Thrust network analysis is usually applied to form finding of compressive-only structure. In order to study existing structures of historic interest, the joints of the structure need to be taken into account. We study the meaning of the three-dimensional thrust network with respect to the two-dimensional historical concepts of the line of pressure and line of resistance. We propose the refinement of the networks using additional branches with specific properties to widen the set of equilibrium solutions that can be computed. Finally, the application of the method to historic approaches of vault calculation is considered, as well as the convergence of the numerical geometrical coefficient of safety toward Heyman’s geometrical coefficient of safety.
O’DwyerD. Funicular analysis of masonry vaults. Comput Struct1999; 73: 1–5.
2.
BlockP. Thrust network analysis: exploring three-dimensional equilibrium. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2009.
3.
BlockPOchsendorfJ. Thrust network analysis: a new methodology for three-dimensional equilibrium. J Int Assoc Shell Spat Struct2007; 48: 1–7.
4.
Van SwinderenTCoendersJ. Tool to design masonry double-curved shells. In: Symposium of the international association for shell and spatial structures
, Valencia, Spain, 28 September–2 October 2009.
5.
RippmannMLachauerLBlockP. Interactive vault design. Int J Space Struct2012; 27: 219–230.
6.
VougaEHöbingerMWallnerJ. Design of self-supporting surfaces. ACM Trans Graph2012; 31: 1–11.
7.
BlockPLachauerL. Three-dimensional funicular analysis of masonry vaults. Mech Res Commun2014; 56: 53–60.
8.
FraternaliF. A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions. Mech Res Commun2010; 37: 198–204.
9.
De GoesFAlliezPOwhadiH. On the equilibrium of simplicial masonry structures. ACM Trans Graph2013; 32: 1–10.
10.
BlockPOchsendorfJ. Lower-bound analysis of masonry vaults. In: Proceedings of the 6th international conference on structural analysis of historical construction, Bath, UK, 2–4 July 2008.
11.
BlockPLachauerL. Three-dimensional (3D) equilibrium analysis of gothic masonry vaults. Int J Archit Herit2014; 8: 312–335.
12.
BenvenutoE. An introduction to the history of structural mechanics: part II: vaulted structures and elastic systems (vol. 2). New York: Springer, 1991.
13.
MoseleyH. The mechanical principles of engineering and architecture. London: Longman, Brown, Green and Longmans, 1843.
14.
HeymanJ. La Coupe des Pierres. In: Proceedings of the third international congress on construction history, Cottbus, Germany, 20–24 May 2009.
15.
SalençonJ. Calcul à la rupture et analyse limite. Paris: Presses de l’École Nationale des Ponts et Chaussées, 1983.
16.
DelbecqJ-M. Analyse de la stabilité des ponts en maçonnerie par la théorie du calcul à la rupture. Thèse de doctorat, Ecole nationale des ponts et chausses, Paris, 1983.
17.
HeymanJ. The stone skeleton: structural engineering of masonry architecture. Cambridge: Cambridge University Press, 1995.
18.
CiblacTFantinM. Rediscovering Durand-Claye’s method using force network method implemented for construction history. In: Proceedings of the fifth international congress on construction history (ed BowenBFriedmanDLeslieT.), Chicago, IL, 3–7 June 2015.
19.
Huerta FernándezS. Designing by geometry. Rankine’s theorems of transformation of structures. In: Hernández-RosRA (ed.) Geometría y proporción en las estructuras: Ensayos en honor de Ricardo Aroca. Madrid: Outer Ediciones, 2010; 263–285.
20.
CiblacTFantinM. Analyse de la stabilité des dômes maçonnés à l’aide de la méthode des réseaux de forces. In: FleuryFBaridonLMastrorilliA. (eds) Les temps de la construction Processus, acteurs, matériaux. Vaulx-en-Velin: Picard Architec, 2016.
21.
OchsendorfJA. Collapse of masonry structures. Cambridge: King’s College, 2002; 1171–1182.
22.
ZessinJF. Collapse analysis of unreinforced masonry domes and curving walls. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2012.
23.
HeymanJ. On shell solutions for masonry domes. Int J Solids Struct1967; 3: 227–241.
