This paper reports the results of an extensive campaign of incremental dynamic analyses (IDA) of rigid rocking blocks under various loading histories, including real ground/floor motions and shake table testing protocol loading histories. Several block geometries are investigated considering various size and slenderness combinations representative of building contents, monumental elements, art objects, components of critical facilities, and other unanchored elements. The spectral response of the block to different loading histories is firstly assessed by highlighting the characteristics of the different seismic input sets. Dimensionless acceleration- and velocity-based parameters are considered as intensity measures, and the block rotation normalized considering the critical angle (i.e., dimensionless rocking amplitude) is assumed as an engineering demand parameter. The IDA curves are evaluated, and the dynamic response of the blocks is characterized in terms of: (a) type of loading history, (b) intensity measure, and (c) block geometry. New information and technical insights are presented regarding the assessment of seismic response of structural and nonstructural rocking systems. The dynamic response of the blocks subjected to the investigated protocols is found to be not always compatible with the capacities related to real ground/floor motions, often producing non-conservative estimations. The discrepancy identified between the block responses associated with the protocol inputs and real motions is found to be significantly affected by both block geometry and intensity measure.
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