Analysis and Assessment of Swedish Vaulted Masonry Structures Using Funicular Methods

Abstract

Practising structural engineers working with historic masonry structures need access to further developed methods to analyse and assess the structural behaviour of masonry vaults. The aim of this study is to evaluate methods to analyse vaulted masonry structures and to develop a methodology for the application of suitable methods to the work of practising structural engineers. A secondary aim is to use the methods studied to analyse and assess the structural behaviour of three Swedish church buildings of different types and with vaulted structures. The churches are Gökhem church, a small parish church built in the 12th century, and the Lund cathedral, also built in the 12th century; both originally in the Romanesque style but with later alterations. The third church is St Johannes church in Stockholm, built in the neogothic style in the late 19th century. The methods used are parametric graphic statics of thrust line analysis and Thrust Network Analysis (TNA), both based on funicular analysis. The results show the strength of using such methods to assess and evaluate the structural behaviour of historic vaulted masonry structures. They provide a pedagogical description of the structural behaviour of masonry vaults and the conditions that affect their load-carrying capacity. Another result is the implementation of a method to perform the analysis in a feasible and effective way. For the analysed church buildings, the results provide an understanding of their structural behaviour and clearly show how different variables affect the magnitude and impact of the thrusting force. Thrust Network Analysis has great potential to become a very effective method to perform advanced 3d analyses of masonry vaults but needs to be developed in order to enable “best fit solutions” to map the thrust network to the shape of the existing vaults. Such methods are under development.

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References

[1] Heyman, J. The Stone Skeleton: Structural Engineering of Masonry Structures. Cambridge University Press, England (1995).

[2] Huerta, S. The Analysis of Masonry Architecture: A Historical Approach. Architectural Science Review, Vol. 51.4: 297-328 (2008).

[3] Block, P. Thrust Network Analysis: Exploring Three-dimensional Equilibrium. Diss. Massachusetts Institute of Technology, Cambridge, MA, USA. (2009).

[4] Block, P., Ciblac, T. & Ochsendorf J. A. Real-time limit analysis of vaulted masonry buildings. Computers and Structures 84 (29-30), 1841-1852. (2006).

[5] Thelin, C., Höst, F. & Rosenberg, C. Att förstå verkningssätt och fånga geometrin ihistoriska murverkskonstruktioner, Bruk av ruiner, Balksten, K. & Mebus U., eds. (2013), Visby: Fornsalens förlag. (2013).

[6] Historic England, 3D Laser Scanning for Heritage: Advice and Guidance on the Use of Laser Scanning in Archaeology and Architecture. Swindon. Historic England. (2018).

[7] Thelin, C., Höst, F. & Rosenberg, C. Analysis of historic masonry structures supported by 3D laser scanning. Proceedings of the 8th International Conference on Structural Analysis of Historic Construction, Jasiénko, J. (red). SAHC-2012, 15–17 October 2012, Poland. (2012).

[8] O’Dwyer, D.W. Funicular analysis of masonry vaults. Computers and Structures 73 (1- 5), 187-197 (1999).

[9] Block P., Lachauer L. & Rippmann M. Thrust Network Analysis - Design of a cut-stone masonry vault, Shell Structures for Architecture: Form Finding and Optimization, Adriaenssens, S., Block, P., Veenendaal, D. and Williams, C. (editors), Routledge, London. (2014).

[10] Rippmann, M., Lachauer, P., & Block, P. Interactive Vault Design. International Journal of Space Structures, Vol 27, No 4: 219-230. (2012).

[11] Rippmann, M. & Block, P. Funicular Shell Design Exploration. Proceedings of the 33rd Annual Conference of the ACADIA, Waterloo/Buffalo/Nottingham, Canada. (2013).

[12] Rhinoceros.

[13] 3DReshaper.

[14] Rippmann, M. Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures. Diss. ETH Zürich, Schweiz. (2016).

[15] Block, P. & Lachauer, L. Three-dimensional (3D) equilibrium analysis of gothic masonry vaults. International Journal of Architectural Heritage, Vol 8: 312-335. (2014).

[16] Block, P. & Lachauer, L. Closest-Fit, Compression-Only Solutions for Free Form Shells, Proceedings of the IABSE-IASS Symposium 2011, London, UK. (2011).

[17] Panozzo D., Block P. & Sorkine-Hornung O. Designing Unreinforced Masonry Models, ACM Transactions on Graphics - SIGGRAPH 2013,32(4): 91:1-91:12. (2013).

[18] Van Mele, T., Panozzo, D., Sorkine-Hornung, O. & Block P. Best-fit thrust network analysis – Rationalization of freeform meshes, Shell Structures for Architecture: Form Finding and Optimization, Adriaenssens, S., Block, P., Veenendaal, D. and Williams, C. (editors), Routledge, London. (2014).

[19] Geogebra.

[20] Revit.