Stirrup Strength Research Articles

Uniaxial compressive stress-strain behavior of steel fiber reinforced geopolymer concrete confined by stirrups: Experimental study and analytical model

The compressive stress-strain relationship of confined steel fiber reinforced geopolymer concrete (SFRGC) is a basis for its structural nonlinear analysis and engineering design. This paper presents an experimental study on the stress-strain behavior of stirrup confined-SFRGC under uniaxial compression, with emphasis on the effects of stirrup spacing, stirrup strength and steel fiber (SF) volume fraction. The failure modes, stress-strain curves, energy absorption capacity and post-peak ductility were analyzed. The results demonstrated that due to the stirrup constraint and SF fiber crack-bridging effects, the integrity of specimens was significantly improved, showing notable ductile failure mode. The stress-strain behavior of core SFRGC was notably affected by the constraint level of stirrups, however, the effect of SF was mainly reflected in post-peak stress-strain branches. Reducing the stirrup spacing, improving the stirrup strength, and increasing the SF content can effectively enhance the strength and deformation characteristics of confined-SFRGC, as well as ductility. Moreover, synergetic effect of SF and stirrups on improving the deformation capacity of SFRGC was observed, whereas the peak stress and corresponding strain changed insignificantly with the SF content. In addition, the stirrups can reach yield around the peak stress point. Based on the analysis of test results, formulae for characterizing the peak stress, peak strain, elastic modulus as well as stress-strain responses of confined-SFRGC were proposed, with the effective confinement index of stirrups and fiber reinforcing factor introduced. The model predicted curves were in great agreement with the test curves.

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.

Shear Performance and Damage Characterization of Prefabricated Basalt Fiber Reactive Powder Concrete Capping Beam Formwork Structure

Basalt Fiber Reactive Powder Concrete (BFRPC) semi-prefabricated composite capping beam structures can effectively improve the shortcomings of ordinary concrete capping beams' construction difficulties and insufficient bearing capacity. In this study, with the objective of analyzing the shear damage and damage characteristics of a prefabricated BFRPC capping beam formwork, structural damage tests under different levels of loading were carried out to obtain the mechanical parameters of key nodes. Acoustic emission (AE) and Digital Image Correlation (DIC) techniques were used to acoustically and visually characterize the formwork damage. The research results showed that the damage stage of the capping beam formwork was divided, and an early damage warning method was proposed based on the acoustic parameters. Using the DIC technique to identify the crack width evolution pattern during the shear process, it was found that the cracks expanded steadily as the load increased. Combining the experimental and simulation results as well as the Subdivision Superposition Theory, a half-open stirrup strength discount factor β was introduced and suggested to take a value of 0.79. The formula for calculating the shear capacity of BFRPC capping beam formwork is proposed to provide a theoretical basis for its application in prefabricated assembled structures.

Experimental study and efficient shear-flexure interaction model of reinforced concrete shear walls with UHPC boundary columns

Traditional reinforced concrete (RC) shear walls have insufficient deformation capacity under strong earthquake conditions and are difficult to repair due to severe post-earthquake damage. Ultra-high performance concrete (UHPC) is a cement-based composite material with high strength and toughness, which can be applied to shear walls. Therefore, a new type of RC shear walls with UHPC boundary columns was proposed. A rectangular-shaped shear wall and two shear walls with barbell-shaped sections were tested under axial force and lateral cyclic load, and the effects of UHPC distribution, sectional shape and stirrup strength were studied. The hysteresis characteristics, ductility behavior, energy dissipation and stiffness degradation of all the specimens were analyzed and discussed. The test showed that the shear wall with UHPC boundary columns had good crack-width control ability and the damage degree was greatly alleviated even under large axial forces. The addition of UHPC could enhance the ductility and energy dissipation capacity of shear walls, especially for rectangular-shaped walls. Besides, an efficient shear-flexure interaction (SFI) model was developed for the shear walls and it could accurately capture the lateral load versus lateral displacement relationship and crack orientations. This nonlinear analysis model had fast calculation speed and effective results, with a prediction error of less than 5 % for peak loads.

