On the use of base isolation for the protection of rigid bodies placed on a multi-storey frame under seismic excitation Alessandro Contento, Angelo Di Egidio ⇑ Dept. of Civil, Construction-Architectural, Environmental Engineering, University of L’Aquila, Italy article info Article history: Received 12 June 2013 Revised 3 December 2013 Accepted 13 January 2014 Available online 6 February 2014 Keywords: 2D rigid block Eccentricity Multi-storey frame Sliding Rocking Overturning abstract The use of base isolation applied to rigid bodies placed on a multi-storey frame is considered with the aim of understanding whether or not seismic isolation is beneficial in preventing their collapse during an earthquake. The rigid body is placed on either a fixed or an isolated oscillating base. It may be subjected to sliding, rocking and sliding–rocking motions. When base isolation is considered, security stops capable of preventing the isolation system from breaking are always assumed to be present. The frame, modelled as a four-storey, shear-type system, is always considered to work in the elastic regime. The geometrical characteristics of the body are chosen so that a collapse event, such as overturning or falling out from the support, is obtained for an excitation for which the behaviour of the frame remains in the elastic regime. Overturning and falling-out curves are plotted against PGA (Peak Ground Acceleration) to demonstrate the role of the geometrical parameters characterising the body, of the spectral characteristics of the earthquake and of the level of the frame at which the object is placed. The analyses performed reveal that base isolation applied to a rigid body placed on a frame is not always appropriate in cases where the same body is placed on a fixed base. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction There is extensive literature concerning rigid bodies. Starting from Shenton and Jones [1], many works present models of rigid body behaviour addressing problems related to works of art or, more generally, to non-anchored substructures. Usually two kinds of excitations are taken into account: either one-sine pulse and harmonic excitations [2–4] or earthquake excitations [5–7]. Differ- ently, in Spanos and Koh [8] a random shacking of the structure, with an excitation of the form of modulated white noise, is consid- ered. Most papers concern two-dimensional models of symmetric rigid bodies placed on the ground while only a small number deal with non-symmetric rigid bodies [9–11]. Some papers highlight specific features of the dynamics of rigid bodies, such as the definition of maps describing the criteria for the different phases of motion [12,13], the existence of survival regions which lie above PGA (Peak Ground Acceleration) associated with the first occur- rence of overturning [3,14] or the correct definition of the impact occurrence [15]. In Spanos et al. [16] the behaviour of two stacked rigid blocks is considered, while in Spanos et al. [17], Spanos and Koh [8] the focus is on blocks on flexible foundations. In some models with a more specific focus on works of art such as Vestroni and Di Cintio [18], Di Egidio and Contento [19], base isolation is considered. Specifically, in Di Egidio and Contento [20] the possi- bility of the rigid body sliding and rocking with its base partially outside the base isolation is taken into account. Only a small num- ber of papers make use of three-dimensional models to describe the behaviour of rigid bodies, for example to study the motion of a disk of finite thickness [21,22], the wobbling of a frustum [23] or sloshing in a tank [24] or to analyse the behaviour of slender bodies such as statues and obelisks [25]. In this paper the use of base isolation applied to rigid objects placed on various floors of a multi-storey frame is analysed in detail in order to understand whether or not seismic isolation is beneficial in preventing collapse during an earthquake. In this field various methods exist to analyse the interaction between the primary and secondary structure (Oropeza et al. [26], Villaverde [27]), considering both linear and nonlinear behaviours of the primary structure. Although the Authors of this paper in Zulli et al. [25] demonstrate that a three-dimensional model of a rigid block should be used to correctly evaluate the collapse event of a near-square-based rigid block, here a simpler 2D model is used. This is justifiable since the rigid block considered here is always assumed to possess a rectangular base with one side considerably longer than the other. In this case the only possible rocking motion is the one around the longer side of the rectangle. Hence, to describe this motion, a classical 2D model of the rigid block is sufficient. 0141-0296/$ - see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2014.01.019 ⇑ Corresponding author. E-mail address: angelo.diegidio@univaq.it (A. Di Egidio). Engineering Structures 62–63 (2014) 1–10 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct