SUMMARY This paper investigates the planar rocking response of an array of free‐standing columns capped with a freely supported rigid beam in an effort to explain the appreciable seismic stability of ancient free‐standing columns that support heavy epistyles together with the even heavier frieze atop. Following a variational formulation, the paper concludes to the remarkable result that the dynamic rocking response of an array of free‐standing columns capped with a rigid beam is identical to the rocking response of a single free‐standing column with the same slenderness yet with larger size, that is a more stable configuration. Most importantly, the study shows that the heavier the freely supported cap beam is (epistyles with frieze atop), the more stable is the rocking frame regardless of the rise of the center of gravity of the cap beam, concluding that top‐heavy rocking frames are more stable than when they are top light. This ‘counter intuitive’ finding renders rocking isolation a most attractive alternative for the seismic protection of bridges with tall piers, whereas its potential implementation shall remove several of the concerns associated with the seismic connections of prefabricated bridges. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARYThis paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top-heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non-dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability.

SUMMARYThis paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the 'static' value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free-standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records.

Summary An argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.

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