Research on the innovation system of physical climbing in college physical education under big data technology

Abstract Rock climbing, as one of the outdoor sports gradually sought after by young people nowadays, plays an important role in innovating the traditional physical education system. This study integrates the training related to physical rock climbing with the conventional college physical education system and utilizes a synergistic teaching method to innovate and improve the college physical education system. Through the implementation of rock-climbing teaching experiments for students in school A, the data related to the experiments were analyzed using the literature method, questionnaire survey method, and mathematical statistics method to explore the effectiveness of the practical application of physical rock-climbing in college physical education. In terms of physical function, the heart rate indexes of students in the experimental group decreased by 8.96 and 9.08, respectively, and the lung capacity and anaerobic threshold were significantly improved, but the male students did not show any significant improvement in the index of maximal oxygen uptake. Except for the lower limb stirrup strength, the p-value of the experimental group of students in seated forward bending, dorsal extension, left-handed grip strength, right-handed grip strength, back strength, and longitudinal jump were all less than 0.05. The capacity of motor memory of the experimental group was higher than that of the control group by 2.91. In terms of social functioning, compared to the control group of students, all the experimental groups showed stronger characteristics.

Reliability-based design method for shear capacity of steel reinforced engineered cementitious composites (ECC) beams

Engineered cementitious composites (ECC) is famous for its excellent tensile deformability and crack width control ability. Steel reinforced ECC beams under shear loading exhibit brittle behaviors, which leads to a lack of structural safety. The reliability-based shear capacity model of steel reinforced ECC beams needs to be established for ensuring the structural shear safety. In this research, a test database of steel reinforced ECC beams under shear loading was constructed based on the given selecting principles. Through considering the shear resistance provided by fibers, the shear capacity model of steel reinforced ECC beams was preliminary established. The statistical characteristics of random variables were described and determined, and reliability index was calculated through Monte Carlo simulation. It is found that reliability index increases with increasing ECC strength, while decreases with increasing stirrup strength or stirrup ratio, especially at the high partial factor of ECC. For different target reliability indexes, the recommended partial factors of ECC are obtained through calibration. This research supplies a useful reference for the shear design of steel reinforced ECC beams in the actual engineering.

Shear design of recycled aggregate concrete beams using a data-driven optimization method

Under the umbrella of sustainable development, recycled aggregate concrete (RAC) is a building material that has attracted a lot of interest. This study proposes a data-driven methodology for shear capacity prediction and design optimization for RAC beams. A comprehensive test dataset with 232 samples was gathered based on clear criteria. Geometric and materials factors are identified as inputs to develop four machine learning (ML) prediction models including artificial neural network, Gaussian process regression, random forest, and categorical gradient boosting (CGB). The winner of ML models is combined with the nondominated sorting genetic algorithm II (NSGA-II) to establish a dual-objective design optimization of RAC beams subjected to shear. Results show that the CGB model achieved the highest accuracy (R2 = 0.972, RMSE = 14.909, and MAPE = 0.086) among four ML models and its standard deviation was more than 80% lower than the five existing equations. The SHapley Additive exPlanations interpreted the CGB model and identified the beam width, nominal strength of stirrups, shear-span ratio, and nominal strength of longitudinal reinforcement are the four main features affecting the shear capacity of a RAC beam. Finally, the Pareto front was created by combining the CGB model with the NSGA-II algorithm. The suggested framework provides a novel route for the structural design of RAC beams subject to shear.

Compression behavior of reactive powder concrete confined with high‐strength spiral stirrups

AbstractThe lateral confinement of stirrups can improve the load‐bearing capacity and ductility of reactive powder concrete (RPC) columns. To explore the compression behavior of RPC confined with high‐strength stirrups, 45 specimens were prepared and tested under axial compression. The concrete strength was in the range of 99.86–138.24 MPa, the tensile strength of stirrups was Grade 800, Grade 970, and Grade 1270, and the volumetric ratios of stirrups were in the range of 0.9%–2.0%. The results showed that the failure modes of RPC confined with stirrups were shear expansion failure. The compressive strength and ductility of confined RPC were improved with the increase of stirrups volumetric ratios, while stirrups strength slightly affected the compressive strength and ductility. In addition, the peak stress, peak strain, and residual stress prediction models were proposed. Furthermore, the ductility index prediction models were proposed, which can be applied to determine the volumetric ratio of stirrups in stirrups confined concrete columns.

