Are Some Top-Heavy Structures More Stable?

Abstract

This technical note investigates the dynamic response and stability of a rocking frame that consists of two identical free-standing slender 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— together with the need to stress that the rocking frame is more stable the more heavy is its cap-beam, a finding that may have significant implications in the prefabricated bridge technology. In this technical note, a direct approach is followed after taking dynamic force and moment equilibrium of the components of the rocking frame, and the remarkable results obtained in the past with a variational formulation (by the same authors) is confirmed—that the dynamics response of the rocking frame is identical to the rocking response of a solitary, free-standing column with the same slenderness, yet with larger size, which produces a more stable configuration. The motivation for reworking this problem by following a direct approach is to show, in the simplest possible way, that the heavier the freely supported cap beam, the more stable is the rocking frame, regardless of the rise of the center of gravity of the cap beam. The conclusion is that top-heavy rocking frames are more stable that when they are top-light.