Chapter 10 Analytical and Experimental Analysis of Rocking Columns Subject to Seismic Excitation Ryan Kent Giles and Thomas John Kennedy Abstract Structures of ancient Mediterranean cultures that have survived numerous earthquakes over the span of millennia relied on multifaceted rocking columns to dissipate seismic energy. Rocking columns are again emerging as an effective mechanism in modern structural systems; understanding the rocking behavior can provide insight into how to best design this type of system. This study examines the analytical and experimental rocking behavior of a rectangular column. Equations of motion that describe the rocking behavior of the polygonal columns are derived and analytical energy dissipation methods compared. A high-speed 3D motion capture system, providing noncontact measurement of the column motion, is used in a series of experiments on a uniaxial shake table to validate the analytical model. These experiments show variation indicating stochastic behavior during the excitation phase. The damping ratio and coefficient of restitution are calculated from the experimental results. The experimental results and analytical solution are compared. Keywords Rocking columns • Coefficient of restitution • Impact damping • 3D metrology • Seismic excitation 10.1 Introduction The ability of ancient Greek temples and other structures to survive seismic events is due to the rocking motion of their columns. When stripped of their architectural adornments and cultural significance, columns are slender, rigid blocks. Many researchers have derived the equations of motion for slender, rigid blocks in two dimensions [1–8] and performed analytical analysis of their behavior under various sources of base excitation [9–13]. The effects of friction and shape of the initiation of rocking or sliding have also been well studied analytically [14]. There has been some extension of the rocking problem to three dimensions accounting for cylinders [4] and general three-dimensional structures with a rectangular base [15, 16]. Fewer studies have experimentally confirmed these analytical equations [2]. This paper presents an experimental validation of the equations of motion of a slender rigid body under seismic excitation. The results draw attention to the typical analytical assumptions for the coefficient of restitution and the probabilistic nature of experiments. 10.2 Background For the case of two-dimensional rocking (see Fig. 10.1), the block is assumed to be located on a rigid base. The column has a height of 2h and a width of 2b. We define a slender column as one where: h b > 1 p1 CIO (10.1) given IO is the moment of inertia of the block about Oor O0 which for a rectangle is equal to (4/3)mR2. The slenderness of the block controls whether, on impact, the rigid block will switch its rotation point fromOor O0 or bounce back and continue to rotate about O. The behavior of interest for structural columns is the switching of the rotation point upon impact. R.K. Giles ( ) • T.J. Kennedy Department of Civil Engineering, Stony Brook University, 2426 Computer Science, Stony Brook, NY, 11794-4424, USA e-mail: ryan.giles@stonybrook.edu © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_10 75
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