This report is concerned with the superficial similarities and fundamental differences 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 complements the response spectrum as an indicator of the shaking potential of earthquakes since it reflects kinematic characteristics of the ground motions that are not identifiable by the response spectrum. The study investigates systematically the fundamental differences in the mechanical structure of the two dynamical systems of interest and concludes that rocking structures cannot be replaced by “equivalent” single-degree-of-freedom-oscillators. The study proceeds by examining the validity of a simple, approximate design methodology, initially proposed in the late 70’s and now recommended in design guidelines to compute rotations of slender structures by performing iteration either on the true displacement response spectrum or on the design spectrum. This report shows that the abovementioned simple design approach is inherently flawed and should be abandoned, in particular for smaller, less slender blocks. The study concludes that the exact rocking spectrum emerges as a distinct, irreplaceable indicator of the shaking potential of ground motions and should be adopted by the profession as a valuable analysis and design tool.
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