### COMPARISON OF DESIGN PROCEDURES OF DISSIPATIVE BRACES FOR THE SEISMIC RETROFITTING OF R.C. FRAMED BUILDINGS

*Fabio Mazza, Mirko Mazza, Alfonso Vulcano*

Ultima modifica: 2011-08-31

#### Sommario

Passive control strategies based on the use of steel braces equipped with dissipative devices are frequently adopted for the seismic retrofitting of reinforced concrete (r.c.) framed buildings. More difficulties than those involved in the design of new structures are expected, because the knowledge of an existing structure can be incomplete and the proportioning of the dissipative braces depends also on the properties of the existing structure. In the present work the attention is focused on metallic yielding hysteretic dampers (HYDs), representing a low cost and reliable solution for energy dissipation. For a widespread application of the hysteretic dissipative braces (HYDBs) design criteria and guidelines should be available. Many new seismic codes allow for the use of dissipative devices (e.g. European code, EC8; Italian code, NTC08), while only few codes provide simplified criteria for their design (e.g. USA code, FEMA 356).

According to the Performance-Based-Design (PBD), a design objective is obtained coupling a performance level with a specific level of ground motion. On the basis of the PBD several simplified nonlinear methods were proposed for HYDBs, combining the nonlinear static (pushover) analysis of the multi-degree-of-freedom model of the actual structure with the response spectrum analysis of an equivalent single-degree-of-freedom (SDOF) system. Among these, two design approaches are selected: a Force-Based Design (FBD) approach combined with required deformation target verification; a Direct Displacement-Based Design (DDBD) approach, in which the design starts from a target deformation of an equivalent elastic (linear) system with effective properties. A proportional stiffness criterion (which assumes, at each storey, the same value of the ratio between the lateral stiffness provided by the HYDBs and that of the unbraced frame) and a constant-drift criterion (to obtain an inverted-triangular first vibration mode of the damped braced frame) are considered for the stiffness distribution law of the HYDBs. Moreover, the distribution law of the yield-load for the HYDs is assumed similar to that of the elastic force induced in the braces by the lateral seismic loads or, alternatively, according to a constant-shear ratio criterion (i.e. a constant value of the ratio between the ultimate and design shears of the damped braced frame is considered at each storey).

In the present work the attention is focused on a typical r.c. framed building, which, originally designed (before the introduction of new seismic codes) for a medium-risk seismic region according to old and not very conservative rules and/or prescriptions, has to be retrofitted by insertion of HYDBs for attaining the performance levels imposed by NTC08 in a high-risk seismic region. Specifically, three simulated designs of a r.c. six-storey residential buildings are made with reference to the Italian codes in force in the following periods: (a) 1962-1975 (law no. 1684, 25/11/1962); (b) 1975-1996 (D.M. 3/3/1975, static analysis); 1996-2008 (D.M. 16/1/1996, dynamic analysis). Moreover, in order to evaluate the effectiveness of the dissipative braces (as specified below), the unbraced frame is also designed according to the provisions of NTC08 (D.M. 14/1/2008), assuming high ductility class.

Then, to check the effectiveness of the above design procedures of HYDBs (i.e. FBD and DDBD) and criteria for stiffness and strength distributions, the nonlinear dynamic responses of unbraced and damped braced structures are compared under real and artificially generated accelerograms, whose response spectra match those adopted by NTC08 for the peak ground accelerations corresponding to the serviceability and ultimate limit states. For this purpose, the r.c. frame members are idealized by means of a classical two-component model, assuming a bilinear moment-curvature law. The effect of the axial load on the ultimate bending moment of the columns (M-N interaction) is also considered. Finally, the behaviour of a HYD is idealized by a bilinear law. An elastic-linear law, in tension and compression, is adopted for the steel braces, providing that the buckling be prevented.

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