Dimensionality reduction of the 3D inverted pendulum cylindrical oscillator and applications on sustainable seismic design of bridges

Abstract

The simplest 3D extension of Housner's planar rocking model is a rocking (wobbling) cylinder allowed to uplift and roll on its circumference, but constrained not to roll out of its initial position. The model is useful for the description of bridges that use rocking as a seismic isolation technique, in an effort to save material by reducing the design moment and the size of the foundations. This paper shows that describing wobbling motion in terms of displacements rather than rotations is more useful. It unveils that a remarkable property of planar rocking bodies extends to 3D motion: A small and a large wobbling cylinder of the same slenderness will sustain roughly equal top displacement, as long as they are not close to overturning. This allows for using the response of an infinitely large wobbling cylinder of slenderness α as a proxy to compute the response of all cylinders having the same slenderness, irrespectively of their size. Thus, the dimensionality of the problem is reduced by one. Moreover, this paper shows that the median wobbling response to sets of ground motions can be described as an approximate function of only two non-dimensional parameters, namely (𝑔 tan 𝛼∕𝑃𝐺𝐴, 𝑢∕𝑃𝐺𝐷)or (𝑔 tan 𝛼∕𝑃𝐺𝐴, 𝑢𝑃𝐺𝐴∕𝑃𝐺𝑉 2 ) where u is the top displacement of the wobbling body.

Seismic pounding damage to adjacent reinforced concrete frame–shear wall buildings and freestanding contents

“…However, a coupled analysis is allowed when modeling the contents and the buildings in an integrated manner in OpenSees. Note also that the three‐dimensional (3D) behavior of rocking contents is considerably more complicated, 44 and 3D rocking oscillators 45 could be used when dealing with these more general 3D loading scenarios.…”

“…However, a coupled analysis is allowed when modeling the contents and the buildings in an integrated manner in OpenSees. Note 5 Comparison of the acceleration spectra of the selected ground motions recommended by the FEMA P-695 report 47 with the code-specified MCE spectrum according to GB50011-2010 48 also that the three-dimensional (3D) behavior of rocking contents is considerably more complicated, 44 and 3D rocking oscillators 45 could be used when dealing with these more general 3D loading scenarios.…”

Intensity measures, fragility analysis and dimensionality reduction of rocking under far‐field ground motions

“…[ 75–77 ] concluded that PGV performs overall better than PGA. Vassiliou and Sieber [ 78 ] studied 3D rocking and concluded that the displacement response scales with a bivariate intensity measure that includes both PGA and PGV.…”

“…Studying free and restrained rocking systems of negative systems under sets of far-field, near-field pulse-like and near-field non-pulse-like ground motions, Manzo et al [75][76][77] concluded that PGV performs overall better than PGA. Vassiliou and Sieber [78] studied 3D rocking and concluded that the displacement response scales with a bivariate intensity measure that includes both PGA and PGV.…”

Chattering: an overlooked peculiarity of rocking motion

“…Subsequently, it finds application on a variety of engineering projects, e.g. from freestanding contents [22,39,40] and classical monuments [23,49,63] to modern buildings and bridges [2,18,21,26,28,54,[59][60][61]. From an earthquake engineering perspective, the transient response of a rocking structure under a finite duration ground excitation is of primary importance, as it directly relates to seismic safety and structural failure [15,19,45,55,56,62].…”