonding mechanism and criterion have not been fully understood. In this study, the typical crack types associated with CCS are comprehensively summarized and investigated in terms of profiles and kinematics of crack. The dowel action and dowelling cracks are proved to be the dominant factors causing CCS. Based on the cracking features, the simplified local debonding strength and average shear strength of fracture interface, which constitutes the contribution of concrete to shear capacity of strengthened RC beams, are analytically derived and verified against the available experiments and code provisions. Through regression analysis of 179 collected shear tests, a formulation based on the Critical Shear Crack Theory (CSCT) is presented to assess the deformability of strengthened RC beams governed by CCS. The commonly overlooked actual stress level in steel stirrups is considered as a function of the rotation capacity of beams and assessed based on the Modified Compression Field Theory (MCFT). Validation of this analytical approach, involving comparison against the empirical models and experimental results from 107 specimens, confirms its superior effectiveness and consistency in predicting CCS and shear strength.

Experimental study on the shear behaviors of inverted castellated T-steel reinforced UHPC (ICTSRU) beams with hollow section

To reduce the production costs of steel reinforced UHPC composite beams and fully utilize the material strength of steel, this paper introduced an innovative prefabricated composite beam comprising a reinforced ultra-high performance concrete beam and an internal castellated inverted T-steel, forming an inverted castellated T-steel reinforced UHPC (ICTSRU) composite beam. Investigating the shear behavior of ICTSRU beams is the primary objective of this research. Seven composite beams were loaded under simply supported four-point loading conditions, and the effects of key parameters such as the shear span-depth ratio, steel fiber volume fraction, and stirrup ratio were studied. The findings from the test indicated that the ICTSRU beams demonstrated superior deformation ability and significant residual shear strength after the peak load. The shear span-to-depth ratio significantly influenced the failure modes and carrying capacity of the ITSRU beams. As the span-to-depth ratio increased from 1.1 to 1.6 and 2.1, the failure mode developed from shear failure to flexural failure and the shear resistance decreased by 19 % and 48 %, respectively. Enhancing the steel fiber volume fraction and the stirrup ratio can mitigate the initiation and propagation of diagonal cracks, thereby augmenting the shear strength and ductility of ICTSRU beams. Following a comprehensive analysis of the experimental results, a predictive model for the shear strength of the ICTSRU beam is proposed. This model posits that the shear capacity of the ICTSRU beam comprises the shear resistance contributions from the UHPC matrix, stirrups, steel web, and steel fibers. A comparative analysis of the computed values and the test results showed that the proposed calculation method has a high accuracy in predicting the ultimate shear strength of ICTSRU beams.

Influence of fine aggregates replaced ratio on shear strength of oyster shell concrete beam using GFRP rebars

The recycle of oyster shell as a component of concrete is a considerable solution around the world, not only ameliorate environment quality due to waste pollution but also decelerate the depletion of traditional aggregates. In this study, the oyster concrete is elaborated and performed in the order to determine many mechanic properties such as compressive strength, tensile strength or modulus of elasticity. These parameters are an important information, allowing to predict the shear strength of concrete in the structure using Glass Fiber Reinforced Polymer (GFRP) rebar, where a part of fine aggregate is replaced by oyster shell. Besides, many 3-points bending test were realized in several beams with different ratios of replacement. The presence of oyster shell crushed replacing the natural sand reduced many mechanic characteristics of concrete, including the shear behaviour. However, compared to theoretical predictions, the results given by experiment seems betters, although there is a diminution of shear strength in almost specimens. This argument leads to the possibility of using this kind of concrete with GFRP rebar in the design of manufacturing precast members, mainly under the load introducing the shear force

Shear behavior of reinforced concrete beams with high-strength reinforcements after high temperatures

This paper investigates the effect of steel reinforcement configured with different strengths after different high temperatures on the shear performance of the test beams, a total of 20 reinforced concrete (RC) beams, through experiments, numerical analyses and theoretical studies, in order to understand the key factors affecting the shear performance of the beams. The test revealed that the mechanical properties of concrete and steel reinforcement showed a trend of increasing and then decreasing after high temperatures. Increasing the stirrup ratio and stirrup strength can significantly improve the crack resistance and shear capacity of the beams, as well as the deformation performance of the beams. The residual shear strengths of test beams with high-strength stirrups after exposure to high temperatures are significantly greater than those of ordinary reinforced concrete beams. Specifically, the shear capacity of beams with high-strength stirrups after exposure to 800°C increased by 23.7 % compared to ordinary beams, and the mid-span deflection performance increased by 28.7 %. The stresses in the shear span region of the test beams after high temperature were more concentrated at the diagonal and the number of cracks was significantly reduced. In this paper, a simplified formula for calculating the residual shear capacity of RC beams after room and high temperatures is proposed, which can well predict the test results.

