An Analytical Step-by-Step Procedure to Derive the Flexural Response of RC Sections in Compression

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. 1. Introduction 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. Especially, this ability plays a decisive role in existing buildings, the safety level of which can be estimated by employing nonlinear analysis tools (like pushover), needing a careful input in terms of strength domains and moment-curvature relationships of the critical sections. The evaluation of the moment-curvature response of critical sections of RC members is a complex issue mainly because of the interaction of various parameters: constitutive laws of materials in the elastic and plastic ranges, member geometry, buckling phenomena in reinforcing steel bars, and loading conditions. In order to include in a computer software the cross-section strength domain and moment-curvature relationships of reinforced concrete members, two different approaches are usually followed: the use of strength domains [1–3] and moment-curvature relationships of a usually bilinear or trilinear prefixed shape [4–6], in which a degrading stiffness model reproduces the effect of yielding and damage of materials; the layered section approach, based on the fibre