Static stability and seismic behavior of the dome of the Hagia Sophia

Abstract

The Hagia Sophia in Istanbul represents a culmination of engineering practice and design aesthetics that were emulated extensively by both Byzantine and Ottoman builders. The resiliency and scale of the brick masonry dome of the Hagia Sophia, particularly with respect to its seismically active location, is a testament to the iterative and empirical construction techniques of its constructors. The existing analyses of the structure have focused primarily on architectural features as well as seismic response using various computational implementations of the Finite Element Method (FEM). This thesis seeks to better understand the static stability of the Hagia Sophia dome and its dynamic failure mechanisms through a combination of analytical and experimental techniques. By utilizing limit analysis, implemented through graphical methods, the stability of the dome can be calculated by assuming the compression-only behavior of masonry. This analysis demonstrates that the horizontal thrust of the dome is 275 kN and the vertical thrust is 1012 kN. Experimentally, a scaled and discretized 3D printed model of the Hagia Sophia dome was tested to find that the minimum lateral ground acceleration necessary to cause collapse is 0.725g. In addition, the minimum outward displacement of supports necessary to induce failure was determined to be 2.1m. The analysis undertaken in this thesis will ultimately inform the maintenance and restoration of the dome and help provide design and structural precedents for masonry construction of large diameter domes.