http://orcid.org/0000-0001-7808-0141
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ABSTRACT
Modern computational resources provide important and efficient tools for analyzing structures of all scales, materials, and typologies, especially historic structures. However, not all methods can correctly answer questions about the structural behavior of inherently discontinuous unreinforced masonry constructions. Such continuous methods, photoelasticity and finite element methods, are pervasively and incorrectly used to analyze masonry structures despite the availability of more appropriate methods. This article addresses the use of these different analyses by comparing the different results of two previous continuous model studies of the pier buttresses of Amiens Cathedral to new results using two discontinuous methods, discrete element methods, and graphical thrust line analysis. This case study validates the use of graphical thrust line analysis and challenges the use of continuous models in analyzing historic masonry constructions. Furthermore, these results resolve a longstanding debate about the placement of pinnacles while providing evidence that the analysis method must reflect physical behavior.
Acknowledgement
This work would not have been possible without the direction and guidance of Professor Maria Moreyra Garlock. The authors would also like to thank Marshall Everett and Robert Mark for sharing their work and providing kind permission to use their figures.
Funding
Funding for the purchase of DEM software was provided by Princeton School of Engineering and Applied Sciences, Civil and Environmental Engineering Department, and Council of the Humanities. Additionally, 3DEC support for DEM was generously provided by Dr. Jim Hazzard, Principle Engineer and Software Manager, from Itasca Consulting Group. Dr. Jorquera-Lucerga would like to thank Universidad Politécnica de Cartagena, which partially provided funding, through the program PMPDI-2015, for this research, carried out during his stay as Visiting Fellow at the Department of Civil and Environmental Engineering at Princeton University. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1148900. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
Notes
1 For wind loading cases, only the true pinnacle placement on the outer edge of the pier buttress was compared to the pier buttress without a pinnacle. Therefore the location of the pinnacle was not explored in the case of wind loading. The dead load only case considered the pinnacle in both a centered and outer-edge position.
2 For the graphical approach to determine the loads in the structure of a cathedral, the reader is referred to the analysis of Mallorca Cathedral presented in Rubió (Citation1912).