Stirrup Reinforcement Ratio Research Articles

A simplified calculation model for maximum diagonal crack width of UHPC-NC composite beams

The study on precast UHPC-NC composite beams investigated the effects of shear span ratio, stirrup reinforcement ratio, and NC strength on cracking shear force and diagonal crack width. Tests on eight UHPC-NC beams and one RC beam revealed that increasing the shear span ratio reduced the cracking shear force and widened diagonal cracks. U-shaped UHPC formwork enhanced cracking shear force and delayed crack development. While stirrup ratio had minimal impact on cracking force, it helped delay crack growth. A proposed model accurately estimated cracking shear force and maximum diagonal crack width, offering valuable insights for engineering applications.

Study on the intermediate crack-induced debonding strain of FRP-strengthened concrete members using the updated BP neural network

Fiber reinforced plastics (FRP) are often used to enhance the capacity of the reinforced concrete beam (RC beam). However, the debonding failure is often observed due to the effect of the complex environment and the random loads. The debonding failure includes three types: plate end interfacial debonding (PE debonding), critical diagonal crack-induced debonding (CDC debonding), and intermediate flexural crack-induced interfacial debonding (IC debonding). In order to investigate the IC debonding strain of RC beam strength by FRP, this paper proposed some data-driven models to explore the IC debonding strain, based on the machine learning approaches The concrete strength, shear span proportion, the proportion of anchorage length to shear width, tensile reinforcement proportion, steel yield strength, stirrup reinforcement ratio, FRP stiffness, and the proportion of sheet span to beamwidth were regarded as the input parameters. The IC debonding strain was regarded as the output. It was found that the BP model can predict the IC debonding strain well. However, the BP data-driven model is easy to fall into a local minimum, and it is very difficult to converge, which has a negative effect on the accuracy of the model. The Sparrow Search Algorithm (SSA) was proposed to update it. The results indicated that the neural network optimized by SSA with lowest relative error, which can predict the IC debonding strain well. In addition, a study on the importance of each input found that the concrete strength, shear span proportion, and reinforcement yield strength will have a big impact on the IC debonding strain.

Experimental study on the reinforced concrete beams with varied stirrup reinforcement ratio under static and impact loads

Experimental study on the reinforced concrete beams with varied stirrup reinforcement ratio under static and impact loads

Shear behavior of ultra-high performance concrete corbels：Experimental study and modified strut-and-tie model

In this study, a static loading test was performed to examine the shear behavior of twelve ultra-high performance concrete ( UHPC) corbels. The impact of key parameters, such as shear-span ratio, steel fiber volume ratio, and stirrup reinforcement ratio on corbels' mechanical behavior, were explored. The test findings reveal that the cracking load of UHPC corbels is significantly higher than that of the corbels without steel fiber, and the failure mode changes from shear failure to flexural failure. Reducing the shear-span ratio and increasing the stirrup reinforcement ratio substantially improved the shear capacity of the corbels. Furthermore, a modified strut-and-tie model was developed for predicting the shear capacity of UHPC corbels. A shear test database for UHPC corbels was compiled to validate the accuracy of the proposed method. The model showed strong agreement with the test results and demonstrated satisfactory adaptability. Finally, four other models from national standards and academic proposals were evaluated under the same conditions. The proposed model showed superior correlation with the experimental data, suggesting its potential to improve the design and application of UHPC corbels in practical engineering contexts.

Torsional strength design method and cost analysis of FRP bars reinforced ECC beams without stirrups

Fiber reinforced plastic (FRP) bars reinforced engineered cementitious composites (ECC) beams without stirrups own excellent torsional performance and good application prospect. However, the corresponding torsional strength design method is not available. In order to predict the torsional strength of the ECC beams, a theoretical design method is established in this research. The proposed design method is based on the variable-angle space truss (VAST) model, and the tensile resistance supplied by fibers is carefully considered. The established design method is verified through the experimental results. It can be found that the predicted values agree well with the experimental values. A parametric analysis is carried out. Ultimate torque (i.e., torsional strength) increases significantly with the increment of ECC strength grade or longitudinal reinforcement ratio. However, at the same cross-section area, ultimate torque decreases slightly with the increment of height/width ratio. In addition, the cost effectiveness of the ECC beams without stirrups is discussed. Compared with mortar beam with a stirrup reinforcement ratio of 0.7%, FRP bars reinforced ECC beams without stirrups have small cost/ultimate torque ratio (a reduction ratio of 39.14%–60.86%), indicating that the ECC beams without stirrups own satisfactory cost effectiveness. This study will provide a torsional strength design guideline for FRP bars reinforced ECC beams without stirrups.

