Design Of Reinforced Concrete Beams Research Articles

Effects of boundary conditions on RC beams subjected to accidental thermal load in nuclear power plants

Reinforced concrete (RC) beams in nuclear safety related structures should be designed for accidental thermal gradient combined with mechanical loads. Design capacity and structural behavior of those beams are affected by constraint boundary conditions at beam ends. In design approaches widely used in nuclear power plants (NPPs), it is commonly assumed that the thermal curvature of a RC member is fully constrained while axial constraint condition is often not specified. In this paper, RC beams with various constraint boundary conditions that are subjected to accidental thermal gradient combined with mechanical loads are studied using both experimental tests and nonlinear finite element (NLFE) models. Both rotational and axial stiffness ratios at boundary and their effects on thermal moments and ultimate flexural capacity of RC beam are evaluated. Results shows that the assumption of a fully constrained rotational boundary condition is practically accurate for most RC beams in NPPs subjected to thermal gradient. On the other hand, results also show that axial constraint boundary condition has considerable influence on both thermal moment and usable design flexural strength thus neglecting its effect may lead to insufficient design of RC beam. In addition, this study established relationship between axial constrain stiffness ratio and thermal moment, as well as relationship between axial constrain stiffness ratio and usable design flexural strength for different accidental temperature gradients and reinforcement ratios. That information can be used for correction of thermal moment and usable design flexural strength in design practice.

Influence of impact velocity on dynamic performance of reinforced concrete beams strengthened with CFRP

In order to study the impact resistance and dynamic damage rule of reinforced concrete (RC) beams strengthened with carbon fiber reinforced plastics (CFRP) under different impact velocities, four CFRP strengthened RC beams were tested by using a drop-hammer impact device. The analysis results of the failure pattern, crack propagation rule, dynamic time history response and energy dissipation of the strengthened beams show that with increase of the impact velocity, the width of the main bending crack in the mid-span of CFRP strengthened beam increases first and then decreases, and the width of the main oblique crack in the mid-span increases continuously. It can also be identified that overall crack distribution converges to the mid-span area. Furthermore, the peak impact force and the mid-span peak displacement are linearly dependent to the impact velocity. The energy dissipation capacity of strengthened beams increases nonlinearly with the increase of impact velocity. The greater the impact velocity is, the less the increase rate of the energy dissipation capacity of the strengthened beam is. In addition, four stages can be divided in the test based on development of mid-span displacement, which are linear growing, nonlinear growing, rebounding and stable stages, respectively. The study can provide reference for optimal design of RC beams strengthened with CFRP.

Shear strength estimations and shear designs on RC beams with limited ductility by FL and FIL methods

In this study, a fuzzy logic model was constituted by using the Fuzzy Logic (FL) method, which is one of the traditional artificial intelligence (AI) methods, in order to estimate the shear strength of reinforced concrete (RC) beams with limited ductility. In this model, beam width(bw), beam height(h), characteristic concrete compressive strength(fck), transverse reinforcement diameter(T), the number of arms bearing the shear force of the transverse reinforcement(n) and transverse reinforcement spacing(s) were taken into account as variable parameters. The model developed by using the problem data containing the solutions of shear force strength of 2640 beams with different cross-section properties were tested with 480 beam solutions different from these data. In the tests of the developed FL model, maximum percentage error, minimum percentage error, average percentage error and correlation coefficient values were obtained as 3.604, -0.091, 1.514 and R2=0.999678. By applying the fuzzy inverse logic method (FIL), which was recently developed by the author of this study, on the FL model, which is seen to have been developed quite sensitively from the test results, a total of 521 designs were obtained for 15 different RC beams with limited ductility subjected to shear. In order to check the accuracy of these designs, after shear strengths were obtained by conventional computations for these designs, % error and correlation coefficients were computed between the obtained strength values and the shear force values taken into account for the design. The promising results show that the FIL method can be used in the design of RC beams under shear force and even in other scientific studies such as design, optimization and control.

Evaluation of the Maximum Strain for Different Steel-FRCM Systems in RC Beams Strengthened in Flexure

The strengthening of existing reinforced concrete (RC) structures by means of steel-fabric reinforced cementitious matrix (Steel-FRCM) systems has been universally recognized in the academic literature as an effective method. Several types of steel fibres can be found in the marketplace, and they are classified according to mass per unit area and tensile strength. In the flexural strengthening design of RC beams, a fundamental parameter is the effective tensile strain level in the Steel-FRCM system attained at failure. Some authors and guidelines suggest evaluating this strain value using the results of bond tests. As is well highlighted in many works, the debonding strain in Steel-FRCM composites applied on concrete beams is usually higher than that from single-lap shear tests. At this point, it can be easily obtained by applying an appropriate amplification coefficient. This study experimentally investigates the difference in the debonding strain between Steel-FRCM composites bonded to concrete blocks in single-lap shear tests (end strain) versus the debonding strain in concrete beams (intermediate strain). The results were used to critically discuss the variability of the amplification coefficient, significantly affected by the mechanical and geometrical properties of the steel fibres. Moreover, a simple predictive formula to evaluate the intermediate strain debonding was used, and the results were compared with the experimental evidence. Finally, a large database of direct shear and flexural tests was used to confirm the experimental and theoretical data obtained herein.

Back-Propagation Neural Network Optimized by K-Fold Cross-Validation for Prediction of Torsional Strength of Reinforced Concrete Beam.

Due to the limitation of sample size in predicting the torsional strength of Reinforced Concrete (RC) beams, this paper aims to discuss the feasibility of employing a novel machine learning approach with K-fold cross-validation in a small sample range, which combines the advantages of a Genetic Algorithm (GA) and a Neural Network (NN) to predict the torsional strength of RC beams. This research study not only utilizes the application of a Back Propagation (BP) neural network and the Gene Algorithm-Back Propagation (GA-BP) neural network in the prediction of the torsional strength of the RC beam, but it also investigates neural network parameter optimization, including connection weights and thresholds, using K-fold cross-validation. The root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE) and correlation coefficient (R2) are among the evaluation metrics used to assess the performance of the trained model. To elaborate on the superiority of the proposed network models in predicting the torsional strength of RC beams, a parametric study is conducted by comparing the proposed model to three commonly used empirical formulae from existing design codes. The comparative findings of this research study demonstrate that the performance of the BP neural network is highly similar to that of design codes; however, its accuracy is inadequate. After improving the weights and thresholds by k-fold cross-validation and GA, the prediction of the BP neural network shows higher consistency with the actual measured values. The outcome of this study can be used as a theoretical reference for the optimal design of RC beams in practical applications.

Eksperimentalno i numeričko ispitivanje armiranobetonskih greda pojačanih CFRP kompozitom

This study aims to strengthen reinforced concrete (RC) beams having insufficient shear capacity using Carbon Fibre Reinforced Polymer (CFRP) members and innovative anchorages. An innovative method is also proposed for strengthening beams in interaction site of adjacent structures. Test results show that the behaviour of beams has been improved with CFRP elements. The nonlinear finite element (FE) method, as well as American and Italian guidelines, are used to estimate theoretical capacity of the beams. Test results are compared with theoretical results. It can be concluded that proposed methods can be used reliably, and that the design of RC beams strengthened with these methods can be performed by design engineers based on simple calculations.

Performance-based design of RC beams using an equivalent standard fire

Purpose The design of buildings for fire events is essential to ensure occupant safety. Supplementary to simple prescriptive methods, performance-based fire design can be applied to achieve a greater level of safety and flexibility in design. To make performance-based fire design more accessible, a time-equivalent method can be used to approximate a given natural fire event using a single standard fire with a specific duration. Doing so allows for natural fire events to be linked to the wealth of existing data from the standard fire scenario. The purpose of this paper is to review and assess the application of an existing time-equivalent method in the performance-based design of reinforced concrete (RC) beams. Design/methodology/approach The assessment is established by computationally developing the moment-curvature response of RC beam sections during fire exposure. The sectional response due to natural fire and time equivalent fire are compared. Findings It is shown that the examined time equivalent method is able to predict the sectional response with suitable accuracy for performance-based design purposes. Originality/value The research is the first to provide a comprehensive evaluation of the moment-curvature diagram of RC beams using time-equivalent standard fire scenarios that model realistic fire scenarios.

Shear Behaviour of RC Beams Strengthened by Various Ultrahigh Performance Fibre-Reinforced Concrete Systems

This study presents a numerical investigation on the shear behaviour of shear-strengthened reinforced concrete (RC) beams by using various ultrahigh performance fibre-reinforced concrete (UHPFRC) systems. The proposed 3D finite element model (FEM) was verified by comparing its results with those of experimental studies in the literature. The validated numerical model is used to analyse the crucial parameters, which are mainly related to the design of RC beams and shear-strengthened UHPFRC layers, such as the effect of shear span-to-depth ratio on the shear behaviour of the strengthened or nonstrengthened RC beams and the effect of geometry and length of UHPFRC layers. Moreover, the effect of the UHPFRC layers’ reinforcement ratio and strengthening of one longitudinal vertical face on the mechanical performance of RC beams strengthened in shear with UHPFRC layers is investigated. Results of the analysed beams show that the shear span-to-depth ratio significantly affects the shear behaviour of not only the normal-strength RC beams but also the RC beams strengthened with UHPFRC layers. However, the effect of shear span-to-depth ratio has not been considered in existing design code equations. Consequently, this study suggests two formulas to estimate the shear strength of normal-strength RC beams and UHPFRC-strengthened RC beams considering the effect of the shear span-to-depth ratio.

Applicability analysis of STM and SMCFT of RC beams with shear span-depth ratios ≤ 3.0

The shear capacity of reinforced concrete (RC) beams is significantly affected by the shear span-depth ratio (av/d). The strut-and-tie model (STM) and simplified modified compression field theory (simplified MCFT) that are utilized in current design codes have both proven to be effective in the shear capacity analysis and the design of RC beams. In order to compare the validity and applicability of the two approaches within the range of av/d ≤ 3.0, 160 RC beams with transverse reinforcements were collected and their shear capacities were evaluated using the two models respectively. The results demonstrated that the ratio of av/d = 1.8 was be the critical point that separated the ranges in which each approach was better able to predict the shear capacity. More specifically, it could be concluded that using the STM approach in the range av/d ≤ 1.8 and the simplified MCFT approach in the range 1.8 < av/d ≤ 3.0 respectively would result in more rational and accurate shear strength predictions.

Numerical Study on The Structural Behavior of RC Beams after Exposure to Elevated Temperature

This paper presents a numerical simulation of the structural response of reinforced concrete (RC) beams under elevated temperature using the commercial finite element package ABAQUS. A numerical model is firstly suggested by selecting the appropriate geometrical and material properties of the RC beam model at elevated temperature. Thereafter, the suggested numerical model was validated against the experimental tests conducted in this study. The validation results in terms of temperatures- time histories; load-mid span deflection of the RC beams have confirmed the accuracy of the suggested numerical model. The validated numerical model was implemented in conducting a parametric study to investigate the effects of two important parameters on the behavior and failure of RC beams under elevated temperature. These parameters are the effect of the high ranges of elevated temperatures; and the effect of heating rate. The parametric study results have revealed that the failure load and the ductility of RC beams under elevated temperature are not considerably influenced by changing the heating rate. It has also been concluded that the ultimate load capacities of RC beams have considerably decreased by 55.49%, 74.72%, and 81.31% comparing with the control RC beam when they exposed to temperature values of 600 ºC, 700 ºC, and 800ºC respectively. These conclusions may be used in the design of RC beams subjected to fire induced temperature.&#x0D; Numerical model

Reinforced Concrete (RC) beam design application for android based on SNI 2847:2013 (CEMA)

In Indonesia RC structures are widely used for high rise, low rise, shop offices, as well as residential buildings. In February 2018, the first author introduced an RC beam design application for Android [12] for two options. Option one is for calculating nominal moment (Mn) and nominal shear force (Vn) of the section when the beam dimensions (b, h) and reinforcements are known; option two is to calculate the number of reinforcements for Mn and Vn when the dimensions (b, h) are known. In this paper, the first author added option three, namely the optimization for the design of RC beams when the internal forces are known and the application calculates the most optimal dimensions (b, h) and reinforcements. The application developed is named Civil Engineering Mobile Application for Concrete Beams (CEMA) and is called C2. In CEMA the user can follow the step by step calculation and the results of the calculation are stored in a database. For option three of CEMA (optimization of RC beam sections), the application was validated by another method called Teaching-Learning-based Optimization (TLBO) method [10]. It is believed that CEMA which is based on SNI 2847:2013 can be useful for Indonesian structural engineers designing and supervising actual construction RC buildings.

