GNGTS 2013 - Atti del 32° Convegno Nazionale

EFFECTIVENESS OF THE N2 METHOD FOR THE SEISMIC ANALYSIS OF STRUCTURES WITH DIFFERENT HYSTERETIC BEHAVIOUR G. Rinaldin 1 , C. Amadio 2 , M. Fragiacomo 1 1 Department of Architecture, Design and Urban Planning, University of Sassari, Alghero, Italy 2 Department of Engineering and Architecture, University of Trieste, Italy Introduction. The seismic design is usually carried out via linear or non-linear static analyses using design spectra, which are obtained on the basis of ductility considerations and/ or equivalent damping of the structure. The introduction of a behaviour factor or an equivalent damping ratio is necessary to allow the elastic design of structures, taking into account the dissipative capacity of the structure due to the seismic actions. This factor reduces the elastic spectrum to a design spectrum, which can be used to find the design acceleration to be applied to the analysed building. The most common methods adopted in seismic engineering are: (i) the N2 method (Fajfar, 1999, 2000), which reduces the elastic spectrum by a behaviour factor q for the verification of the structure in a linear or non-linear analysis (this method was adopted by Eurocode 8 [CEN 2003]); and (ii) the overdamped spectrum method (Freeman, 1978) [that was adopted by the US code ATC-40 (ATC, 1996)], which is based on the use of an elastic spectrum calculated for an appropriate equivalent damping. In a pushover analysis, both methods compare the capacity of a structure with the demand of an earthquake ground motion. From this type of non-linear static analysis, the capacity of the structure is represented by a force-displacement curve, calculated on an equivalent SDOF system, while the demand curve is represented by the elastic spectra reduced by q for the N2 method or by the overdamped elastic spectra. While the overdamped spectrum method is directly related to the shape of the hysteretic response, which depends on the hysteretic behaviour of the structure and the material, the N2 method works on a procedure based on ductility. A study conducted on the former method (Krawinkler, 1994) identified a fundamental flow: the relationship between the hysteretic energy dissipation at the maximum displacement and the equivalent viscous damping is not justified. In order to clarify and validate the N2 and overdamped spectrum methods, in this work inelastic spectra are calculated via non-linear time-history analyses and compared with the ones provided by the two methodologies. N2 method. The behaviour factor q in this method is calculated using the equations (Fajfar, 2000): (1) (2) where µ =δ u /δ y is the ductility value, T is the natural vibration period of the structure, and T C the period value at the end of the constant acceleration part of the elastic spectrum. Overdamped spectrum method. For the overdamped spectrum method, the equivalent damping ratio, in the hypothesis of an equivalent viscous elastic behaviour of a SDOF system in a harmonic motion, depends upon the energy dissipated in a cycle E D and the elastic deformation energy in a half cycle E S 0 as reported in Eq. (3). (3) A previous investigation (Fragiacomo et al. , 2006) demonstrated that the use of the N2 method leads to the best accuracy for elasto-plastic SDOF systems, with and without stiffness degradation and with bilinear or Clough hysteretic behaviour. In this work, different hysteretic 131 GNGTS 2013 S essione 2.1