1 A FINITE ELEMENT APPROACH FOR MODELLING CONTROLLED ROCKING SYSTEMS Dimitrios KALLIONTZIS 1 and Sri SRITHARAN 2 ABSTRACT Unbonded post-tensioned structural systems have gained momentum in recent years for seismic applications as they enable structures to re-center after experiencing an earthquake load. Accurate modelling of controlled rocking is of paramount importance for understanding the expected seismic performance of these structural systems. Considering the intricacy associated with rocking mechanisms, use of finite element models routinely employed for dynamic problems is inadequate to characterize the response of a system subjected to controlled rocking. This paper presents a study which has developed an efficient approach to quantify the dynamic response of a rocking system with unbonded post-tensioning. Details of a three-dimensional model combined with an explicit finite element technique are provided for a rocking column designed with unbonded post-tensioning. The analytical results are validated with experimental data to confirm the accuracy of the modelling technique. INTRODUCTION Free Rocking. The survival of seemingly unstable structures during strong earthquake events of the past was attributed to their ability to enter rocking motion. This behaviour, associated with structural systems not firmly attached to the ground, triggered researchers to examine rocking as a potential mechanism for seismic protection. Housner (1963) was the first to present important steps for modelling of rocking behaviour by proposing piecewise equations that describe the free rocking motion of a uniform block rocking on its flat base. The work of this researcher was based on several assumptions: (a) both rocking block and base are rigid; (b) there is no sliding between the block and the base; (c) no bouncing of the block occurs; (d) energy dissipation takes place instantaneously at the time of the impact and is expressed through a coefficient of restitution (COR) dependent on the geometric properties of the block; (e) the impact takes place at the corners of the bottom edge; and (f) the block oscillates in a two-dimensional fashion. A novel approach to rigid body-rigid base modeling was proposed by Prieto and Lourenco (2005), who suggested that energy dissipation can be estimated by simulating the impulsive force response taking place at the impact. This way, these researchers were able to bridge the piece-wise equations introduced by Housner with the impact phenomenon by substituting the initially proposed COR approach with a Dirac-delta force function applied during the impact. The capacity of the simple rocking model (SRM) developed by Housner was investigated by Lipscombe and Pellegrino (1993) who conducted experimental tests on four unanchored blocks of various aspect ratios. It was shown that in 1 Graduate Research Assistant, Iowa State University, Ames, United States, dk1@iastate.edu 2 Wilson Engineering Professor, Iowa State University, Ames, United States, sri@iastate.edu