Ductility of RC beams under torsion

In this article, the torsional ductility of reinforced concrete (RC) beams with rectangular cross section is studied. For this, the experimental results of several RC beams found in the literature were compiled and analyzed. A torsional ductility index was used to characterize the torsional ductility of the studied beams. The following variables study were considered: compressive concrete strength, torsional reinforcement ratio and cross section type (plain or hollow). The influence of each variable study on the torsional ductility is studied and important findings are pointed out which could help for the design of RC beams under torsion. An additional comparative analysis with the rules from some codes of practice in use is also performed. It is shown that, in general, the codes are too much restrictive as far as the maximum torsional reinforcement is concerned. As a consequence, this can leads to the unacceptance of several beams with ductile behavior.

MECHANICAL PROPERTIES OF REINFORCED CONCRETE BEAM WITH RECYCLED COARSE AGGREGATES

The significant increment of waste concrete in recent years that is happening worldwide has a tremendous consequence to the environment. Recycling concrete wastes will reduce the amount of waste as well as save natural resources, thus help promote green and sustainable development. This study presents an experimental investigation dealing with the development of green concrete using recycled concrete waste (RCWA) as coarse aggregate replacement materials. The mechanical properties of reinforced concrete (RC) beams in terms of its compressive and flexural strengths were determined. The main parameter considered is the percentage of RCWA in the concrete design of RC beams that ranges from 0% to 50%. From the test results, it was observed that the flexural strength and the compression strength decreased as the percentage of recycled concrete waste aggregate used increased. Generally, the flexural strength of RC beam with RCWA can be 5% to 12.4% lower than that of conventional concrete made with natural course aggregate.

Shear capacity assessment of reinforced concrete beams with corroded stirrups

This paper presents proposed design procedures for quantifying the residual shear strength of reinforced concrete (RC) beams with corrosion-damaged stirrups. Most of the building codes worldwide prescribe different approaches for shear design of RC beams in their provisions based on the type of beams: slender or deep. Conventional sectional method is widely recommended for slender beams while strut and tie model which is based on member analysis is recommended for deep beams. To account for the corrosion effects on shear, modifications to the current design methods were proposed. For sectional design method of slender beams, the reduction in cross-sectional area of steel stirrups due to corrosion was considered along with the reduction in geometry of concrete cross section due to spalling. For strut and tie modeling for deep beams, the reduction in effective concrete compressive strength because of corrosion cracks was considered along with the reduction in geometry of concrete cross section. One important feature of the proposed procedures is that the corrosion effects can be determined based on the width of corrosion cracks which can be easily determined in real situations. The proposed design procedures were validated using the experimental test data available in the literature.

Effect of small axial force on flexural ductility design of high‐strength concrete beams

SummarySmall axial forces may appear in beams in a reinforced concrete (RC) structure. The presence of compressive axial force, even at a low level, has an adverse effect on the flexural ductility of RC beams, which is a key attribute for seismic design. For example, Eurocode EN1998‐1 explicitly specifies such minimum flexural ductility, whereas Chinese code GB50011 limits the depth of equivalent rectangular stress block at peak resisting moment to achieve indirectly a certain nominal flexural ductility. Therefore, ignoring the presence of compressive axial force may be risky. In this study, the effect of small compressive axial force on the flexural ductility performance of both normal‐strength and high‐strength concrete beams is evaluated on the basis of a rigorous full‐range moment–curvature analysis. An effective strategy for flexural ductility design of RC beams with small compressive axial force is identified so that various flexural ductility requirements can be satisfied. The essential control parameter proposed is the maximum difference of tension and compression reinforcement ratios. Empirical formulae and tables are developed for convenient implementation. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Concurrent flexural strength and ductility design of RC beams via strain-gradient-dependent concrete stress-strain curve

The authors have previously conducted an experimental study that showed that strain gradient would improve the maximum concrete stress and strength of reinforced concrete (RC) members under flexure. As a continued study, the authors herein will extend the investigation of strain gradient effect on flexural strength and ductility of RC beams to higher strength concrete up to 100 MPa by theoretical analysis. In this study, the flexural strength of RC beams is evaluated using nonlinear strain-gradient-dependent stress–strain curves of concrete applicable to both normal-strength and high-strength concrete. On the basis of this, a parametric study is conducted to investigate the combined effects of strain gradient and concrete strength on the flexural strength and ductility of RC beams. It was evident from the results that both the flexural strength and ductility of RC beams would be improved with strain gradient considered. From the results, two formulas are proposed for the strain-gradient-dependent concrete stress block parameters α and β. A constant value of 0.0032 is proposed for the ultimate concrete strain in flexural strength design with strain gradient effect considered. Lastly, for practical engineering design purpose, design formulas and charts have been presented for flexural strength and ductility of RC beams incorporating strain gradient effect.

