Empirical Equations for Estimation of the Fundamental Vibration Frequency of Historical Masonry Towers

Historical buildings are valuable structures. Therefore, performance evaluation of these structures under different loadings such as seismic effects has been considered in several research projects in recent years. Masonry towers are known as one of the common types of historical structures that exist in different countries. To evaluate the seismic performance of masonry towers, their dynamic properties are needed. Among the dynamic characteristics of the towers, fundamental vibration frequency is known as the most important one. In this regard, formulations for estimation of the vibration frequency of these structures in useful. For this purpose, a database consisting properties of 38 towers which were identified through in-situ dynamic tests or numerical analysis before, are collected. Then, based on a nonlinear regression on the collected database, empirical equations are proposed for estimation of the vibration frequency of historical masonry towers. Evaluation of the database indicates that height of the towers is the most effective parameter on their vibration frequency. In addition, thickness of the perimeter walls, cross-section dimensions of the towers and elastic modulus of masonry can affect the dynamic response of the towers. The average errors of the estimated frequencies by means of the proposed equations indicate that the proposed equations have acceptable accuracy.