Summary A new modeling for the seismic response assessment of free‐standing, rigid or flexible, pure rocking systems is presented. The proposed modeling is based on equivalent single degree‐of‐freedom (SDOF) oscillators that can be implemented with common engineering software or user‐made structural analysis codes. The SDOF models adopted use beam elements that are connected to a nonlinear rotational spring with negative stiffness that describes the self‐centering capacity of the rocking member. The loss of energy at impact is treated with an “event‐based” approach consistent with Housner's theory. Different variations pertinent to rigid blocks are first presented, and then the concept is extended to the flexible case. The implementation of the method requires some minor programming skills, while thanks to the versatility of the finite element method, it is capable to handle a variety of rocking problems. This is demonstrated with two applications: (a) a vertically restrained block equipped with an elastic tendon and (b) a rigid block coupled with an elastic SDOF oscillator. The accuracy and the efficiency of the proposed modeling is demonstrated using simple wavelets and historical ground motion records.
SummaryMultistorey buildings often have a valuable inventory consisting of objects that their possible damage during an earthquake will cause unacceptable losses. The paper presents a novel, fully performance‐based seismic reliability and risk assessment framework for freestanding structural components and contents that can be modelled as rocking rigid blocks. The seismic response of building contents depends on several parameters such as the geometry of the object, the dynamic characteristics of the building and the storey that the object is located. The demand at the storey level is first obtained, and then the response of the contents is calculated using the storey acceleration response history. The demand of the structure is obtained with the aid of a modified version of the Incremental Dynamic Analysis method and subsequently the fragility curves of the rocking building contents are derived for every storey of interest. Different options for fragility assessment are discussed, and the underlying details of the problem are investigated. A simplified approach, where the fragility of the freestanding components and the structure are derived separately, is also presented. The method combines existing fragility curves and thus is suitable for quickly assessing the reliability of a building's inventory, offering sufficient risk estimates.
A novel modeling approach for the seismic response assessment of rocking frames is presented. Rocking frames are systems with columns that are allowed to fully, or partially, uplift. Despite the apparent lack of a mechanism to resist lateral forces, they have a remarkable capacity against earthquake loading. Rocking frames are found in old structures, for example, ancient monuments, but it is also a promising design concept for modern structures such as bridges or buildings. The proposed modeling can be implemented in a general‐purpose structural analysis software, avoiding the difficulties that come with the need of formulating and solving specifically tailored differential equations, or the use of detailed computational models. Different configurations of a rocking portal frame problem are examined. The model is based on rigid, or flexible, beam elements that describe the members of the frame. Negative‐stiffness rotational springs are smartly positioned at the rocking interfaces in order to simulate the rocking restoring moment, while the mass and the rotational moment of inertia are considered either lumped or distributed. Both the cases of rigid and flexible piers/columns are discussed, while it is shown that frames with restrained columns can be considered in a straightforward manner. A simple alternative based on an equivalent oscillator that follows the generalized rocking equation of motion is also investigated. The efficiency and the accuracy of the proposed modeling is demonstrated with the aid of carefully chosen case studies.
The paper proposes the use of supervised machine learning (ML) methods for quickly predicting the seismic response of rocking systems when subjected to seismic excitations. Different supervised ML algorithms are discussed, while a relatively simple and a more sophisticated algorithm are examined in detail. Specifically, the two algorithms compared are the k-Nearest Neighbor (k-NN) and the Support Vector Machine (SVM). The performance of the ML models is demonstrated considering both sine pulses and different sets of natural ground motion records. The results are practically perfect for sine pulses, while accurate results were also obtained for the case of natural ground motions. The proposed ML-based tool allows to quickly assess the risk of damage for rocking systems, while it is also very important when a large number of rocking blocks have to be studied, e.g. in the case of a building’s inventory.
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