Nous annonçons la création de BESTREMA, un bureau d'études structure spécialisé dans les monuments anciens. Un des objectifs de cette société est de participer à la diffusion des connaissances sur la structure des monuments anciens auprès du grand public.

Les nouveaux articles que nous écrirons seront désormais mis en ligne sur bestrema.fr. Les anciens articles qui ont déjà été publiés ces deux dernières années resteront à votre disposition sur Combien ça porte. Nous vous remercions d'avoir suivi ce blog, et nous remercions tout particulièrement les lecteurs qui ont partagés avec nous leurs observations sur les structures des monuments anciens.

### Masonry network analysis for construction history

See english version below.
Le deuxième congrès francophone d'histoire de la construction a eut lieu à Lyon du 29 au 31 janvier 2014. Nous avons mis au point dans le cadre de ce congrès un nouveau logiciel d'études des structures maçonnées basée sur la méthode des réseaux de forces. Cette méthode, développée notamment par O'Dwyer (1999 [9]) et Block (2009 [1]), permet l'étude de structures tridimensionnelle, en substituant un réseau de forces à la ligne de pression. Le logiciel que nous avons développé est destiné aux chercheurs et étudiants qui s'intéressent à la stabilité des structures maçonnées anciennes. Le logiciel et son manuel d'utilisation sont disponibles uniquement en anglais.

English version:
MaNACoH was written by Mathias Fantin for the second French conference on history construction that took place in Lyon in January 2014, with the help of Thierry Ciblac, teacher-researcher at MAP-Maacc Laboratory in Paris (CNRS-MCC UMR 3495).
Manacoh is an open-source software addressed primarily to scholars and students who study ancient methods for assessing the stability of masonry vaults, in the field of construction history. It is well suited to study structures that have a strong 3D geometry (for example ellipsoid vaults, as opposed to simple arches that can be studied easily in 2D). Classical 2D geometries can be studied as well. It uses the thrust network analysis. This method replaces the well-known inverted catenary by an inverted net, called thrust network. Passing from 2D to 3D widens the possible equilibrium solutions that can be searched. The drawback is the increased difficulty to solve the equilibrium equations in three dimensions. Manacoh is an all-in-one tool to study 3D structures: it builds the geometry for parametric pre-set examples, solves the equilibrium equations, and offers the possibility to explore various equilibrium solutions, through optimization strategies.
Fig 1: Example of figures created by Manacoh
The force network method was first published by O'Dwyer in 1999 [9], and then extended by Block in 2009 [1] under the name of thrust network analysis1. Tools using thrust network analysis exist (Van Swinderen et Coenders 2009 [12], Rippmann et al. 2012 [11]), and several advances and extensions have already been proposed in recent years, concerning the optimization procedures (Vouga et al 2012 [13], Block et Lachauer 2014 [2]), and/or the related variational formulations (Fraternali 2010 [7], De Goes et al. 2013 [4]). Our implementation of the technique focus on the field of construction history. It aims at providing a tool capable of reproducing various equilibrium solutions of published studies of historic interest, using for each of them their own stability criterion. Also, the study of more complex 3D geometries using these historic criteria is possible. The signification of the thrust network was re-evaluated with respect to the line of thrust and the line of pressure. To do so the geometric characteristics of the joints were taken into account, whereas previous studies usually disregard this aspect of the modelisation and consider only vertical joints. Thus Manacoh is designed primarily to study existing structures, the drawback being that it offers only restricted possibilities for form finding of innovative 3D forms.
The main application of Manacoh so far has been to investigate existing studies of various authors: Bossut 1776 [3], Rankine 1858 [10], Eddy 1877 [6], Durand-Claye 1880 [5], Wolfe 1921 [14], Heyman 1967 [8] etc. Equivalent formulations in term of optimization under constraints have been formulated, and checked against results published in scientific literature. Although there is an obvious risk of anachronism by studying all these authors with a numeric tool, this technique proved fast and effective to compute results that help understand and compare these historic methods. It allows also to rediscover forgotten techniques that would be very difficult to apprehend without a numerical tool (Durand-Claye is a good example in that respect).
This manual has been divided in four chapters. The first chapter provide the context of this work, the installation procedure of the program, and a quick overview of the program with a basic example. The second chapter describes the program use, its functions, options, and results. The third chapter addresses the theory of the thrust network analysis, its signification with respect to the line of thrust and line of pressure, and the definition of coefficients of safety. The fourth chapter examines various examples from construction history, in order to demonstrate the possibilities of the program. These examples were studied as a preparation for an oral communication by Mathias Fantin and Thierry Ciblac at the second French conference on history construction that took place in Lyon in January 2014.