Axial compressive behavior of predamaged RC columns retrofitted with precast steel-reinforced grout jackets

Steel jacketing and concrete jacketing are popular retrofitting techniques to strengthen the axial compressive behavior of reinforced concrete (RC) columns. However, these retrofitting methods lack efficiency in practical application due to intensive labor and time-consuming installation. In order to improve the retrofit efficiency of damaged RC columns, this study proposed a novel precast steel-reinforced grout jacket (PSRGJ) consisting of early-strength cementitious grout and a steel frame. Ten columns were tested to investigate the axial compressive behavior of predamaged RC columns retrofitted with PSRGJ. The tested parameters were the stirrup reinforcement ratio, the transverse reinforcement ratio of PSRGJ, and the predamage level. The results indicated that the columns’ peak load and ductility index I10 were significantly improved by PSRGJ retrofitting and increased with the increase of transverse reinforcement ratio of PSRGJ. Besides, the peak load and the initial stiffness of PSRGJ-retrofitted RC columns decreased with the predamage level, while the ductility index I10 increased. In addition to the confinement effect, PSRGJ carried 11%−17% of the peak load through the interfacial bonding effect. Based on the test results, the actual confinement pressure model and interfacial bonding strength model were proposed. Further, peak load models considering the size effect were developed for PSRGJ-retrofitted intact and predamaged RC columns. The predictions of the proposed models agreed well with the test results from this study and the literature.

Study of the Seismic Behavior of Simplified RCS Joints via Nonlinear Finite Element Analysis

Compared to more complex structures, simply configured reinforced concrete column–steel beam (RCS) composite structures have more promising application prospects, especially in regions with moderate–high seismic levels, due to their ease of construction. However, the current understanding of the seismic performance of simplified RCS joints is not sufficient. Validated by experimental results, a nonlinear finite element analysis (FEA) model was developed in this study to reveal the seismic behavior of simplified RCS joints. Six vital design parameters, namely axial load ratio, concrete strength, yield strengths of steel webs and flanges, and diameters of transverse and longitudinal reinforcements, were comprehensively studied. Research has shown that the axial compression ratio has a significant impact on the failure mode and bearing capacity of joints. When the concrete strength increases, the load-bearing capacity of the joints significantly increases, while the brittleness of high-strength concrete leads to a decrease in its deformation capacity. In addition, when the steel beam strength is constant, higher flange and web yield strengths have a limited influence on crack propagation and strain development. The stirrup reinforcement ratio and longitudinal reinforcement ratio play a significant role in inhibiting crack propagation and improving the bearing capacity, respectively. With the help of the numerical results, six theoretical models introduced by national codes and other researchers were compared. Among them, the modified model proposed by Kanno demonstrated the highest accuracy and was the most suitable for simply configured RCS joints.

Push-out tests of interfacial bond slip between H-shaped steel and ultra-high performance concrete

The effects of steel fiber content, stirrup reinforcement ratio, cover thickness of ultra-high performance concrete (UHPC) and embedded length of H-shaped steel on interfacial bond performance were studied through pull-out tests of ten specimens. The crack development process and damage mode of the specimens were analyzed by the load-slip(P-S) curves obtained at the loading end and the strain distribution of the H-shaped steel web. A formula for characteristic bond strength of H-shaped steel and UHPC was established, and a constitutive relationship for bond slip was proposed. A finite element model based on nonlinear springs was established to simulate the bond-slip relationship and the whole process of loss of performance at the interface of H-shaped steel and UHPC. The results showed that the strain of H-shaped steel decreased gradually along its embedment length, and the amount of steel fiber content, cover thickness and embedding length had large influences on the ultimate bond stress.

