Abstract
Ancient columns, made with a variety of materials such as marble, granite, stone or masonry are an important part of the European cultural heritage. In particular columns of ancient temples in Greece and Sicily which support only the architrave are characterized by small axial load values. This feature together with the slenderness typical of these structural members clearly highlights as the evaluation of the rocking behaviour is a key aspect of their safety assessment and maintenance. It has to be noted that the rocking response of rectangular cross-sectional columns modelled as monolithic rigid elements, has been widely investigated since the first theoretical study carried out by Housner (1963). However, the assumption of monolithic member, although being widely used and accepted for practical engineering applications, is not valid for more complex systems such as multi-block columns made of stacked stone blocks, with or without mortar beds. In these cases, in fact, a correct analysis of the system should consider rocking and sliding phenomena between the individual blocks of the structure. Due to the high non-linearity of the problem, the evaluation of the dynamic behaviour of multi-block columns has been mostly studied in the literature using a numerical approach such as the Discrete Element Method (DEM). This paper presents an introductory study about a proposed analytical-numerical approach for analysing the rocking behaviour of multi-block columns subjected to a sine-pulse type ground motion. Based on the approach proposed by Spanoset al.(2001) for a system made of two rigid blocks, the Eulero-Lagrange method to obtain the motion equations of the system is discussed and numerical applications are performed with case studies reported in the literature and with a real acceleration record. The rocking response of single block and multi-block columns is compared and considerations are made about the overturning conditions and on the effect of forcing function’s frequency.
Highlights
Made with a variety of materials such as marble, granite, stone or masonry are an important part of the European cultural heritage
In particular columns of ancient temples in Greece and Sicily which support only the architrave are characterized by small axial load values
This feature together with the slenderness typical of these structural members clearly highlights as the evaluation of the rocking behaviour is a key aspect of their safety assessment and maintenance [1, 2]
Summary
Made with a variety of materials such as marble, granite, stone or masonry are an important part of the European cultural heritage. A very limited number of authors investigated analytically the behaviour of stacked rigid block systems The analysis of these types of structures is made complex due to the fact that the number of rocking patterns increases. The Open Construction and Building Technology Journal, 2016, Volume 10 151 exponentially with the number of superimposed blocksand this affect the equations of motion governing the response of the system Because of these difficulties, the most common way to approach the problem is by means of numerical methods. [16] developed the equations of motion for a two-block system on a rigid foundation and considered the four possible patterns response under free and induced vibrations and the transition from one pattern to another This approach is not scalable to multi-block system. The numerical results of equivalent one-, twoor three-block systems are compared to the exact solution of one single block subjected to a pulse-type base excitation as studied by Zhang et Makris [4]
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