Assessment of the effective stiffness in R/C frames subjected to seismic loads"

The current design codes and technical recommendations often provide rough indications for the assessment of the effective stiffness in R/C frames subjected to seismic loads, which is a key factor when a linear analysis is performed. The Italian design code (NTC-08), the Eurocode 8 and ACI 318 do not take into account all the structural parameters affecting the effective stiffness, something that may not be on the safe side when second-order effects P-Δ occur, or when incorrect distributions of the internal forces are obtained. In this paper the factors influencing the effective stiffness of R/C beams, columns and walls under seismic forces are analyzed. Five different approaches are adopted in order to evaluate the effective stiffness of R/C members, in accordance with the scientific literature and the international design codes. A parametric analysis is performed on an actual R/C building and its results are presented and discussed, as a contribute to the improvement of design practice. The main variables considered in the analysis are: the reinforcement ratio, the ratio of the axial load, the compressive strength of the concrete, and the type of the shallow beams (ordinary or wide beams). The second-order effects are quantified and the resulting displacements related to the Damage Limit State (DLS) under seismic loads are discussed. The analytical results show that, although the effective stiffness increases with the steel ratio, the limit of 50% of the initial stiffness turns out to be an upper bound for small values of the axial-load ratio, rather than a lower bound as indicated by both the Italian Design Code and EC-8. As a result, in some cases the current Italian and European provisions tend to underestimate second-order P-Δ effects, when the DLS is investigated under seismic loading.