Revisiting the Frequency Laws for Ottoman Minarets. Analysis of Uncertainties

Abstract

ABSTRACT The knowledge of frequencies of vibration of the first modes of minarets is essential to anticipate their behaviour under seismic loads. Masonry minarets are very slender structures with an extensive history of many centuries of construction and damages inflicted by earthquakes. Their construction techniques did not change much throughout the historical epochs, and only very recently, new minarets of the same type were built with Reinforced Concrete. Minarets lately have been the object of several studies because both the monitoring technologies for in-situ vibration observations and the existence of non-linear large-displacement software have become available. Many teams dedicated their attention to analysing frequencies of these structures and a few to study their behaviour. Several formulae were proposed to obtain frequencies as a function of their geometrical and mechanical characteristics, trying to arrive at some law valid for the set of minarets they studied. Others tried to extend their formulae to other slender traditional masonry structures such as towers, or chimneys. In this state-of-the-art review paper, the authors use a large set of data (79 Ottoman minarets) on frequency values as obtained by the authors as well as data compiled from the literature, to revisit this problem and discuss the details of how accurate the estimate of the frequencies might be. This large set confirms the trend of published formulae but includes uncertainties. A proposal for a simple formula, anchored on theoretical grounds, of the type is presented with a minimum number of aggregated variables and better Coefficient of determination, R2.