Probabilistic models for curvature ductility and moment redistribution of RC beams

It is generally accepted that, in the interest of safety, it is essential to provide a minimum level of flexural ductility, which will allow energy dissipation and moment redistribution as required. If one wishes to be uniformly conservative across all of the design variables, curvature ductility and moment redistribution factor should be calculated using a probabilistic method, as is the case for other design parameters in reinforced concrete mechanics. In this study, simple expressions are derived for the evaluation of curvature ductility and moment redistribution factor, based on the concept of demand and capacity rotation. Probabilistic models are then derived for both the curvature ductility and the moment redistribution factor, by means of central limit theorem and through taking advantage of the specific behaviour of moment redistribution factor as a function of curvature ductility and plastic hinge length. The Monte Carlo Simulation (MCS) method is used to check and verify the results of the proposed method. Although some minor simplifications are made in the proposed method, there is a very good agreement between the MCS and the proposed method. The proposed method could be used in any future probabilistic evaluation of curvature ductility and moment redistribution factors. © 2015 Techno-Press, Ltd

Reliability-based study on ductility measures of reinforced concrete beams in ACI 318

This paper presents a reliability-based investigation into the ductility requirements of reinforced concrete beams designed based on the ACI Code. Results showed that the code-specified model for predicting ductility measures, such as the neutral axis depth, is considerably less reliable than it is for predicting the flexural strength. The ratio of the strain at tensile reinforcement to yield strain of steel was used to define a limit state to ensure adequate ductility in reinforced concrete beams. Due to variability in the material properties and model error, there is high variability in ductility measures, leading to a high probability of compressive failure. Based on a target probability of failure taken from the literature, it was found that modification of the current ductility requirements is desired. This research highlights the need for more reliability-based studies into the safety factors provided by the ACI Code for ensuring adequate ductility in reinforced concrete beams. © 2016, American Concrete Institute. All rights reserved

Investigating the reliability of RC beams of tall buildings designed based on the new ACI 318-05/ASCE 7-05

The level of safety achievable in reinforced concrete (RC) beams designed based on the new ACI 318-05/ASCE 7-05 is investigated in this study. The study makes use of the more recent statistical data on flexure and shear provided by Szerszen and Nowak. Due to the importance of using real ratios of lateral/gravity loads in any such reliability analysis, a set of RC buildings was chosen, loaded and designed and the actual nominal wind-to-dead load ratios were derived. Using these and the statistical data mentioned above, reliability indices for moment and shear were calculated. The resulting reliability indices for moment and shear are then presented in comparison. In addition, the reliability index variations along the beam at the controlling stations are compared to each other. The results of the study indicate that reliability indices at the controlling stations obtained for different limit states are not consistent for low values of nominal wind-to-dead load ratios, but converge consistently for high ratios. It seems that the use of older shear strength factors provides a reliable safety margin and that the use of the more recent statistical data for material combined with the older shear strength factors leads to more consistency. Copyright © 2010 John Wiley & Sons, Ltd

Effect of relative intensity of wind load on the RC column reliability in tall buildings

Wind loads are very important in the design of tall buildings as often the load combinations containing the wind load govern the design. As for reliability, however, because of the higher inherent uncertainty in the wind load in comparison to the gravity load, safety indices decrease as the ratio of wind load to gravity load increases. The safety indices in RC columns depend on the nominal wind to gravity load ratios. Due to the interaction between bending moment and axial force, a single ratio cannot be defined, because the eccentricity is not similar for wind and gravity loads. In this paper, the ratio of wind to gravity loads is considered separately for axial force and bending moments. Unlike conventional approach, here it is assumed that the wind and gravity loads' eccentricities are not equal, and the final load eccentricity used in either the design or the reliability analysis is a function of applied loads. The results demonstrate that the sensitivity of RC columns' safety indices to bending moment ratios is higher than that of axial force ratios. Furthermore, the variation of RC columns' safety indices with a low rebar percentage is very different from RC columns with high rebar percentages. Copyright © 2010 John Wiley & Sons, Ltd