Predicting shear strength of fiber-reinforced concrete beams reinforced with longitudinal FRP bars with machine learning techniques

ABSTRACT This study investigates the shear strength prediction of Fibre-Reinforced Concrete (FRC) beams reinforced with Fibre-Reinforced Polymer (FRP) bars and without stirrups through the application of Machine Learning (ML) techniques. The utilisation of FRP bars, particularly Glass Fibre-Reinforced Polymer (GFRP) and Basalt Fibre-Reinforced Polymer (BFRP) bars, has emerged as a promising alternative to traditional steel reinforcement due to their superior mechanical properties and corrosion resistance. Moreover, the incorporation of macro- and micro-discrete fibres into concrete compositions enhances both shear and flexural behaviour while reducing crack propagation induced by tensile stresses. The primary objective of this research is to develop accurate predictive models for the shear capacity of FRP-reinforced concrete beams, considering various influential parameters. Six different ML techniques, namely Multiple Linear Regression (MLR), Gaussian Process Regression (GPR), k-Nearest Neighbors (KNN), Support Vector Machines (SVMs), Artificial Neural Networks (ANNs) and Random Forest Regression (RFR), are employed to analyse the complex interactions between input variables, such as fibre type, bar diameter, concrete compressive strength, beam dimensions and the resulting shear strength. By leveraging these computational approaches, we aim to overcome the limitations of conventional analytical methods and provide robust predictions for structural design and optimisation.

Experimental Study on Shear Strengthening of Reinforced Concrete Beams by Fabric-Reinforced Cementitious Matrix.

In this study, an experiment was conducted to investigate the shear performance of reinforced concrete (RC) beams strengthened using fabric-reinforced cementitious matrices (FRCM). Four reinforced concrete beams, including a control specimen, were fabricated, and the shear strengthening effect of the FRCM was investigated on eight shear specimens, with the strengthening type and shear reinforcement as key variables. In particular, the digital image correlation (DIC) technique was applied to closely analyze the deformation of reinforced concrete beams subjected to shear forces. The average shear strain-shear stress curve of each specimen was derived, and the contributions of shear and bending to the vertical deflection and the change in the principal strain angle with increasing shear force were analyzed. The experiment results showed that all specimens failed with diagonal cracks within the shear span. In the specimens without shear reinforcement, the shear strength increased by up to 65% according to the FRCM strengthening, while in the specimens with shear reinforcement, only the sided bond strengthened specimen showed a strength increase of 16% compared to the control specimen. Based on displacement data of the DIC, it was confirmed that FRCM strengthening can control the deformation of the RC beam. To evaluate the shear strength of the FRCM-strengthened RC beams, a shear strength model was proposed by considering the contributions of the concrete section, shear reinforcement, and FRCM. The proposed model was capable of reasonably evaluating the shear strength of RC beams strengthened with FRCM, considering the shear contribution of FRCM and bond capacity between FRCM and concrete substrate, in which the shear strength of specimens was underestimated by 28% to 35%.

Novel sustainable techniques for enhancing shear strength of RC beams mitigating construction failure risk

The aim of this study is to evaluate the effectiveness of various innovative and sustainable methods for improving the shear performance of reinforced concrete (RC) beams. The potential risk of failure for such elements is considered a potential threat, therefore, this study addresses it through experimental tests and numerical analyses to be mitigated carefully in order to enhance the safety and sustainability of buildings. A total of eleven specimens, comprising two control specimens and nine strengthened specimens, underwent three-point testing. Several proposed strengthening techniques, each involving multiple parameters, were examined. In the initial approach, glass fiber-reinforced polymer (GFRP) textile embedded in an external fiber-reinforced cementitious mortar (FRCM) jacket was utilized, with an evaluation of the number of the GFRP textile layers (1, 2, and 3 layers). The second technique incorporated near surface mounted (NSM) GFRP bars along with the FRCM jacketing, where the diameter of the GFRP bars (10, 12, and 16 mm) served as the primary parameter. In the final technique, externally bonded stainless-steel strips (SSSs) of varying thicknesses (1, 1.25, 1.50 mm) were affixed to the beams’ surface. The obtained results revealed that the application of the FRCM jacketing method yielded positive results, showing a significant 30.7 % average increase in the crack initiation load and a 17.1 % improvement in the failure load compared to the defected beam. However, issues of debonding beneath the loading point were observed in the FRCM jacket, particularly with three layers of the GFRP textile, leading to the separation of the concrete cover. Moreover, combining the NSM GFRP bars with an FRCM jacket addressed the absence of shear stirrups. The most remarkable improvement was noted utilizing the NSM GFRP bars and an FRCM jacket, followed by employing SSSs with an FRCM jacket.

