Parametric study of the bending stiffness of RC cracked building beams

Abstract

The bending stiffness of RC cracked building beams is evaluated for the lateral analysis of frames or building structures subjected to seismic loading related to service loads, one of the most relevant and controversial issues in the overall seismic design process. As a first stage, the influence of the following variables are evaluated on the assessment of the cracked moment of inertia (Icr) of typical low-ductility detailed RC sections: a) the shape of the cross sections (rectangular, inverted L and T), b) the width (b), c) the aspect ratio (h/b), d) the concrete compressive strength (f'c), e) the tensile reinforcement ratio (ρ = Ast/bd), f) the tensile and compression reinforcement ratio (ρ/ρ') and, g) the transverse steel confinement (considered through the specified separation of stirrups, s). A total of 37,800 sectional analyses are performed. As a result of the extensive parametric study, an equation for the assessment of Icr is proposed as a function of the observed relevant variables. As a second stage, effective flexural stiffness (EIe) of typical RC building beams is assessed. In this case, stiffness equations derived from the flexibility method for prismatic members with cracked segments of pre-defined length at both beam ends are used. EIe is assessed taking into account the span-to-depth ratio (L/h) and the proposed moment of inertia of the cracked section (Icr). From the obtained results, it is possible to conclude that the use of effective stiffness in structural beams as proposed in current Mexico seismic code for the elastic lateral analysis of a seismic-resistant system is not correct. Therefore, the current assessment of displacements should be critically reviewed and, if necessary, modified.