Probabilistic curvature-and-drift limit states predictive models of high-strength bridge columns

This study presents the derivation of closed-form component limit state expressions for high-strength concrete columns reinforced with high-strength steel bars (HSC-HSSB) from an extensive database through the moment–curvature analysis approach. Initially, sensitivity analysis was conducted to investigate the regularity of the parameters (section size, axial-load ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, concrete compressive strength, and yield strength of longitudinal reinforcement) on the curvature limit state. The approach being convenient, massive samples were obtained in a short time, therefore, 6^7(279936) levels were generated to derive the predictive expressions of curvature and moment limit states by using the logarithm linearity model. Subsequently, based on the cross-section expressions, the drift displacement and shear force limit states predictive expressions were derived and verified by experimental studies, and these limit states were predicted with high precision. Moreover, after considering the uncertainty of material and section size, the curvature and drift displacement of the HSC-HSSB column exhibited a lognormal distribution, and the useful suggested standard deviations (βc) in different limit states were proposed for practical application of fragility curves to assess the vulnerability of bridge columns to earthquakes.

Experimental Study of Shear Performance of High-Strength Concrete Deep Beams with Longitudinal Reinforcement with Anchor Plate.

As a transfer member at the discontinuous place of vertical load, the deep beam has a complex stress mechanism and many influencing factors, such as compressive strength of concrete, shear span ratio, and reinforcement ratio. At the same time, the stress analysis principle of traditional shallow beams is no longer applicable to the design and calculation of deep-beam structure. The main purpose of this paper was to use the strut-and-tie model to analyze its stress mechanism, and to verify the applicability of the model. Nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate of the same size were tested by two-point concentrated loading method. The effects of shear span ratio (0.3, 0.6, and 0.9), longitudinal reinforcement ratio (0.67%, 1.05%, and 1.25%), horizontal reinforcement ratio (0.33%, 0.45%, and 0.50%), and stirrup reinforcement ratio (0.25%, 0.33%, and 0.50%) on the failure mode, deflection curve, characteristic load, crack width, steel bar, and concrete strain of the specimens were analyzed. The results showed that the failure mode of deep-beam specimens was diagonal compression failure. The normal section cracking load was about 15 to 20% of the ultimate load, and the inclined section cracking load was about 30~40% of the ultimate load. The shear span ratio increased from 0.3 to 0.9, and the bearing capacity decreased by 32.9%. When the longitudinal reinforcement ratio increased from 0.67% to 1.25%, the ultimate load increased by 42.6%. The shear span ratio and longitudinal reinforcement ratio have a significant effect on the bearing capacity of the high-strength concrete deep beams with longitudinal reinforcement with an anchor plate. The shear capacity of nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate was calculated by national standards, and the results were compared with the calculation results of the Tan-Tang model, the Tan-Cheng model, SSTM, and SSSTM. The analysis showed that the softened strut-and-tie model takes into account the softening effect of compressive concrete, and is a more accurate mechanical model, which can be applied to predict the shear capacity of high-strength concrete deep-beam members with longitudinal reinforcement with an anchor plate.

Experimental Investigation on Shear Capacity of Steel-Fiber-Reinforced High-Strength Concrete Corbels.

As short cantilever members, corbels are mainly used to transfer eccentric loads to columns. Because of the discontinuity of load and geometric structure, corbels cannot be analyzed and designed using the method based on beam theory. Nine steel-fiber-reinforced high-strength concrete (SFRHSC) corbels were tested. The width of the corbels was 200 mm, the cross-section height of the corbel column was 450 mm, and the cantilever end height was 200 mm. The shear span/depth ratios considered were 0.2, 0.3, and 0.4; the longitudinal reinforcement ratios were 0.55%, 0.75%, and 0.98%; the stirrup reinforcement ratios were 0.39%, 0.52%, and 0.785%; and the steel fiber volume ratios were 0, 0.75%, and 1.5%. According to the test results, this paper discusses the failure process and failure mode of corbel specimens with a small shear span/depth ratio and analyzes the effects of variables such as shear span/depth ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, and steel fiber volume content on the shear capacity of corbels. The shear capacity of corbels is significantly affected by the shear span/depth ratio, followed by the longitudinal reinforcement ratio and the stirrup reinforcement ratio. Moreover, it is shown that steel fibers have little impact on the failure mode and ultimate load of corbels, but can enhance the crack resistance of corbels. In addition, the bearing capacities of these corbels were calculated by Chinese code GB 50010-2010 and further compared with ACI 318-19 code, EN 1992-1-1:2004 code, and CSA A23.3-19 code, which adopt the strut-and-tie model. The results indicate that the calculation results by the empirical formula in the Chinese code are close to the corresponding test results, while the calculation method based on the strut-and-tie model of a clear mechanical concept yields conservative results, and hence the related parameter values must be further modified.

