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Buildings 2017, 7(3), 69; doi:10.3390/buildings7030069

Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

1
Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Forno vecchio, 36, 80124 Naples, Italy
2
Department of Energy Systems, Territory and Constructions Engineering, University of Pisa, Largo Lucio Lazzarino, 1, 56100 Pisa, Italy
3
ISISE, Department of Civil Engineering, University of Minho, Campus de Azurem, 4800 - 058 Guimarães, Portugal
*
Author to whom correspondence should be addressed.
Received: 12 April 2017 / Revised: 24 July 2017 / Accepted: 1 August 2017 / Published: 4 August 2017
(This article belongs to the Special Issue Traditional and Innovative Approaches in Seismic Design)
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Abstract

The assessment of the rocking and overturning response of rigid blocks to earthquakes is a complex task, due to its high sensitivity to the input motion, variations in geometry and dissipation issues. This paper presents a literature review dealing with classical and advanced approaches on rocking motion with particular reference to masonry walls characterized by a monolithic behavior. Firstly, the pioneering work of Housner based on the concept of the inverted pendulum is discussed in terms of the most significant parameters, i.e., the size and slenderness of the blocks, the coefficient of restitution and ground motion properties. Free and restrained rocking blocks are considered. Then, static force-based approaches and performance-based techniques, mostly based on limit analysis theory, are presented to highlight the importance of investigating the evolution of the rocking mechanisms by means of pushover curves characterized by negative stiffness. From a dynamic perspective, a review of probabilistic approaches is also presented, evaluating the cumulative probability of exceedance of any response level by considering different earthquake time histories. Some recent simplified approaches based on the critical rocking response and the worst-case scenario are illustrated, as well. View Full-Text
Keywords: rocking; dynamics of rigid blocks; restrained blocks; out-of-plane behavior; force-based approaches; displacement-based approaches rocking; dynamics of rigid blocks; restrained blocks; out-of-plane behavior; force-based approaches; displacement-based approaches
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Casapulla, C.; Giresini, L.; Lourenço, P.B. Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments. Buildings 2017, 7, 69.

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