High-dimensional multi-objective optimization of coupled cross-laminated timber walls building using deep learning

This paper introduces a deep learning-based multi-objective optimization framework, applying for advancing the design of the Cross-Laminated Timber Coupled Wall system. While traditional optimization methods often struggle with the curse of dimensionality in high-dimensional problems, the approach proposed in this study employs an autoencoder to effectively reduce the dimensionality of the design space. Subsequently, a neural network establishes a mapping between input variables and latent spaces, with another neural network forming the crucial link between these latent variables and the output responses. The proposed framework is integrated into the design process of a 20-story Cross-Laminated Timber Coupled Wall system, where uncertainties inherent in connection elements are systematically addressed to optimize the structural parameters. The non-dominated sorting genetic algorithm-II is utilized to estimate optimal design variables by minimizing three conflicting objective functions, thereby generating a Pareto front. This optimized design is then bench-marked against three deterministic models with varying coupling beam shear strengths. A two-dimensional numerical model developed in OpenSees facilitates nonlinear time history analysis using 50 bi-directional ground motion records, representative of the seismicity of Vancouver, Canada. The results of this study not only highlight the efficacy of the deep learning-based framework in enhancing the structural integrity and resilience of high-rise timber structures in seismic regions but also significantly contribute to the evolution of computational approaches in structural engineering.

Improving Shear Strength Prediction in Steel Fiber Reinforced Concrete Beams: Stacked Ensemble Machine Learning Modeling and Practical Applications

Existing machine learning (ML) models often encounter challenges in accurately predicting the shear strength of steel fiber reinforced concrete (SFRC) beams, mainly due to a lack of generalization. This study introduces an advanced stacked ensemble ML architecture to overcome this limitation by utilizing a comprehensive data set of 394 experimental observations and a 20-feature matrix. The model exhibits exceptional performance with a mean absolute error of 0.391 and a correlation coefficient (R2) of 93.7%, and surpasses traditional ML algorithms. Furthermore, a sensitivity analysis of the developed model yields that shear strength is highly responsive to the shear span-to-effective depth ratio, with an increase from 1 to 4 resulting in a significant reduction (about 50%) in strength. Increasing the percentage of longitudinal steel from 1 to 2% leads to a 14.6% gain, whereas doubling its yield strength has a more modest 3.7% effect. Increasing the compressive strength of concrete from 25 to 50 MPa, notably increases the shear strength by 19.6%. Fiber length, diameter, and aspect ratio exhibit varying impacts, with shear strength most influenced by the fiber volume fraction, which leads to a peak enhancement of 30.7% at 2% fibrous volume; however, the tensile strength of fibers minimally affects the shear strength. Additionally, this research presents a simplified empirical model to predict the shear strength of SFRC beams based on the key determinants. This model employs the iterative Gauss–Newton algorithm, demonstrates reasonable predictive capability, and boasts an R2 of 83.3% and mean prediction-tested strengths of around 1.039. The practical implications of these findings are substantial for the construction industry as they enable a more accurate and reliable design of SFRC beams, optimize material usage, and potentially reduce construction costs as well as enhance structural safety.