Study on Shear Behaviors and Damage Assessment of Circular Concrete Short Columns Reinforced with GFRP Bars and Spiral Stirrups.

This study investigated the shear resistance and damage evolution of glass fiber-reinforced polymer (GFRP)-reinforced concrete short columns. Five circular concrete short columns reinforced with GFRP bars and spiral stirrups were fabricated and tested under lateral thrust in the laboratory. The test variables involved the stirrup reinforcement ratio, the longitudinal reinforcement ratio and the type of stirrups. The failure modes, load-displacement curves, strain responses and crack characteristics of these columns were documented and discussed. The accuracy of shear design equations in predicting shear capacity of such columns was evaluated. In addition, the digital image correlation (DIC) instrument was used to identify the full-field strain and damage zones of circular concrete short columns. Several smart aggregate (SA) transducers coupled to the surface of these columns were used to monitor its damage status. The energy ratio index (ERI) and the damage index based on smart aggregate were established to characterize damage level of such columns. The test results indicate that the shear capacity is improved 5.6% and 31.1% and the lateral ultimate displacement is increased 67.7% and 400% as the stirrup reinforcement ratio of the concrete short column is increased from 0 to 0.19% and 0.47%, respectively. The shear capacity equation proposed by Ali and his co-workers, considering a strain limit of 0.004Efv, gives accurate predictions of the shear capacity of circular concrete short columns reinforced with GFRP bars and spiral stirrups. The variation in ERI values is explained by the development of damage zones of the column obtained with DIC technology and with the proposed damage index based on the smart aggregate it is feasible to evaluate the damage level of circular short concrete columns.

A new method to investigate the intermediate crack-induced debonding strain

In order to investigate the interfacial debonding (IC) strain of the reinforced concrete structures strengthened by fiber-reinforced polymer (FRP), this paper proposed some data-driven models to explore it, considering the effect of random factors both in material and environment. The concrete strength, shear span proportion, the proportion of anchorage length to shear width, tensile reinforcement proportion, steel yield strength, stirrup reinforcement ratio, FRP stiffness, the proportion of sheet span to beamwidth, ratios of environmental temperature to the maintenance standard temperature, and ratios of environmental humidity to the relative humidity were regarded as the inputs, the IC debonding strain was regarded as the output. The results indicate that the neural network optimized by the sparrow search algorithm not only has a relatively small error but also has stronger robustness. In addition, a study on the importance of the inputs on the IC debonding strain indicates that the concrete strength, FRP stiffness, and ratios of environmental temperature to the maintenance standard temperature are the most significant factor to influence the IC debonding strain.

Deep HystereticNet to predict hysteretic performance of RC columns against cyclic loading

This article attempts to reproduce hysteretic performance of HRB600 bar reinforced concrete columns under cyclic loading by adopting multivariate deep learning methods. Bidirectional long short-term memory (BiLSTM) and bidirectional gated recurrent units network (BiGRU) have been modified for temporal sequence related strength prediction with the consideration of multivariate parameters. To this end, a database with a 79,244 (row) × 12 (column) matrix is prepared for training, validation, and testing purposes. The inputs to the model include time intervals, loading displacement, concrete strength, axial compression ratio, longitudinal reinforcement tensile grade, longitudinal reinforcement diameter, longitudinal reinforcement ratio, stirrup tensile strength, stirrup diameter, spacing, and stirrup reinforcement ratio while the target is the cyclic load. By comparing the energy dissipation, accumulated energy dissipation, stiffness degradation and backbone curve of the hysteretic performance, the capacity of the adopted methods is compared with that of the finite element analysis. The comparison shows that the adopted method can recovery the hysteretic curves very well and the GRU method exhibits the most accurate prediction performance because of the highest R2 and the lowest MAE, MSE, and RMSE. The originality and innovation are mainly reflected in the use of time series data-driven deep learning model to replace the existing empirical formula and finite element method to reconstruct the nonlinear hysteretic behavior, so as to predict the seismic performance of the structure.