On the FE modeling of FRP-retrofitted beam-column subassemblies

The use of fiber reinforced polymer (FRP) composites in strengthening reinforced concrete beam-column subassemblies has been scrutinised both experimentally and numerically in recent years. While a multitude of numerical models are available, and many match the experimental results reasonably well, there are not many studies that have looked at the efficiency of different finite elements in a comparative way in order to clearly identify the best practice when it comes to modelling FRP for strengthening. The present study aims at investigating this within the context of FRP retrofitted reinforced concrete beam-column subassemblies. Two programs are used side by side; ANSYS and VecTor2. Results of the finite element modeling using these two programs are compared with a recent experimental study. Different failure and yield criteria along with different element types are implemented and a useful technique, which can reduce the number of elements considerably, is successfully employed for modeling planar structures subjected to in-plane loading in ANSYS. Comparison of the results shows that there is good agreement between ANSYS and VecTor2 results in monotonic loading. However, unlike VecTor2 program, implicit version of ANSYS program is not able to properly model the cyclic behavior of the modeled subassemblies. The paper will be useful to those who wish to study FRP strengthening applications numerically as it provides an insight into the choice of the elements and the methods of modeling to achieve desired accuracy and numerical stability, a matter not so clearly explored in the past in any of the published literature. © 2013 The Author(s)

Reliability analysis of moment redistribution in reinforced concrete beams

Design codes allow a limited amount of moment redistribution in continuous reinforced concrete beams and often make use of lower bound values in the procedure for estimating the moment redistribution factors. Here, based on the concept of demand and capacity rotation, and by means of Monte Carlo simulation, a probabilistic model is derived for the evaluation of moment redistribution factors. Results show that in all considered cases, the evaluated mean and nominal values of moment redistribution factor are greater than the values provided by the ACI code. On the other hand, the 5th percentile value of moment redistribution factor could be lower than those specified by the code. Although the reduction of strength limit state reliability index attributable to uncertainty in moment redistribution factors is not large, it is comparable to the reduction in reliability index resulting from increasing the ratio of live to dead load

A reliability-based investigation into ductility measures of RC beams designed according to fib Model Code 2010

A reliability-based investigation into the ductility measures for reinforced concrete (RC) beams designed according to the current fib Model Code for Concrete Structures 2010 is presented in this paper. Based on the ductility ratio (= ratio of strain in tensile rebar to yield stress of steel), a limit state to ensure adequate ductility in RC beams is proposed. Results show that the ductility ratio generally follows a right-skewed distribution, and due to variability in the material properties and model error, there is high variability in the strain ductility. This high variability in the ductility ratio leads to a high probability of non-ductile behaviour for RC beam designs based on the code. This is more pronounced for normal-strength concrete and grade S500 steel. Based on a target probability taken from the literature, a modification to the allowable neutral axis depth advised by the code is proposed. The results presented in this paper indicate that more reliability-based studies of the safety factors provided by fib Model Code 2010 are needed in order to ensure adequate ductility in RC beams. Copyright © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

Effects of cross-sectional shape on the reliability of RC columns

This paper studies the effects of cross-sectional shape and rebar configuration on the reliability indices of concrete columns. Three sections with rectangular, square and circular shapes are selected. Using the Monte Carlo simulation technique, the statistical parameters for reinforced column resistance are calculated along several load eccentricities using the most recent statistical data available in the literature. The statistical parameters show that the magnitude and the variation of bias factors and the coefficients of variation are not similar for the sections selected. The coefficients of variation of the square and circular sections are greater than that of the rectangular section. The results of reliability analysis indicate the importance of sectional shape, especially at low load eccentricities. In some cases, the effect of cross-sectional shape or reinforcement configuration is found to be more important than the effect of the compressive strength of the concrete. It is recommended to include the shape factor and the reinforcement configuration in the code calibration process for the capacity reduction factors. © 2011 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

A probabilistic study on the ductility of reinforced concrete sections

Although the current design codes apply reliability-based calibration procedures to evaluate safety factors for the strength based limit state, the safety factors used to ensure minimum ductility capacities are rather simple and are not resulted from a probability-based procedure. This study examines level of safety delivered by the current design codes with regards to providing minimum curvature ductility for reinforced concrete (RC) beams made with normal strength concrete. Reliability analysis results show that with regard to the strength limit state, the considered design codes are in good agreement with one another. However, there is considerable disparity in the level of safety provided for minimum curvature ductility amongst the codes. The provided reliability for the design to remain ductile is too low in some and just about acceptable in the others. This signifies the importance and the need to introduce reliability based methods of design for ductility.© 2014 Advances in Structural Engineering