Estimation of lateral stress of stirrups at peak stress and residual stress of confined concrete at stirrups fractured in confined concrete under axial compression

The lateral stress of stirrups at the peak stress of confined concrete was closely related to the load-bearing capacity and deformability of concrete columns, while the fracture of stirrups affected the axial deformability of concrete columns after the peak stress of confined concrete. In this paper, 156 circular concrete columns confined with spiral stirrups and 141 square concrete columns confined with mesh stirrups were tested under axial compression. The effects of the compressive strength of unconfined concrete, the volumetric ratio and the yield strength of stirrups on the lateral stress of stirrups at peak stress and the residual stress of confined concrete at stirrups fractured were analyzed. Furthermore, the prediction models for evaluating the lateral strain of stirrups at the peak stress of confined concrete were established by considering the effects of the volumetric ratio and type of stirrups and the compressive strength of concrete, which had high prediction performance. In addition, the method for judging whether stirrups fractured or not was developed, which was suitable for evaluating the stirrups with and without yield platform. The prediction model for evaluating the residual stress of confined concrete at stirrups fractured was proposed.

Predicted compressive stress–strain model for high-strength stirrup confined concrete

Concrete may be successfully contained by high-strength steel bar, increasing its strength and deformation capacity. This research conducts an analytical and experimental investigation to better understand the confining mechanism of high-strength bar on concrete. The impact of concrete strength, stirrup strength, volume-stirrup ratio, and stirrup spacing is explored using regression analysis on test data of stress–strain curves of concrete confined by high-strength stirrup. Stress analysis and regression are used to provide techniques for calculating peak stress and strain, as well as ultimate strain, in confined concrete. Based on current stress–strain curve models, a stress–strain curve model for confined concrete with high-strength stirrup with ascending, descending, and horizontal branches is developed. The findings reveal that the suggested model's stress–strain curves correlate very well with the experimental curves.

Shear Strength Prediction of Concrete Beams Reinforced with FRP Bars and Stirrups Using Gene Expression Programming

Existing reinforced concrete (RC) structures in humid regions suffer from deterioration due to the corrosion of ordinary reinforcement bars damaging the whole system. The deterioration of the transverse reinforcement leads to shear failure, which is one of the most dangerous failure modes. Therefore, researchers suggested using fiber-reinforced polymer (FRP) bars as a replacement for reinforcement bars in humid regions to integrate sustainability and improve their serviceability and durability. A simple model that can accurately estimate the shear strength of concrete beams designed with FRP longitudinal bars and stirrups is lacking. This research proposed a simplified Gene expression programming (GEP) based model to estimate the shear strength of FRP concrete beams. Seven parameters that principally dominate the shear behavior of FRP beams were utilized to create the GEP model. The parameters are the beam width, beam depth, concrete compressive strength, FRP tensile longitudinal reinforcement ratio, area of stirrups, spacing between the stirrups, and the ultimate FRP strength of stirrups. A comparison was made between the GEP and ACI-440 models; the R2 values of the total database were 92% and 54% for the GEP and ACI models, respectively. The R2 of the GEP model is considerably higher than that measured for the ACI model, and the errors of the GEP model are low, which affirms that the GEP is superior to the ACI model in estimating the shear strength of FRP beams. The trends of the GEP and ACI-440 models and the empirical results are similar, confirming the GEP model’s consistency. Using the GEP model to estimate the shear strength of concrete beams designed with FRP longitudinal bars and stirrups is recommended.