Experimental Study and Calculation Methods of Shear Capacity for High-Strength Reinforced Concrete Full-Scale Deep Beams.

The shear behavior of 8 high-strength concrete full-scale deep beams with high-strength steel bars was studied. The depth beam size was 100 mm × 900 mm × 2200 mm, the test parameters included the shear span-to-depth ratio ( = 0.9, 0.6, 0.3), longitudinal reinforcement ratio (.66%, 1.06%, 1.26%) and stirrup reinforcement ratio ( = 0, 0.26%, 0.34%, 0.5%). The ratio of the cracking load of the inclined section to the ultimate load is between 30% and 50%, and the bending deformation of the deep beam is small, showing the characteristics of brittle failure for deep beams. Under the action of a concentrated load, the failure mode of deep beams with a small shear span ratio is the failure of the diagonal compression struts, which is very different from that of shallow beams with a large shear span ratio. With the increase of shear span ratio from 0.3 to 0.9, the ultimate shear capacity of deep beams decreases by 19.33%. With the increase of longitudinal reinforcement ratio from 0.67% to 1.27%, the ultimate shear capacity of deep beams increased by 45.02%. With the increase of vertical stirrup reinforcement ratio from 0% to 0.5%, the ultimate shear capacity of deep beams increased by 8.93%. Increasing the area of longitudinal bars or stirrups limited the transverse tensile strain of the compression struts, which is conducive to improving the compressive strength of the compression struts of deep beams and then improving the bearing capacity of deep beams. The strut-and-tie model (STM) is more suitable for analyzing the shear capacity of deep beams. The calculation methods for calculating the shear capacity of deep beams were compared with ACI 318-19, CSA A23 3-19, EN 1992-1-1:2004, Tan–Tan model, Tan–Cheng model, softened STM (SSTM) and simplified SSTM (SSSTM). The results showed that the shear capacity of deep beams could be well predicted by reasonably determining the STM parameters.

Confinement behavior and stress–strain response of square concrete columns strengthened with carbon textile reinforced concrete (CTRC) composites

In this study, with the aim of investigating the confinement behavior and stress–strain response of concrete columns strengthened with carbon textile reinforced concrete (CTRC) under a uniaxial load, a total of 20 column specimens with square cross-sections were cast and subjected to monotonic axial compression. Next, the effects of the number of textile layers, stirrup reinforcement ratio, concrete strength and short fibers on the efficiency of CTRC confining system were evaluated. The experimental results indicated that the CTRC-confined columns obtained a maximum improvement of up to 67.3% in bearing capacity and 65.2% in displacement ductility compared to the un-strengthened reference columns, and exhibited a more significant ductile failure characteristic. Moreover, the bearing capacity and displacement ductility of the confined columns were characterized by increasing with an increase in the number of textile layers and stirrup ratio, and a decrease in the concrete strength. The short fibers mixed in the strengthening layers also made a beneficial contribution to the bearing capacity and displacement ductility, particularly to the cracking load of the confined columns. Finally, a semi-empirical model was proposed to predict the axial stress and strain of concrete column specimens strengthened with CTRC based on the experimental results and theoretical analysis. The results calculated by the proposed model were evidenced to be fundamentally consistent with the experimental results. Therefore, the proposed model in this study could effectively predict the stress–strain response of square RC columns confined with CTRC composites.