### Video tutorials

See new webpage for Manacoh, following new developments : http://bestrema.fr/manacoh/.

### Versions history

v1.0.1 (10/02/2014) macros "Compute typology" and "Compute equilibrium" are not executed automatically after macro "Create Geometry" anymore. No change to the user manual
v1.0.0 (30/01/2014) first release

Article mis en ligne le : 12/01/2014.
Révisé le : 10/02/2014.

### Bibliographie

[1]
P.  BLOCK : Thrust Network Analysis : exploring three-dimensional equilibrium. Thèse de doctorat, Massachusetts Institute of Technology, Dept. of Architecture, 2009. URL http://dspace.mit.edu/handle/1721.1/49539.
[2]
P.  BLOCK et L.  LACHAUER : Three-dimensional funicular analysis of masonry vaults. Mechanics Research Communications, 56: 53-60, mars 2014. URL http://www.sciencedirect.com/science/article/pii/S0093641313002012.
[3]
C.  BOSSUT : Nouvelles recherches sur l'équilibre des voûtes en dôme. In Histoire de l'Académie Royale des sciences. Imprimerie royale, Paris, 1776. URL http://gallica.bnf.fr/ark:/12148/cb32786820s/date.
[4]
F.  DE GOES, P.  ALLIEZ, H.  OWHADI et M.  DESBRUN : On the Equilibrium of Simplicial Masonry Structures. ACM Transactions on Graphics, 32(4), 2013. URL http://hal.inria.fr/hal-00826280/.
[5]
A.  DURAND-CLAYE : Vérification de la stabilité des voûtes et des arcs - Application aux voûtes sphériques. Annales des ponts et chaussées, 1880. URL http://gallica.bnf.fr/ark:/12148/cb34348188q/date.
[6]
H. T. EDDY : New constructions in graphical statics. D. Van Nostrand, New York, 1877. URL http://archive.org/details/newconstruction00eddygoog.
[7]
F.  FRATERNALI : A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions. Mechanics Research Communications, 37(2): 198-204, mars 2010. URL http://linkinghub.elsevier.com/retrieve/pii/S0093641309001785.
[8]
J.  HEYMAN : On shell solutions for masonry domes. International Journal of Solids and Structures, 3(2): 227-241, mars 1967.
[9]
D.  O'DWYER : Funicular analysis of masonry vaults. Computers & structures, 73(1-5): 187-197, 1999.
[10]
W. J. M. RANKINE : A manual of applied mechanics. Griffin, London, 1858.
[11]
M.  RIPPMANN, L.  LACHAUER et P.  BLOCK : Interactive Vault Design. International Journal of Space Structures, 27(4): 219-230, déc. 2012. URL http://block.arch.ethz.ch/brg/publications/260.
[12]
T.  VAN SWINDEREN et J.  COENDERS : Tool to design masonry double-curved shells. In Symposium of the International Association for Shell and Spatial Structures, Valencia, 2009. URL http://dspace.cc.upv.es/handle/10251/7002.
[13]
E.  VOUGA, M.  HöBINGER, J.  WALLNER et H.  POTTMANN : Design of self-supporting surfaces. ACM Transactions on Graphics (TOG), 31(4): 87, 2012. URL http://dl.acm.org/citation.cfm?id=2185583.
[14]
W. S. WOLFE : Graphical analysis - a text book on graphic statics. McGraw-Hill book company, New York, 1st édn, 1921. URL http://archive.org/details/graphicalanalysi00wolfrich.

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### Notes:

1 The thrust network analysis by Block directly stems from the force network method, with a decisive advance: the use of reciprocal figures. Our implementation only partially use the potentiality of the thrust network analysis of Block, since we produce the reciprocal figures without using their full potential. Our implementation is a middle-way between the force network method and the thrust network analysis. For simplification, we will use Block's denomination of the technique.