Rocking Analysis of Towers Subjected to Horizontal Forces

In seismic-prone areas, ecclesiastical masonry complexes have shown very high vulnerability, as detected after the last Italian earthquakes, such as those that occurred in L’Aquila (2009), Emilia-Romagna (2012), Central Italy (2016), and Ischia (2017). Partial collapses often affect these types of aggregate buildings due to the presence of highly vulnerable elements, such as bell towers. Preliminary analyses, including straightforward and quick methods, are necessary to assess their vulnerability. This paper proposes a simplified method to analyse bell tower dynamic behaviour and the results obtained are compared with several different approaches. The first is based on the dynamics of two rigid blocks (bell tower and lower building), and the second concerns a single block (bell tower only). The proposed method can be considered as a quick procedure involving few parameters to provide a preliminary analysis before use of more complex models such as finite element models. It aims to provide a valuable tool for the initial evaluation of the stability and risk index of the structure. The double-block model considers the associations between the rocking of the bell tower and the sliding motion of the underlying building. A parametric evaluation for different friction coefficients is proposed. The results are represented as rotation time histories and compared with analysis of the single vulnerable element, i.e., the bell tower subjected to the floor spectrum. The results show that high excitation frequency and friction coefficient values make the bell tower stable, and that the simplified model provides a clear safety advantage.