Optimal design of reinforced concrete beams: A review

This paper summarizes available literature on the optimization of reinforced concrete (RC) beams. The objective of optimization (e.g. minimum cost or weight), the design variables and the constraints considered by different studies vary widely and therefore, different optimization methods have been employed to provide the optimal design of RC beams, whether as isolated structural components or as part of a structural frame. The review of literature suggests that nonlinear deterministic approaches can be efficiently employed to provide optimal design of RC beams, given the small number of variables. This paper also presents spreadsheet implementation of cost optimization of RC beams in the familiar MS Excel environment to illustrate the efficiency of the exhaustive enumeration method for such small discrete search spaces and to promote its use by engineers and researchers. Furthermore, a sensitivity analysis is performed on the contribution of various design parameters to the variability of the overall cost of RC beams.

Effect of Shear Resistance on Flexural Debonding Load-Carrying Capacity of RC Beams Strengthened with Externally Bonded FRP Composites

Debonding failure is the main failure mode in flexurally strengthened reinforced concrete beams by externally bonded or near surface mounted fibre reinforced polymer (FRP) composites. It is believed that FRP debonding will be initiated if the shear stress on the concrete-FRP interface reaches the tensile strength of concrete. However, it was found through experimental and analytical studies that the debonding mechanism of FRP composites has the potential of shear failure in combination with debonding failure. Moreover, the shear failure probably influences the debonding failure. Presently, there are very little experimental and analytical studies to investigate the influence of shear resistance of reinforced concrete (RC) beam on FRP debonding failure. The current study investigates and analyzes the effect of shear resistance on FRP debonding failure based on test results. The analytical results show that the shear resistance of RC beam has a great effect on flexural debonding load-carrying capacity of FRP-strengthened RC beam. The influence of shear resistance on flexural debonding load-carrying capacity must be fully considered in flexural strengthening design of RC beams.

Uncertainly Analysis of Flexural Overstrength for Capacity Design of RC Beams

To ensure an overall ductile structural behavior, the reinforcing steel used in the seismic design of reinforced concrete (RC) structures is governed by certain specific requirements given in many international codes, such as the Eurocodes and the recently released Italian Building Code (IBC). This study’s primary focus is the statistical analysis of reinforcing steel properties, based on data from over 600 material tests. The data sets considered include a wide range of reinforcing steel bars (from 12 to 26 mm) provided by different Italian industries and used for a large structure built in Naples (Southern Italy). The test results are analyzed to determine the appropriate cumulative distribution function for yield and ultimate strengths, as well as the ultimate deformation, and other statistical parameters of interest as defined in the codes. The comparison with previous tests confirms an improvement in the quality of materials, as reflected in reduced variability and increased bias factors, consistent with other investigators’ recent findings. Finally, this study investigates the flexural overstrength of RC beams designed according to the current IBC—consistent with Eurocodes—and the accuracy of code requirements in light of realistic material models both for concrete and reinforcing steel and of uncertainties associated with mechanical models, structural members geometry, and material properties (as obtained in this study for reinforcing steel). The obtained results show that code provisions do not seem conservative and provide a basis for an improved calibration of future editions of seismic design codes for buildings.

Finite element modeling of reinforced concrete beams exposed to fire

The practical implementation of performance-based fire safety design of reinforced concrete (RC) structures hinges on the availability of accurate numerical simulation tools for the behavior of RC members exposed to fire. This paper presents a three-dimensional (3D) finite element (FE) model for the accurate prediction of both the thermal and the mechanical behavior of RC beams exposed to fire. In this FE model, particular attention is paid to the modeling of interfacial bond-slip behavior between the reinforcing steel and the concrete, an aspect which has rarely been considered by previous numerical studies. Results obtained from this FE model are compared with existing test data to examine the accuracy of the model. This comparison shows that the inclusion of the steel-to-concrete interfacial behavior leads to more accurate predictions of the deflection of RC beams exposed to fire. Predictions from this FE model also allow the complex distribution and evolution of stresses in the reinforcing steel and the concrete to be examined in detail, leading to a better understanding of the local responses of RC beams exposed to fire. The FE model presented in the paper can be used directly in performance-based fire safety design of RC beams; it can also be employed in parametric studies aimed at developing simple design rules.