Abstract
This paper presents a methodology based on Rankine’s Theorem for form-finding of cable-supported structures. The procedure involves linear equations and helps designers quickly identify the optimal cable layout for a given problem. The use of graphics statics provides powerful insight in the design with the visualization of the forces in the structure and allows control of a number of parameters which can be tuned for the problem at hand. An optimization routine is paired with the method proposed in this paper to identify cable nets of maximum stiffness. A detailed example of form-finding of a cable net is given to illustrate the effectiveness of the proposed methodology for a cable-stayed canopy of a high-rise building that is currently under-construction. Examples of applications to other type of structures are also included.
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Baker WF, Beghini A, Mazurek A (2012) Application of structural optimization in architectural design. In: Proceedings of the structures congress, Chicago
Baker WF, Beghini LL, Mazurek A, Carrion J, Beghini A (2013) Maxwell’s reciprocal diagrams and discrete michell frames. Struct Multidisc Optim. Published Online doi:10.1007/s00158-013-0910-0
Beghini LL, Carrion J, Beghini A, Mazurek A, Baker WF (2013) Structural optimization using graphic statics. Struct Multidisc Optim, Submitted
Bendsoe MP, Sigmund O (2002) Topology optimization: Theory, methods and applications. Springer, Berlin
Bletzinger KU, Ramm E (1999) A general finite element approach to the form finding of tensile structures by the updated reference strategy. Int J Space Struct 14(2):131–144
Block P, Ochsendorf J (2007) Thrust network analysis: a new methodology for three-dimensional equilibrium. J IASS 48(3):1–8
Block P, Ochsendorf J (2008) Lower-bound analysis of masonry vaults. In: Conf Struct Anal Hist Constr Preserv Saf Signif, pp 593–600
Block P, DeJong M, Ochsendorf J (2006) As Hangs the Flexible Line: Equilibrium of Masonry Arches. Nexus Network Journal 8(2):13–24
Chan ASL (1960) The design of Michell optimum structures. Ministry of aviation aeronautical research council report December (3303)
Chi Tran H, Lee J (2010) Advanced form-finding for cable-strut structures. Int J Solids Struct 47(14–15):1785–1794
Cremona L (1872) Le figure reciproche nella grafica statica. Tipografia Giuseppe Bernardoni, Milano
Culmann K (1864) Die graphische Statik. Meyer und Zeller, Zurich
Fivet C, Zastavni D (2012) Robert Maillart’s key methods from the salginatobel bridge design process (1928). J IASS 53(1):39–47
Geiger DH, Stefaniuk A, Chen D (1986) The design and construction of two cable domes for the Korean Olympics. Shell, Membranes and Space frames. In: Proceedings IASS symposium, Osaka
Greco L, Cuomo M (2012) On the force density method for slack cable nets. Int J Solids Struct 49(13):1526–1540
Grundig L, Moncrieff E (2000) A history of the principal developments and applications of the force density method in Germany 1970-1999. In: Proc IASS-IACM Fourth int colloq comput shell spat struct. Chania-Crete, Greece
Hansen S, Vanderplaats G (1988) An approximation method for configuration optimization of trusses. AIAA J 28(1):161–168
Huerta Fernández S (2010) Designing by Geometry: Rankine’s Theorems of Transformation of Structures. In: Geometría y proporción en las estructuras. Ensayos en honor de Ricardo Aroca, pp 263–285
Linkwitz K, Schek HJ (1971) Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen. Ingenieur-Archiv 40:145–158
Malerba PG, Patelli M, Quagliaroli M (2012) An Extended Force Density Method for the form finding of cable systems with new forms. Struct Eng Mech 42(2):191–210
Maxwell JC (1864) On reciprocal figures and diagrams of forces. Phil Mag 26:250–261
Maxwell JC (1870) On reciprocal figures, frames, and diagrams of forces. Edinb Roy Soc Proc 7:160–208
Mazurek A (2012) Geometrical aspects of optimum truss like structures for three-force problem. Struct Multidisc Optim 45(1):21–32
Mazurek A, Baker WF, Tort C (2011) Geometrical aspects of optimum truss like structures. Struct Multidisc Optim 43(2):231–242
Meek JL, Xia X (1999) Computer shape finding of form structures. Int J Space Struct 14(1):35–55
Micheletti A (2008) On generalized reciprocal diagrams for self-stressed frameworks. Int J Space Struct 23(3):153–166
Michell AGM (1904) The limits of economy of material in frame-structures. Phil Mag 8(47):589–597
Pellegrino S (1990) Analysis of prestressed mechanisms. Int J Solids Struct 26(I):1329–1350
Prager W (1970) Optimization of structural design. J Optim Theory Appl 6(I):1–21
Rankine WJM (1858) A manual of applied mechanics. C. Griffin and Co., London
Rankine WJM (1864) XVII. Principle of the equilibrium of polyhedral frames. Phil Mag Series 4:92
Schek HJ (1974) The force density method for form finding and computation of general networks. Comput Meth Appl Mech Eng 3(1):115–134
Varignon P (1687) Projet d’une nouvelle mechanique. Chez C. Jombert, Paris
Varignon P (1725) Traitee du mouvement, et de la mesure des eaux coulantes et jaillissantes: avec un traitee preliminaire du mouvement en general. Pissot [etc.], Paris
Veenendaal D, Block P (2012) An overview and comparison of structural form finding methods for general networks. Int J Solids Struct. doi:10.1016/j.ijsolstr.2012.08.008
Wang Y, Gao J (2011) Force density algorithm for truss structures with geometric nonlinearity. Yingyong Lixue Xuebao Chin J Appl Mech 28(5):509–513
Wolfe W (1921) Graphical analysis. McGraw-Hill Book Co. Inc., New York
Zalewski W, Allen E (1998) Shaping structures: Statics. Wiley, New York
Zastavni D (2008) The structural design of Maillart’s Chiasso Shed (1924): a graphic procedure. Struct Eng Int: J Int Assoc Bridge Struct Eng 18(3):247–252
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The second author gratefully acknowledges the support from the National Science Foundation Graduate Research Fellowship Program (GRFP).
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Beghini, A., Beghini, L.L., Schultz, J.A. et al. Rankine’s Theorem for the design of cable structures. Struct Multidisc Optim 48, 877–892 (2013). https://doi.org/10.1007/s00158-013-0945-2
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DOI: https://doi.org/10.1007/s00158-013-0945-2