Revisiting the Frequency Laws for Ottoman Minarets. Analysis of Uncertainties

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 $f=\alpha \cdot \surd \left(K/M\right)$ $+c=\alpha \cdot \frac{R_g}{H^2}+c,$ is presented with a minimum number of aggregated variables and better Coefficient of determination, R².

KEYWORDS:

• Coefficient of determination R²
• estimation of frequencies
• Ottoman minarets

Acknowledgments

The authors would like to express their gratitude to Mr Nafiz Kafadar, Ahmet Korkmaz, Gὄkhan Kesti and Orhan Erşah for carrying out the in-situ testing of several field campaigns made in the last ten years and to several students that help to treat data. Kὄkcan Dὄnmez helped in recognition of minaret location. Emrullah Dar analysed data from Blue Mosque Minarets. Prof. A. Bayraktar from Technical University Trabzon and Dr I. Çalik from Directorate Regional Foundations, Erzurum, provided consistent geometric data for the 19 minarets from the third campaign. Prof. Pinar Usta from Isparta University of Applied Sciences provided data on 5 minarets in Antalya. A special acknowledgement to Dr J. V. Lemos from Laboratório Nacional de Engenharia Civil (LNEC), Lisbon, for the friendship and great interest in matters dealing with minaret seismic behaviour. Boğaziçi University and Instituto Superior Técnico/CERis supported our mutual study visits. The author is grateful for the Portuguese Foundation for Science and Technology’s support through partial funding UIDB/04625/2020 from the research unit CERIS.

Three anonymous Reviewers made essential contributions to the improvement of the text.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/15583058.2022.2057881

Additional information

Funding

This work was supported by the Portuguese Foundation for Science and Technology’s support through partial funding UIDB/04625/2020 from the research unit CERIS. [UIDB/04625/2020].