The existence of ‘complete similarities’ in the response of seismic isolated structures subjected to pulse‐like ground motions and their implications in analysis

Abstract

In this paper the seismic response of isolated structures supported on bearings with bilinear and trilinear behavior is revisited with dimensional analysis in an effort to better understand the relative significance of the various parameters that control the mechanical behavior of isolation systems. An isolation system that consists of lead rubber bearings or of single concave spherical sliding bearings exhibits bilinear behavior; whereas, when a double concave configuration is used the behavior is trilinear. For the case of bilinear behavior it is well known that the value of the normalized yield displacement is immaterial to the response of the isolated superstructure-or, in mathematical terms, that the response of the bilinear oscillator exhibits complete similarity in the dimensionless yield displacement. Similarly, for the case of trilinear behavior the paper shows that the presence of the intermediate slope is immaterial to the peak response of most isolated structures-a finding that shows the response of the trilinear oscillator exhibits a complete similarity in the difference between the coefficients of friction along the two sliding surfaces as well as in the ratio of the intermediate to the final slope. This finding implies that even when the coefficients of friction of the two sliding surfaces are different, the response of isolated structures for most practical configurations can be computed with confidence by replacing the double concave spherical bearings with single concave spherical bearings with an effective radius of curvature and an effective coefficient of friction.

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

“…Recently, Makris and Vassiliou 24 have shown that for most practical configurations the area of the shaded triangles shown in Figure 10 (right) is immaterial to the peak response of an isolated deck; therefore, the deck exhibits merely the same maximum displacement regardless whether it is supported on a double concave ( R 1 − h 1 , R 2 − h 2 , µ 1 , µ 2 ) or single concave ( R e , µ e ) spherical sliding bearing provided that and The aim of this analysis is to examine whether the selection of a lower coefficient of friction in one sliding surface may increase the merit of seismic isolation to protect rocking structures. The friction coefficients of two alternative DCSS systems are selected so that their equivalent coefficient of friction given by Equation (39) is µ e = 5%.…”

Direct estimation of seismic response in reduced‐degree‐of‐freedom isolation and energy dissipation systems

“…The behaviour of the bilinear isolator is intrinsically determined by three parameters, which can be selected as V 0 , u y , and k p . u y was reported in earlier studies (eg, ) to have a minor impact on the maximum inelastic response; herein, a constant value associated with different groups of yielding isolators was introduced in order to capture more accurately the peak response, and at the same time limit the complexity of the proposed GDEs. In addition, u y was considered constant for different values of the post‐yield stiffness k p (ie, instead of assuming a constant ratio of k e / k p ) resulting to an initial stiffness ( k e = V 0 / u y + k p ) that is directly proportional to the yield strength ( V y = k e u y ) (ie, k e and V y expressed as functions of V 0 , u y , k p to define the bilinear hysteresis for modelling purposes).…”

Dynamics of rocking podium structures

“…Strong ground motions often contain a distinguishable acceleration pulse, which is responsible for most of the inelastic deformation of fixed-base structures [58][59][60]. Physically realizable ground motion analytical pulses can qualitatively describe the impulsive character of near-fault ground motions.…”