Machine learning intelligence to assess the shear capacity of corroded reinforced concrete beams

The ability of machine learning (ML) techniques to forecast the shear strength of corroded reinforced concrete beams (CRCBs) is examined in the present study. These ML techniques include artificial neural networks (ANN), adaptive-neuro fuzzy inference systems (ANFIS), decision tree (DT) and extreme gradient boosting (XGBoost). A thorough databank with 140 data points about the shear capacity of CRCBs with various degrees of corrosion was compiled after a review of the literature. The inputs parameters of the implemented models are the width of the beam, the effective depth of the beam, concrete compressive strength (CS), yield strength of reinforcement, percentage of longitudinal reinforcement, percentage of transversal reinforcement (stirrups), yield strength of stirrups, stirrups spacing, shear span-to-depth ratio (a/d), corrosion degree of main reinforcement, and corrosion degree of stirrups. The coefficient of determination of the ANN, ANFIS, DT, and XGBoost models are 0.9811, 0.9866, 0.9799, and 0.9998, respectively. The MAPE of the XGBoost model is 99.39%, 99.16%, and 99.28% lower than ANN, ANFIS, and DT models. According to the results of the sensitivity examination, the shear strength of the CRCBs is most affected by the depth of the beam, stirrups spacing, and the a/d. The graphical displays of the Taylor graph, violin plot, and multi-histogram plot additionally support the XGBoost model's dependability and precision. In addition, this model demonstrated good experimental data fit when compared to other analytical and ML models. Accurate prediction of shear strength using the XGBoost approach confirmed that this approach is capable of handling a wide range of data and can be used as a model to predict shear strength with higher accuracy. The effectiveness of the developed XGBoost model is higher than the existing models in terms of precision, economic considerations, and safety, as indicated by the comparative study.

Seismic Fragility Analysis of the Aging RC Columns under the Combined Action of Freeze–Thaw Cycles and Chloride-Induced Corrosion

The combined action of freeze–thaw cycles and chloride-induced corrosion are generally recognized as one of the main causes of the degradation of the mechanical properties and seismic performance of reinforced concrete (RC) structures in the northern frozen coastal regions. To investigate the degradation mechanisms of the seismic performance of RC columns subjected to the combined action of freeze–thaw cycles and chloride-induced corrosion, the impact of freeze–thaw cycles on the chloride diffusion coefficient of concrete was studied through concrete deterioration tests and theoretical analysis. This paper proposed a time-dependent deterioration model for RC columns, which is suitable to consider the combined action of freeze–thaw cycles and chloride-induced deterioration. The proposed deterioration model could be applied to the investigations of time-dependent seismic performance and the seismic fragility of RC columns. Based on the established deterioration model, this paper proposed a time-dependent seismic fragility analysis framework for the aging RC columns, considering the combined action of freeze–thaw cycles and chloride-induced corrosion. In addition, a representative three-span RC continuous T-shaped girder bridge that is located in the high-latitude northern frozen coastal regions of China was taken as the case study, and the time-dependent seismic fragility analysis of RC columns was conducted considering the involved uncertainties in geometric parameters, the deterioration mechanisms of the materials, and ground motions. The time-dependent seismic fragility curves of RC columns were obtained at different service time points. The results indicated that the combined action of freeze–thaw cycles and chloride-induced deterioration had a significant influence on the time-dependent seismic responses of the deteriorating RC columns. Under the combined action of freeze–thaw cycles and chloride-induced corrosion, when the RC bridge was in service for 75 years, the stirrup strength decreased by 3.88% and the cross-sectional area decreased by 30.03%. The peak stress of the confined concrete decreased by 52.1% and its peak strain increased by 12.2 times, respectively. Moreover, the time-dependent seismic fragilities of the aging RC columns under different damage states exhibited a nonlinear increase as the service life increased.

Mechanical Property Analysis and Calculation Method Modification of Steel-Reinforced High-Strength Concrete Columns.

