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. 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
Download Manacoh and its user manual
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 releaseArticle 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.
License
The MIT License (MIT) Copyright (c) 2014 Mathias Fantin Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.