SUMMARYThis paper is concerned with the superÿcial similarities and fundamental di erences between the oscillatory response of a single-degree-of-freedom (SDOF) oscillator (regular pendulum) and the rocking response of a slender rigid block (inverted pendulum). The study examines the distinct characteristics of the rocking spectrum and compares the observed trends with those of the response spectrum. It is shown that the rocking spectrum re ects kinematic characteristics of the ground motions that are not identiÿable by the response spectrum. The paper investigates systematically the fundamental di erences in the dynamical structure of the two systems of interest and concludes that rocking structures cannot be replaced by 'equivalent' SDOF oscillators. The study proceeds by examining the validity of a simple, approximate design methodology, initially proposed in the late 1970s and now recommended in design guidelines to compute rotations of slender structures by performing iteration either on the true displacement response spectrum or design spectrum. This paper shows that the simple design approach is inherently awed and should be abandoned, in particular for smaller, less-slender blocks. The study concludes that the exact rocking spectrum emerges as a distinct intensity measure of ground motions.

SUMMARYThis paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retroÿtting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times.The numerical study presented in this paper is conducted with the commercially available software Working Model 2D TM , which can capture with ÿdelity the sliding, rocking, and slide-rocking response of rigid-body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in-house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment.The study reveals that relative sliding between drums happens even when the g-value of the ground acceleration is less than the coe cient of friction, , of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes Mw = 6:0 -7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal e ect on the sliding response of the drums; and (d) sti metallic shear links in-between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided.

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SUMMARYThis paper presents results of a comprehensive experimental program on the seismic response of fullscale freestanding laboratory equipment. First, quasi-static experiments are conducted to examine the mechanical behavior of the contact interface between the laboratory equipment and floors. Based on the experimental results, the response analysis that follows adopts two idealized contact friction models: the elastoplastic model and the classical Coulomb friction model. Subsequently, the paper presents shake table test results of full-scale freestanding equipment subjected to ground and floor motions of hazard levels with corresponding displacements that can be accommodated by the shake table at the UC Berkeley Earthquake Engineering Research Center. For the equipment tested, although some rocking is observed, sliding is the predominant mode of response, with sliding displacements reaching up to 60 cm. Numerical simulations with the proposed models are performed. Finally, the paper identifies a physically motivated intensity measure and the associated engineering demand parameter with the help of dimensional analysis and presents ready-to-use fragility curves.

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This paper investigates the seismic response of freestanding equipment when subjected to strong earthquake motions (2% probability of being exceeded in 50 years). A two-step approach is followed because the displacement limitations of the shake table do not permit full-scale experiments. First, shake table tests are conducted on quarter-scale wooden block models of the equipment. The results are used to validate the commercially available dynamic simulation software Working Model 2D. Working Model is then used to compute the response of the full-scale freestanding equipment when subjected to strong, 2% in 50 years hazard motions. The response is dominated by sliding, with sliding displacements reaching up to 70 cm. A physically motivated dimensionless intensity measure and the associated engineering demand parameter are identified with the help of dimensional analysis, and the results of the numerical simulations are used to obtain a relationship between the two that leads to ready-to-use fragility curves.

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Summary The seismic response of rocking frames that consist of a rigid beam freely supported on rigid freestanding rectangular piers has received recent attention in the literature. Past studies have investigated the special case where, upon planar rocking motion, the beam maintains contact with the piers at their extreme edges. However, in many real scenarios, the beam‐to‐pier contact lies closer to the center of the pier, affecting the overall stability of the system. This paper investigates the seismic response of rocking frames under the more general case which allows the contact edge to reside anywhere in‐between the center of the pier and its extreme edge. The study introduces a rocking block model that is dynamically equivalent to a rocking frame with vertically symmetric piers of any geometry. The impact of top eccentricity (ie, the distance of the contact edge from the pier's vertical axis of symmetry) on the seismic response of rocking frames is investigated under pulse excitations and earthquake records. It is concluded that the stability of a top‐heavy rocking frame is highly influenced by the top eccentricity. For instance, a rocking frame with contacts at the extreme edges of the piers can be more seismically stable than a solitary block that is identical to one of the frame's piers, while a rocking frame with contacts closer to the centers of the piers can be less stable. The concept of critical eccentricity is introduced, beyond which the coefficient of restitution contributes to a greater reduction in the response of a frame than of a solitary pier.