The existing studies lack research on the ductility of steel-reinforced high-strength concrete (SRHC) columns and current specifications restricted the use of high-strength concrete in steel-reinforced concrete (SRC) columns. To compensate for the shortcomings of the existing research and promote the application of high-strength concrete in SRC structures, we test six SRHC columns and one SRC column to examine the effects of the steel content, eccentric distance, and slenderness ratio on the ductility, bearing capacity, and failure mode of SRHC columns. Further, Abaqus finite element models are established to predict the influences of more parameters on post-peak ductility and analyze the relationship between strain development of the concrete and the decrease in bearing capacity of SRHC columns. The results show that the penetration of cracks into aggregate during failure is the primary reason for the poor ductility of the SRHC columns. Improving the confinement effect of the stirrups on concrete is the most effective measure to enhance the ductility of the SRHC columns. The decline in the stirrup spacing from 100 mm to 50 mm increased the ductility coefficient from 1.47 to 5.56. The effect of the steel content, stirrup strength, and slenderness ratio on the ductility coefficient of SRHC columns is less than 30%. After analyzing the reason for the error of current specifications, a modified formula with an error of less than 5% is developed.

Experimental study on seismic behavior of T‐shaped steel fiber reinforced concrete columns

AbstractSix T‐shaped columns in which steel fiber concrete is integrated with a high‐strength stirrup (SFRC) and two control specimens are tested under a cyclic lateral load and constant axial load. The effectiveness of the steel fiber concrete and high‐strength stirrup to enhance its ductility and earthquake resistance is described at high‐and low‐axial compression ratios. The failure patterns, hysteresis response, backbone curves, ductility, and strain behavior analysis of the columns are studied systematically in the test. The effects of the stirrup strength, stirrup spacing, steel fiber content, and axial load ratio were investigated. The test results demonstrated that all specimens exhibited flexural failure. Steel fibers could prevent the cracked concrete from spalling. Specimens with high‐strength stirrups, close stirrup spacing, and steel fiber exhibited a higher lateral bearing capacity, energy dissipation capacity, initial stiffness, and displacement ductility. A new strength model for predicting the lateral ultimate capacity of T‐shaped concrete columns strengthened with SFRC subjected to cyclic loading is proposed. The calculated results agree well with the test results. Eight T‐shaped column specimens were simulated using ABAQUS finite element analysis software. A comparison of the results of the numerical study with the experimental results demonstrates that the finite element model can accurately predict the structural behavior.

Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams

Estimating shear strength is a crucial aspect of beam design. The goal of this research is to develop a shear strength calculation technique for ultra-high performance fiber reinforced concrete (UHPFRC) beams. To begin, a shear test database of 200 UHPFRC beam specimens is established. Then, random forest (RF) is used to evaluate the importance of influence factors for the shear strength of UHPFRC beams. Subsequently, three machine learning (ML)-based models, including artificial neural network (ANN), support vector regression (SVR), and eXtreme-gradient boosting (XGBoost), are proposed to compute shear strength. Results demonstrate that the area of longitudinal reinforcement has the greatest influence on the shear capacity of UHPFRC beams, and ten parameters with high importance (e.g., the area of longitudinal reinforcement, the stirrup strength, the cross-section area, the shear span ratio, fiber volume fraction, etc.) are selected as input parameters. The models of ANN, SVR, and XGBoost have close accuracy, and their R2 are 0.8825, 0.9016, and 0.8839, respectively, which are much larger than those of existing theoretical models. In addition, the average ratios of prediction values of ANN, SVR, and XGBoost models to experimental results are 1.08, 1.02, and 1.10, respectively; the coefficients of variation are 0.28, 0.21, and 0.28, respectively. The SVR model has the best accuracy and reliability. The accuracy and reliability of ML-based models are much better than those of existing models for calculating the shear strength of UHPFRC beams.

