Stress-Strain Relation Laws for Concrete and Steel Reinforcement Used in Non-Linear Static Analytical Studies of the Moment Resisting Reinforced Concrete (RC) Frame Models (original) (raw)
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Nonlinear behaviour of reinforced concrete moment resisting frame with steel brace
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There has been considerable research on modelling inelastic behaviour of reinforced concrete. However, nonlinear material models used for seismic response history analyses and for nonlinear static analysis (NSA) procedures tend to be simple. It can be argued that sophisticated material models for a complex material like reinforced concrete are perhaps not essential for earthquake analysis in view of several other uncertainties associated with the seismic phenomenon. This paper examines the influence of material modelling on RHA responses for a simple reinforced concrete frame structure. Five acceleration time histories compatible to elastic design spectrum of Eurocode 8 are used for RHA. Two material models are considered: a concrete damaged plasticity model that uses the Drucker Prager criterion and in which concrete and reinforcement are modelled separately and a homogenized Drucker Prager model. In both cases the influence of strain hardening and strain rate effects are considered. The results show that the design response from RHA analyses is significantly different for the two models. The paper then compares the NSA and RHA responses for the two material models for reinforced concrete. The NSA procedures considered are the Displacement Coefficient Method (DCM) and the Capacity Spectrum Method (CSM). A comparison of RHA and NSA procedures shows that there can be a significant difference in local response even though the target deformation values at the control node match. Moreover, the difference between the mean peak RHA response and the pushover response is not independent of the material model.
Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015), 2019
The study of the hysteretic behavior of reinforced concrete members that undergo static cyclic and dynamic loading conditions in cases where the loading level is close to their carrying capacity, is a challenging open research subject, which currently is being investigated by many researchers. The development of an objective and robust 3D constitutive modeling approach that will be able to account for the accumulated material damage and stiffness deterioration is of great importance in order to realistically describe the physical failure mechanisms thus numerically study the seismic performance of RC structures. The adopted concrete material model in this research work is based on the material model proposed by Markou and Papadrakakis, which was an extension of the Kotsovos and Pavlovic work. Furthermore, the use of two newly proposed damage factors that are computed through the use of the number of opening and closing of cracks during the nonlinear cyclic analysis, are further investigated and their ability in capturing the accumulated material damage in both steel and concrete is further discussed in this research work. The numerical accuracy of the proposed method is validated by comparing the numerical results with the experimental data of two beam-column frame joints, a shear wall and a threestorey three-bay RC frame. According to the experimental setups, the RC joint and the shear wall specimens were tested under ultimate limit state cyclic loading, whereas the RC frame was tested under dynamic loading conditions. Based on the numerical findings, the proposed algorithm manages to capture the experimental results in an accurate manner and the numerical response of the understudy algorithmic implementation was found to exhibit computational robustness and efficiency.
A developed algorithm for the inelastic analysis of reinforced concrete frames
Computers & Structures, 1995
A mathematical algorithm is developed and presented for use in conjunction with the Imposed Rotation Method as reformulated by Kaneko as a (n * 2n) linear complementarity problem. The inelastic tri-linear moment rotation law which is modelled to reflect behaviour at critical sections is adjusted during the incremental analysis in order to adhere to the non-holonomic behaviour of reinforced concrete when stress unloading occurs. The developed algorithm also incorporates the two relevant failure criteria, namely local failure and failure by the formation of a collapse mechanism. A typical reinforced concrete frame is analyzed under different load combinations to show the features of the developed algorithm.
Dynamic analysis of reinforced concrete frames including joint shear deformation
Engineering Structures, 1999
The rehabilitation of existing buildings requires an assessment of their lateral load resisting capacity which may be limited by the strength and ductility capacity of their critical regions. From this assessment, a rehabilitation strategy can be formulated. Lack of adequate confinement and shear reinforcement in the beam-column joints of existing reinforced concrete frames may be the cause of brittle failure during a seismic event. Most of the nonlinear dynamic analysis programs assume infinitely rigid beamcolumn joints in concrete frames regardless of the reinforcement detail. To properly analyze existing structures, a joint element is proposed and introduced in the nonlinear dynamic analysis. The developed joint element accounts for inelastic shear deformation and bar bond slip. The response of three-and nine-story existing frames with joint elements when subjected to dynamic loading was compared with the response of frames with rigid joint assumption and the response of rehabilitated frames. The results show that the modelling of inelastic shear deformation in joints has a significant effect on the seismic response in terms of drift and damage. The rigid joint assumption was found to be inappropriate when assessing the behaviour of existing nonductile structures.
Nonlinear Cyclic and Earthquake Response Analysis of Reinforced Concrete Structures
This paper presents a simplified method based on energy formulation for nonlinear analysis of reinforced concrete frame structures up to ultimate failure, which has been implemented in Open System for Earthquake Engineering Simulation framework (OpenSees). In the simplified method, a reinforced concrete member is modeled by an equivalent member of homogeneous nonlinear material with a derived stress-strain relationship, which satisfies the requirement that the equivalent member has the same moment-curvature behaviour as the original member. One advantage of the simplified method is its simplicity which can be easily implemented in most structural analysis computer program with nonlinear modeling capacities. The developed model can accurately predict the nonlinear hysteretic behaviour of reinforced concrete structures with frame members of arbitrary shapes and reinforcing details under severe earthquake excitations. Numerical examples of single bridge column structures of regular reinforced concrete members or double-skinned concrete filled tube members and a 2-story 2-bay reinforced concrete frame are analyzed using the simplified method under monotonic, cyclic and earthquake loadings to demonstrate the validity and accuracy of the simplified method. The effects of confinement, steel hardening, stiffness degradation and softening, pinching, and strength deterioration are simulated in the developed method. A correlation study has been carried out to compare the computer simulation results by the developed method with the experimental measurements of a full scale 3-story 3-bay reinforced concrete steel frame tested at the National Center for Research on Earthquake Engineering (NCREE) Taiwan, as a part of the joint research between Carleton University and NCREE. Results from the proposed method agree well with experiment test results and predictions from finite element and fiber models.
1st Croatian Conference on Earthquake Engineering, 2021
Capacity design concept for reinforced concrete frame systems is based on a hierarchy of the strength and stiffness properties of the structural elements so that the seismic energy dissipation mechanism occurs in a certain way. This theoretical concept of seismic energy dissipation by allowing the occurrence of plastic hinges at the end of the beams and the columns located at the ground floor was not observed / identified in post-earthquake inspection of damaged RC frame structures. On the other hand, various failure mechanisms were observed that are not compliant with theoretical considerations specified in the seismic design codes. The damages produced during the latest seismic events, (2020 Zagreb earthquake, 2020 Aegean Sea earthquake, 2020 Caribbean earthquake, 2020 Puerto Rico earthquake, 2020 Mexico earthquake, etc.) raised some concerns related to the theoretical ductile failure mechanism (Strong Column-Weak Beams, SCWB) versus the practical approach. Consequently, a possible improvement of the capacity design concept through the consideration of different values for the behaviour factor "q" applied to structural elements (beams and columns) was investigated and presented in this paper. The goal was to reach the expected theoretical structural degradation mechanism. Thus, by considering different values for the behaviour factor "q", at the design stage, for beams and columns, it was possible to reach a favourable value for the ratio Kc/Kb between the bending stiffness of columns (Kc) and beams (Kb). Consequently, a good correlation between the real seismic response and the theoretical mechanism of structural deformation was obtained.