Data-driven model for predicting intermediate crack induced debonding of FRP-strengthened RC beams in flexure

There are a kinds of failure modes in flexurally strengthened RC beams using externally bonding FRP sheets. To evaluate the flexural strength of FRP-strengthened RC beam, the failure mode of the strengthened beam must be determined first. Intermediate crack (IC) induced debonding is the main failure mode in flexurally FRP-strengthened RC beams. In this study, a Back-Propagation Neural Network (BPNN) model is proposed to predict the intermediate crack (IC) induced debonding of FRP-strengthened RC beams. A database of 101 beams from different researchers are used to train and test the BPNN model. This model established in this study has eight inputs, including concrete strength, shear span ratio, tensile reinforcement ratio, the yield strength of reinforcement, stirrup reinforcement ratio, FRP stiffness, the ratio of sheet width to beam width, and the ratio of anchorage length to shear span, the output is FRP strain at the initial debonding, that is, the ultimate debonding strain of FRP reinforcements. The importance and sensitivity of the parameters are studied by the BPNN model and collected data. Based on the parametric study and Levenberg-Marquardt algorithm for nonlinear fitting, a design model is established for the prevention of IC debonding failure. The BPNN model and design model established in this study can accurately predicted the IC debonding of FRP-strengthened RC beams.

Experimental and Numerical Investigation of Seismic Performance of UHPC Thin‐Walled Short Piers

Rigid frame bridges with different heights of adjacent piers are inclined to crack the main girder at the pier‐beam connection. This cracking occurs due to a significant difference in thrust stiffness between tall and short piers. This problem can be resolved by applying ultra‐high performance concrete (UHPC) materials. Thus, in the present paper, the seismic performance and failure behavior of UHPC thin‐walled short piers were tested under low‐frequency cyclic loads. Based on previous studies, the test was conducted using a proposed experimental model, where the effects of longitudinal reinforcement ratio, stirrup reinforcement ratio, and axial load ratio were considered. The failure mode, ultimate bearing capacity, stiffness, displacement ductility factor, and other performance parameters were analyzed. It was found that the specimens present the bending‐shear failure mode. Also, the load‐bearing capacity of the UHPC thin‐walled piers was significantly improved by increasing the longitudinal ratio of the thin‐walled short piers, while the contribution of the stirrup ratio was limited. In addition, compared with traditional short piers, the ductility of UHPC thin‐walled short piers increased by 53.36%, and the thrust stiffness decreased by 23.73%, indicating that UHPC thin‐walled short piers have more efficient seismic performance than RC short piers. Note that, in the present paper, UHPC thin‐walled short piers’ internal behavior was also analyzed by establishing a finite element model. The analysis proves that the numerical results are consistent with the experimental data, which is promising to better understand the failure behavior.

Shear Behavior of Reinforced Post-Filling Coarse Aggregate Concrete Beams Produced by Creative Construction Process

Different from the traditional concrete mixing procedure, the innovative post-filling coarse aggregate concrete (PFCC) reduces the cost of pumping concrete by increasing the coarse aggregate content and reducing the usage of cement. Previous studies have shown that PFCC enhances the compressive strength, elastic modulus, and flexural strength of concrete. In this paper, the shear behavior of 13 post-filling coarse aggregate concrete beams and 3 control beams was tested to determine the relationships between the shear performance of the beam and the post-filling coarse aggregate ratio, concrete strength grade, shear span ratio and stirrup reinforcement ratio. The results showed that the ultimate shear capacity of beam specimen increases first and then decreases with the increase in post-filling coarse aggregate ratio, reaching the maximum at 15% post-filling ratio. The results also indicated that the ultimate shear capacity of the beam increases with the increase in concrete strength grade and stirrup ratio. However, experimental results exhibited that the ultimate shear capacity decreases as the shear span ratio increases. This study provides a reference for the application of post-filling coarse aggregate concrete in engineering practice.

Performance evaluation of self-centering rocking shear walls: Part 1 — Quantification of structural damages

Self-centering rocking shear wall (SCRSW) is an innovative structural system which is designed to achieve low damage after strong earthquake shaking. In this paper, an effective damage quantification method is developed to quantify the damages of SCRSWs. The procedure is applied in the performance evaluation and damage quantification for 24 SCRSWs. An equation of the critical parameter β in the damage model is proposed. The results show that increasing stirrup reinforcement ratio, self-centering parameter and concrete strength can reduce the damage developed in SCRSWs effectively, while higher prestress in post-tensioned (PT) tendons tends to increase the damage. An empirical equation between the critical parameter β and structural features is proposed. The critical parameter is then used to quantify the damage index (DI) of SCRSW. The result shows that the proposed β can be used to evaluate and quantify the damages developed in SCRSWs efficiently and accurately.