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.

Nonlinear dynamics of self-centring rocking steel frames using finite element models

“…Research encompassing various aspects of the design and behaviour of di↵erent classes of rocking structures has spanned over the last two decades. While some of this research did not consider the self-centring e↵ects of post-tensioning and focussed on free-standing rocking structures [3,4,5], other studies examined the response of a range of self-centring systems, including steel-braced, pre-cast concrete and timber frames, as well as concrete and timber shear wall configurations with significant levels of energy-dissipation coming from sacrificial components [6,7,8,9,10,11]. The presence of energy-dissipation diminishes the inherent nonlinearity of a rocking structure, and limits the examination of its raw nonlinear dynamic response.…”

Seismic vulnerability assessment of precast post-tensioned segmental bridge piers subject to far-fault ground motions

“…Nonlinear mechanics of these single blocks were also examined under seismic ground motions ( (Yim et al 1980), (Aslam et al 1980), (Pompei et al 1998), (DeJong and Dimitrakopoulos 2014)). Some other studies investigated single and multiple rigid blocks to simulate rocking motion and stability of art objects subject to impulse excitations ( (Kounadis 2015), (Kounadis and Papadopoulos 2016), (Kounadis 2018), (Makris and Vassiliou 2015)).…”

Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

“…This dynamic property of rocking structures contributes very significantly to improving their seismic performance for downtime and repair cost performance objectives. This behavior, as well as the survival of ancient Greek and Roman temples (that are essentially rocking structures) in high seismicity areas [52][53][54][55] has led researchers to suggest the use of rocking as a seismic response modification technique [56][57][58][59][60][61][62][63][64][65][66][67][68].…”