Behavior and shear strength of prestressed steel reinforced concrete composite deep beam

In order to optimise the utilisation of material properties, simplify the construction process and enhance the industrialisation of steel reinforced concrete beams, an innovative prestressed steel reinforced concrete composite beams(PSRCC) was proposed, which was achieved by integrating prestressing technology and prefabricated technology to steel reinforced concrete structure. To investigate the shear PSRCC deep beams, a static load test was conducted on 7 PSRCC deep beams. The study investigated the effects of parameters such as shear span-depth ratio, prestressed tendons degree, form, height and application sequence on the failure mode, crack pattern, load-displacement behavior, strain response and damage evolution. A model was established to predict the shear strength of PSRCC deep beams, considering the steel-concrete interaction, using the von Mises yield criterion and the SST model, which assessed the contributions of composite strut, prestressed tendons and shear steel web for shear strength. The test results showed that the prefabricated and cast-in-situ concrete components maintained good integrity, and PSRCC deep beams eventually experienced typical diagonal compression failure. Applying prestressing and reducing the shear span-depth ratio under identical conditions would reduce the deformation capacity of PSRCC deep beams. When the shear span-depth ratio was reduced from 1.0 to 0.5, the cracking load and peak load of the specimens increased by 17.31 % and 16.53 % respectively. Increasing the prestress level from 0 to 0.3 and 0.6 increased the cracking load of the specimens by 1.41 and 2.36 times, respectively, but the peak load of the specimens increased by only 3.37 % and 8.17 %. The cracking load of the parabolic tendon specimen increased by 2.18 for the comparison specimen but was 8.33 % lower than that of the linear tendon specimen with the same degree of prestressing. Comparison of the two prestressing sequences showed that the cracking load of the specimen with tensioning prestressed tendons after pouring the entire beam section increased by 29.84 %, but the peak load increased by only 3.11 %. As the height of the prestres tendons increased, the cracking and peak loads of the specimen reduced by 5.84 % and 5.71 % respectively. Consequently, the shear strength of PSRCC deep beams was significantly influenced by the shear span-depth ratio and minimally affected by prestress-related parameters. The proposed model accurately predicted the shear strength of PSRCC deep beams compared to existing codes, offering valuable guidance for design.

Prediction and reliability analysis of shear strength of RC deep beams

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

GFRP COMPOSITES: A MATERIAL TO STRENGTHEN REINFORCED CONCRETE BEAMS WITH WEB OPENINGS FOR SHEAR

Buildings that require mechanical and electrical services must have utility pipes and ducts. The services include air conditioning, power supply, telephone lines, network cables, sewerage lines, water supply and etc. A reinforced concrete (RC) deep beam with web openings experiences excessive cracking and deflection, as well as a decrease in beam stiffness. Enlargement of these openings near supports would reduce beams’ capacity for shear. Hence, analysis and design of such beams require careful consideration, particularly with regard to their performance. In addition, design compliance to relevant codes and standards, and selection of suitable material properties and construction techniques are needed. When such an enlargement is unavoidable, strengthening of beam for shear and flexure is necessary. In this study, the use of GFRP (Glass-Fiber Reinforced Polymer) composites for strengthening of RC beams with openings is experimentally investigated. As compared to the control beam, test results showed that using GFRP was found to be effective in increasing the shear strength of beams with openings by 40% to 60%. Test results of beams with web openings exhibited higher shear strength than the predicted values whereas for strengthened beams with GFRP, code predictions are found conservative.

Prediction of the shear strength of lightweight concrete beams without web reinforcement based on a machine learning model optimized by a genetic algorithm

The shear performance of concrete beams is affected by several factors, and some of effective variables and control mechanisms should be considered in predicting shear strength. Compared with ordinary concrete, lightweight concrete (LWC) is more unique, which greatly increases the difficulty of prediction. This is also why it is necessary to introduce machine learning (ML) technology with stronger data processing capabilities to predict the shear performance of LWC. Therefore, the aim of this study is to employ four well-known machine learning methods to predict the shear performance of LWC beams, namely, support vector machine (SVM), artificial neural network (ANN), radial basis function (RBF) neural network and random forest (RF). First, the shear test results of 220 LWC beams were collected, and the corresponding datasets were established based on possible influencing factors. Then, the optimal dataset partitioning methods for four different ML models were explored and determined. The parameter search process of the four models under the optimal dataset partitioning ratio was optimized using a genetic algorithm (GA), and four GA-ML prediction models were developed. The results show that the developed GA-RF model achieves a train set accuracy of 95.3 % and a test set accuracy of 93.3 %. The GA-ML technology significantly improves the accuracy of the prediction of shear strength compared to the formulaic model based on current international design standards. The prediction mechanism of the model is further analyzed to ensure that the model is reliable. The results indicate that it can be applied to predict the shear strength of LWC. In summary, the GA-RF model and importance analysis proposed in this article are practical methods for predicting and explaining the shear strength of LWC.

