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A nonlinear SDOF model for the simplified evaluation of the displacement demand of low-rise URM buildings


The determination of displacement demands for masonry buildings subjected to seismic action is a key issue in the performance-based assessment and design of such structures. A technique for the definition of single-degree-of-freedom (SDOF) nonlinear systems that approximates the global behaviour of multi-degree-of-freedom (MDOF) 3D structural models has been developed in order to provide useful information on the dependency of displacement demand on different seismic intensity measures. The definition of SDOF system properties is based on the dynamic equivalence of the elastic properties (vibration period and viscous damping) and on the comparability with nonlinear hysteretic behaviour obtained by cyclic pushover analysis on MDOF models. The MDOF systems are based on a nonlinear macroelement model that is able to reproduce the in-plane shear and flexural cyclic behaviour of pier and spandrel elements. For the complete MDOF models an equivalent frame modelling technique was used. The equivalent SDOF system was modelled using a suitable nonlinear spring comprised of two macroelements in parallel. This allows for a simple calibration of the hysteretic response of the SDOF by suitably proportioning the contributions of flexure-dominated and shear-dominated responses. The comparison of results in terms of maximum displacements obtained for the SDOF and MDOF systems demonstrates the feasibility and reliability of the proposed approach. The comparisons between MDOF and equivalent SDOF systems, carried out for several building prototypes, were based on the results of time-history analyses performed with a large database of natural records covering a wide range of magnitude, distance and local soil conditions. The use of unscaled natural accelerograms allowed the displacement demand to be expressed as a function of different ground motion parameters allowing for the study of their relative influence on the displacement demand for masonry structures.

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This work was carried out with the partial financial support of the EUCENTRE Executive Project 2012–2014 e3 “Seismic vulnerability of masonry buildings”, funded by the Italian Department of Civil Protection, and the bilateral cooperation project between Italy and Slovenia, funded by Italian Ministry of Foreign Affairs “Protection of cultural heritage buildings against earthquakes” (2011). Special thanks go to Prof. M. Dolšek, Dr. A. Galasco, Dr. M. J. Fox, Dr. A. Mouyiannou and Dr. I. Senaldi for the theoretical and practical support.

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Correspondence to F. Graziotti.

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Graziotti, F., Penna, A. & Magenes, G. A nonlinear SDOF model for the simplified evaluation of the displacement demand of low-rise URM buildings. Bull Earthquake Eng 14, 1589–1612 (2016).

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  • SDOF model
  • Displacement demand
  • Masonry structures
  • Macroelement
  • Intensity measures