Abstract
This paper proposes an analysis procedure able to determine the flexural response of rectangular symmetrically reinforced concrete sections subjected to axial load and uniaxial bending. With respect to the usual numerical approaches, based on the fibre decomposition method, this procedure is based on the use of analytical expressions of the contributions to the equilibrium given by the longitudinal reinforcement and the concrete region in compression, which depend on the neutral axis depth and the curvature at each analysis step. The formulation is developed in dimensionless terms, after a preliminary definition of the geometrical and mechanical parameters involved, so that the results are valid for classes of RC sections. The constitutive laws of the materials include confinement effect on the concrete and postyielding behaviour of the steel reinforcement, which can be assumed to be softening behaviour for buckled reinforcing bars. The strength and curvature domains at the first yielding of the reinforcement in tension and at the ultimate state are derived in the form of analytical curves depending on the compression level; therefore, the role of a single parameter on the shape of these curves can easily be deduced. The procedure is validated by comparing some results with those numerically obtained by other authors.
Highlights
The performance of reinforced concrete frames under severe earthquakes largely depends on the ability of the beam and column sections to undergo large inelastic deformations
This ability plays a decisive role in existing buildings, the safety level of which can be estimated by employing nonlinear analysis tools, needing a careful input in terms of strength domains and moment-curvature relationships of the critical sections
The resisting components of the section give a contribution to the equilibrium that can be expressed by analytical functions depending on the normalized neutral axis depth and the curvature of the section
Summary
The performance of reinforced concrete frames under severe earthquakes largely depends on the ability of the beam and column sections to undergo large inelastic deformations. The application of this approach to large structures with many degrees of freedom has some limitations, because numerical integrations and a prediction of the state of materials must be carried out considering the entire layers of each region where a plastic hinge can occur; a high amount of information is required to characterize each section involved, and a large number of numerical operations is needed to reach an acceptable level of error This results in heavy computational efforts and convergence problems for nonlinear structural analysis. This paper confirms that the values of the ultimate bending moment and curvature in any direction can be efficiently related to the values corresponding to two separate conditions of uniaxial bending In this context the present paper proposes an analytical model for the evaluation of the moment-curvature relationship of rectangular RC sections subjected to axial load and uniaxial bending, by using an incremental strain technique, which could be an alternative to the classical fibre decomposition method. The use of the proposed model to define the moment-rotation response of the critical region to which the section considered ideally belongs requires a suitable modeling of the potential “plastic hinges” which is not discussed here
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