RC beams retrofitted by FRP oriented in any direction: Influence of the effectiveness factors

Shear strength of FRP-retrofitted RC beams is usually influenced by different brittle failure modes characterizing the collapse of the FRP reinforcement. The most significant analytical models for assessing the shear strength of FRP-retrofitted RC beams reflect the effect of brittle failure through an effectiveness factor “R”, which reduces the ultimate tensile strength of FRP. The brittle collapse of FRP reinforcement often leads to a lower shear contribution by steel stirrups due to hindering of the yielding of all stirrups involved by critical cracking. Some analytical models consider this phenomenon introducing a further effectiveness factor “r”, which reduces the yielding strength of stirrups. The key differences characterizing many of the shear models are represented by the expressions used for assessment of the effectiveness factors. This paper focuses on the influence of effectiveness factor models in analytical predictions provided by different shear models. The reduction of the shear contribution of steel stirrups due to FRP brittle failure is modeled as dependent on the FRP wrapping scheme, through the ratio between FRP effective strain and steel yielding strain. To highlight the influence of the effectiveness factor for steel stirrups, two analyses are performed through different shear models, considering the effectiveness factor for FRP only, and considering the effectiveness factor for both FRP reinforcement and steel stirrups. The results are discussed considering two databases, one constituted by beams whose FRP reinforcement and steel stirrups are arranged at right angles to the beam axis, and one in which the FRP is arranged at angles different from 90°.

Research on compressive performance of high-strength concrete confined by high-strength stirrups

Axial compressive test of high-strength concrete prism specimens confined by high-strength stirrups are carried out. The yield strength of stirrups, volumetric stirrup ratio and concrete strength are investigated for the impact of pressure performance. The results show that the confined concrete specimens with high stirrup ratio, high strength, exhibits good ductility. The use of high-strength stirrups is an effective measure to prevent a sudden drop in the falling section of the high-strength concrete stress-strain curve; under the circumstances, the application of high-strength stirrups can reduce the volumetric stirrup ratio.

Artificial neural network model for predicting the local compression capacity of stirrups-confined concrete

The local compression capacity is a key mechanical property for several constructions, such as the post-tensioned prestressed concrete. Due to the disordered stress distribution caused by the introduction of the concentrated load, it is a huge challenge to predict accurately the local compression capacity of stirrups-confined concrete to avoid the whole structure damage caused by local failure. This study explored a new approach to obtain the local compression capacity for stirrups-confined concrete using artificial neural networks (ANN). The ANN model was trained by a reliable database consisting of 180 samples from previous literature, which had a large application range, covering concrete strengths 15–112 MPa while the stirrup yield strengths 230–660 MPa. The main parameters, including the concrete strength, the local area aspect ratio, the core area aspect ratio, the ratio of duct diameter to the section width, the yield strength of stirrups, and the volumetric ratios of stirrups, were selected as input variables. To evaluate the proposed ANN model, the k-fold cross-validation approach was adopted to determine the generalization and reliability, and the sensitivity analysis was conducted to investigate the importance of the input parameters. Moreover, an empirical ANN equation was generated based on the proposed ANN model for design. Finally, the ANN model and the ANN equation were evaluated and verified against experimental data and existing models. The findings indicated that the ANN approach was highly applicable and reliable for estimating the local compression capacity of stirrups-confined concrete.

Cyclic test and numerical analysis of the seismic performance of concrete columns reinforced by HRB600 steel bars

As a new type of high-strength steel bar, hot-rolled ribbed bar (HRB) 600 reinforcement has an obvious yield platform and high elongation. To better understand the seismic performance of HRB600 steel bar reinforced concrete columns, cyclic tests are first conducted to examine the effect of the reinforcement strength, stirrup spacing, and axial compression ratio on their seismic performance. Then, finite element (FE) models of the column specimens are established by OpenSees, and the accuracy is verified by comparison with the experimental results. Finally, parametric analysis is conducted to investigate the effects of the concrete strength, longitudinal reinforcement strength, volume-stirrup ratio, and stirrup strength on the seismic performance of concrete columns. The research results show that the column specimens reinforced by HRB600 reinforcement can achieve an excellent drift ratio capacity of 4.2% when the axial load ratio is 0.5, and have a deformation capacity similar to that of normal-strength bar reinforced concrete columns. The established FE model can simulate well the behavior of HRB600 bar reinforced concrete columns under cyclic loading. The parametric analysis shows that when adopting equal strength replacement of longitudinal reinforcement, the columns built by high- and normal-strength reinforcement have similar strength and deformation capacity, but the high-strength bar reinforced columns have a slightly smaller energy dissipation.