Displacement‐based analysis and design of rocking structures

Self Cite

Rocking motion is sensitive to the boundary and initial conditions of a rocking structure, making experiments nonrepeatable. Thus, the claims that numerical rocking motion models are not only inaccurate but that all rocking structures behave unpredictably. Hence, rocking is not used as a seismic design approach. This paper revisits the issue of rocking motion unpredictability. Seismic behavior of structures is inherently stochastic, because the loading is stochastic. Therefore, the question of interest is not whether models can predict the seismic response to a single ground motion, but if the statistical characteristics of the ensemble of responses to a set of ground motions that define the seismic hazard can be predicted. For this purpose, a rocking podium, which is a three‐dimensional structure comprising an aluminum slab supported by four tubular steel columns, was tested on a shake table excited by two sets of 100 consistently generated ground motions. It was found that the cumulative distribution function (CDF) of the experimentally obtained displacements is statistically stable. Next, a blind prediction contest was organized. The contestants were invited to predict the CDFs of the slab lateral displacement. They were able to predict the slab displacement CDF relatively well. Both finite element and discrete element modeling approaches were used, but no clear pattern emerged as it was found that the performance of either approach depends on the input parameters used and the assumptions made. It was also observed that the contestants who did not use Rayleigh damping in their models produced better predictions.

Section: Introductionmentioning

confidence: 99%

Shake table testing of a rocking podium: Results of a blind prediction contest

Vassiliou

Broccardo

Cengiz

et al. 2020

Self Cite

“…So, when the system is not close to failure, instead of computing a different spectrum for each displacement capacity, one can compute the spectrum for the ZSBE system (i.e., for an NSBE with u cap → ∞) and use it to calculate the displacement demand on any NSBE of the same strength. This forms a generalization of the Equal Displacement rule for rocking structures described in Reggiani Manzo and Vassiliou 68 As the system gets closer to collapse, the “Equal Displacement rule” does not apply and is unconservative: Systems with smaller displacement capacity exhibit larger displacements than the ones with larger displacement capacity.…”

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

confidence: 86%

“…Moreover, close to failure, the slope of the spectrum increases dramatically, that is, a small decrease of the system strength would lead to a tremendous increase of the maximum displacement. As in the case of free rocking structures, 68 this trend dictates that a rational design of a negative stiffness system would require that this steep part of the spectrum be avoided, because an earthquake slightly stronger than the design one would cause a tremendous increase in displacement. Therefore, the Equal Displacement rule is more accurate where it is actually needed: in the rational design region. The form of the spectrum for all three sets of ground motion presents a repetitive pattern: For zero strength ( f up = 0), the maximum displacement ( u max ) reaches a finite value.…”

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

confidence: 99%

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

Manzo

Vassiliou

2020

Self Cite

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.

“…Important differences may be found between the methods, 5 being the displacement-based method scale dependent, while the force-based method not. 6 Studies performed using the previous version of the standard 7 show that the displacement-based method appears to be more robust, accurate, and safer than the force-based method in predicting the acceleration capacity leading the structure to failure. 8 The displacement-based method recommended in the Italian technical standard is based on the derivation of the pushover curve.…”

Section: Introductionmentioning

confidence: 99%

A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

Portioli

Godio

Calderini

et al. 2021

Displacement-based methods contained in recent standards for seismic safety assessment require the determination of the full nonlinear pushover curve for local failure mechanisms in historic masonry structures. This curve should reflect both the initial elastic behavior and the rigid body behavior after the activation of rocking. In this work, a rigid block model is proposed for the displacement-based seismic assessment of local collapse mechanisms of these structures. Masonry is modeled as an assemblage of two-dimensional rigid blocks in contact through frictional interfaces. Two types of contact models are formulated to capture, respectively, the pre and postpeak branches of the pushover curve: a unilateral elastic contact model, capturing the initial nonlinear behavior up to the force capacity of the structure, corresponding to the activation of the collapse mechanism, and a rigid contact model with finite friction and compressive strength, which describes the rigid-body rocking behavior up to the attainment of the displacement capacity of the structure. Tension-only elements are also implemented to model strengthening interventions with tie-rods. The contact problems associated with the elastic and rigid contact models are formulated using mathematical programming. For both models, a sequential solution procedure is implemented to capture the variation of the load multiplier with the increasing deformation of the structure (P-Δ effect). The accuracy of the modeling approach in reproducing the pushover curve of masonry panels subjected to horizontal seismic loads is evaluated on selected case studies. The solution is first tested against hand calculations, existing analytical models, and distinct element simulations. Then, comparisons against experimental tests follow. As a final application, the failure mechanism and pushover curve of a triumphal masonry arch are predicted by the model and its seismic assessment is performed according to codified force-and displacement-based methods, demonstrating the adequacy of the proposed tool for practice.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.