The dynamics of the rocking frame

Abstract

This paper investigates the planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam. Part of the motivation for this study is the emerging seismic design concept of allowing framing systems to uplift and rock along their plane in order to limit bending moments and shear forces. Following a variational formulation the paper reaches 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.