A new approach to calculate the shear strength of high-performance reinforced concrete beams fibered with micro polypropylene (experimental and analytical study)

Micro polypropylene (PP) fibers are commonly utilized to increase concrete's durability and fire resistance in building projects. High-Performance-Fiber-Concrete (HPFC) has become increasingly popular in the sustainable buildings industry in the past two decades. Some important structures were constructed using HPFC with micro polypropylene fibers to limit corrosion and increase fire resistance. This paper presents an experimental and analytical investigation to study the effect of micro PP fibers on the shear strength of HPFC beams with and without stirrups. The experimental results were used to obtain a new and simple approach that can calculate the shear strength of HPFC beams without needing for experimental findings. Also, the effect of PP fibers was compared with that of using steel (ST) fibers only or the hybridization of both PP and ST fibers. Twelve simply supported beams were fabricated and loaded with a concentrated load up to failure and all the required data were obtained and examined. The results indicated that adding PP fibers was effective in increasing both the shear capacity and the toughness of HPFC beams, either with or without stirrups, especially for beams with 1 % PP fibers. For beams without stirrups either with or without PP fibers, the mode of failure was diagonal tension shear failure. The presence of stirrups and / or ST fibers changed the failure mode from diagonal tension shear failure to compression shear failure. Analytically, a new approach of ten equations, was proposed based on the angle of compression struts and the splitting tensile concrete strength, to calculate the shear strength of HPFC beams. The equations of the proposed approach were compared with the results of forty five experimental specimens from four different research studies to examine their validity. The results were in a very good agreement and accuracy with the experimental results.

Analysis of deformation and failure mechanism of sandwich beams with lattice core under three-point bending load

This paper investigates sandwich beams with lattice cores under quasi-static bending, owing to their lightweight nature and high energy absorption capabilities. Utilizing analytical methods governing beams, an investigation into their failure mechanisms is conducted, incorporating experimental and numerical results. The influence of thickness and core cell sizes on energy absorption are examined. The analysis delves into the elastic and plastic behavior of the beam, which is refined and validated against the numerical and experimental tests and failure modes of sandwich panel beams. The alignment of analytical predictions with both experimental and numerical results in terms of mean forces, and energy absorptions was remarkably precise. Moreover, evidence has been presented that the face yield and core shear failure regions are significantly impacted by variances in core dimensions. Additionally, the thickness of core cell strands was found to be pivotal in influencing the compressive and shear strengths of sandwich panel beams.

Estimation of the shear strength of UHPC beams via interpretable deep learning models: Comparison of different optimization techniques

In this article, optimized deep learning (DL) models with different algorithms are adopted to estimate the shear strength of rectangular ultra-high performance concrete beams (UHPC-Bs) in order to overcome the challenges in traditional mechanics-based approaches. Long short-term memory (LSTM) and gated recurrent unit (GRU) are chosen as the DL models, whereas the recent popular optimization algorithms are phasor particle swarm optimization (PPSO), dwarf mongoose optimization (DMO), mountain gazelle optimizer (MGO), and atom search optimization (ASO). A thorough and reliable dataset of 244 UHPC-Bs test results with ten input features has been used to construct the hybrid DL models. The performance of the optimized hybrid LSTM and GRU models with different algorithms is extensively assessed and compared based on various statistical metrics, error, and score analyses. Then, the model with the best estimation performance is determined and compared with the mechanics-based formulas in the current international design codes. Additionally, Shapley additive explanations (SHAP) analysis is used to assist in the interpretability of DL models and to reveal the effects of input features that contribute to the model's estimation. According to the results of the present work, all DL models successfully estimate the shear strength of UHPC-Bs. Among these models, the MGO-LSTM model stands out compared to the other models in terms of several performance measures for both the training and testing phases, like a higher R2 value, lower RMSE, MAPE, and MAE values, as well as a smaller error ratio and a higher final score. The performance of the algorithms applied to optimize the hyper-parameters of the LSTM and GRU models can be ranked as follows: MGO > DMO > PPSO > ASO. Moreover, a graphical user interface (GUI) was constructed based on the best estimation model that was built so that the shear strength of UHPC-Bs could be estimated in real-world situations without the need for any extra software or tools. This enables more users to quickly and easily estimate the shear strength of UHPC-Bs, optimize design processes, and decrease experimental testing costs.