On the role played by the openings on the first frequency of historic masonry towers

The manuscript provides a wide database for historic masonry towers collecting their modal, mechanical and geometrical features. This large amount of data was collected according to a literature review, then summing up as many as 56 different case studies. The collected data was then used to identify the main physical parameters influencing the modal behaviour of slender masonry towers, including the openings on the façades. After a critical discussion of the data reported in the database, the existing empirical or semi-empirical formulations available for the estimation of the first natural frequency of such structural typology are first evaluated. Subsequently the effects of the openings, as revealed through the analysis of the experimental results reported in the database, are discussed by comparison with a simple but effective numerical model. Despite the difficulties to quantify the effect of the openings along the height of the tower on the main frequency due to a cross-contribution of mass and stiffness, a simple but effective formulation is proposed which is able to account for this parameter.