Rocking spectrum intensity measures for seismic assessment of rocking rigid blocks

This work studies the dynamics of the Negative Stiffness Bilinear Elastic (NSBE) oscillator. Such a mathematical idealization can be used to describe deformable rocking systems equipped with restraining tendons or with curved extensions of their bases. First, this paper establishes the characteristic quantities of the bilinear system to make it equivalent to the actual rocking structures. Then, it proceeds by proposing a simpler "equivalent" system that can be used to study the behavior of the NSBE. The equivalent system is not some linear elastic oscillator but a bilinear elastic system with zero stiffness of the second branch: the Zero Stiffness Bilinear Elastic (ZSBE) system. ZSBE is useful because it needs one parameter less than NSBE to be defined. Next, "Equal Displacement" and "Equal Energy" rules that provide estimates of the maximum displacement of the NSBE based on the response of the ZSBE are defined. The concept is similar to the RμΤ relations that provide estimates of the response of bilinear yielding systems based on the response of an equivalent linear elastic system, with one major difference: it does not resort to a linear elastic system but to the ZSBE. The proposed methodology is applied on the FEMA P695 ground motions scaled at three different levels. The results show that ZSBE is a good proxy of NSBE and, hence, indicate that an exhaustive study of the ZSBE is useful for the design of rocking structures.

Section: Response Of Rigid—negative Stiffness Systems To Recorded Grosupporting

confidence: 93%

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

Manzo

Vassiliou

2020

“…As rocking is a highly nonlinear phenomenon due to the negative stiffness of the rocking oscillator, small changes in the characteristics of both the rocking system and the seismic excitation can cause large changes in the rocking response. The above fact gives rise to the necessity of a probabilistic treatment of the rocking response, given the uncertainties related to the characteristics of ground motions 25–28 . Furthermore, refined models are needed to reduce the uncertainties associated with the dynamics of the rocking system 28,29 .…”

Section: Introductionmentioning

confidence: 99%

Seismic response of elastic multidegree of freedom oscillators placed on the top of rocking storey

Bantilas

Kavvadias

Vasiliadis

2020

Self Cite

In the present study, the seismic response of multistorey structures placed on the top of a rocking storey is examined. For this purpose, an analytical model that allows the interaction of all vibration modes of the superstructure with the rocking base is introduced. As uplift of the rocking base modifies the dynamic properties of the superstructure, modal analysis is performed and the vibration mode properties during rocking are demonstrated. Subsequently, dynamic time history analyses are performed and the effect of higher vibration modes of the superstructure on the rocking response is investigated. In addition, the seismic demands of the superstructure as well as their distribution throughout the storeys are examined. The results indicate that the higher vibration modes affect the rocking response of the base, although their influence depends on the stiffness of the superstructure. Furthermore, the seismic demands of the superstructure depend primarily on the size of the rocking columns. Finally, during rocking response all the vibration modes are excited and contribute to the distribution of the seismic loads throughout the floors of the superstructure.

“…Based on the above, a design method that uses a size‐independent rocking spectrum is suggested. This should be taken into account when intensity measures for rocking structures designed not to get close to overturning are explored.…”

Section: Discussionmentioning

confidence: 99%

Displacement‐based analysis and design of rocking structures

Manzo

Vassiliou

2019

Summary The response of a rigid rocking block is traditionally described by its tilt angle. This is a correct description, but this paper suggests that describing rocking via displacements is more meaningful, because it uncovers that two geometrically similar blocks of different size will experience the same top displacement, provided that they are not close to overturn. The above is illustrated for both analytical pulse excitations and for recorded ground motions. Thus, the displacement demand of a ground motion on a rocking block is only a function of its slenderness, not of its size. This reduces the dimensionality of the problem and allows for the construction of size‐independent rocking demand spectra.