Innovative Families of Double-Layer Tensegrity Grids: Quastruts and Sixstruts
Publication: Journal of Structural Engineering
Volume 139, Issue 9
Abstract
Double-layer tensegrity grids (DLTGs) are spatial reticulated systems based on tensegrity principles, which have been studied in detail over recent years. The most important investigations have been carried out focusing on a short list of tensegrity grids. This paper explains, using real examples, how to use Rot-Umbela manipulations, a unique technique developed for generating innovative typologies of tensegrity structures. It is applied to two already existing tensegrity grids to obtain two new DLTGs. Their analysis permits us to identify, inside these novel grids, the modules that compose them, which were unknown until now. A brief description of these components and some information about their static analysis, for example states of self-stress and internal mechanisms, is provided. These novel modules belong to a family, all of them with similar characteristics in terms of geometry and topology, and can be used to generate a wide catalog of DLTGs. Some examples of new grids are presented, describing the methodology on how to obtain more models for other designers interested in creating and studying innovative DLTGs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful to Landolf Rhode-Barbarigos and Professor Smith, from IMAC at EPFL, for their generosity of sharing their useful tools for the analysis of the structures (Bel Hadj Ali et al. 2011), and Julien Averseng, from LMGC at the University of Montpellier, for valuable help contributed by his software (Averseng et al. 2012). Comments on the origins of the Quastrut, by Simon Guest, were also very appreciated.
The corresponding author would also like to thank the Basque Delegation of the Spanish College of Civil Engineers for their support during the time the research was carried out.
References
Averseng, J., Quirant, J., and Dubé, J.-F. (2012). “Interactive design and dynamic analysis of tensegrity systems.” Int. J. Space Struct., 27(2–3), 97–106.
Bel Hadj Ali, N., Rhode-Barbarigos, L., and Smith, I. (2011). “Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm.” Int. J. Solids Struct., 48(5), 637–647.
Connelly, R. (1999). “Tensegrity structures: Why are they stable?” Rigidity theory and applications, M. F. Thorpe and P. M. Duxbury, eds., Kluwer/Plenum, New York, 47–54.
Dalilsafei, S., and Tibert, G. (2012). “Design and form-finding analysis of tensegrity power lines.” Int. J. Space Struct., 27(2–3), 139–154.
Emmerich, D. G. (1964). Structures linéaires autotendants, Patent No. 1,377,291 (in French).
Emmerich, D. G. (1988). Structures tendues et autotendantes, Ecole d’architecture de Paris la Villette, Paris (in French).
Francis, A. J. (1980). Introducing structures: A textbook for students of civil and structural engineering, building, and architecture, Pergamon, Oxford, U.K.
Gancedo Lamadrid, E., Álvarez Gómez, J. M., Suárez González, J., and Vega Menéndez, J. (2004). “A new method to obtain and define regular polyhedra.” Geom. Dedicata, 106(1), 43–49.
Gomez-Jauregui, V. (2010). Tensegrity structures and their application to architecture, Universidad de Cantabria, Santander, Spain.
Gomez-Jauregui, V. (2012). “Mallas tensegríticas de doble capa y manipulaciones de Rot-Umbela.” Informes de la Construcción, 64(527), 331–344.
Gomez-Jauregui, V., Arias, R., Otero, C., and Manchado, C. (2012a). “Novel technique for obtaining double-layer tensegrity grids.” Int. J. Space Struct., 27(2–3), 155–166.
Gomez-Jauregui, V., Otero, C., Arias, R., and Manchado, C. (2011). “New configurations for double-layer tensegrity grids.” Struct. Eng. World Congress 2011, Como, Italy.
Gomez-Jauregui, V., Otero, C., Arias, R., and Manchado, C. (2012b). “Generation and nomenclature of tessellations and double-layer grids.” J. Struct. Eng., 138(7), 843–852.
Grünbaum, B., and Shephard, G. (1975). Lectures in lost mathematics, mimeographed notes, Univ. of Washington, Seattle.
Guest, S. (2011). “The stiffness of tensegrity structures.” IMA J. Appl. Math., 76(1), 57–66.
Hanaor, A. (1991). “Double-layer tensegrity grids: Static load response. II: Experimental study.” J. Struct. Eng., 117(6), 1675–1684.
Knight, B., Duffy, J., Crane, C., and Rooney, J. (2000). “Innovative deployable antenna developments using tensegrity design.” Collection of Technical Papers—AIAA/ASME/ASCE/AHS/ASC Structures, Struct. Dyn. Mater. Conf., American Institute of Aeronautics and Astronautics, Reston, VA, 984–994.
Kono, Y., and Kunieda, H. (1996). Tensegrity grids transformed from double-layer space grids, Stuttgart.
Mitsos, I., Guest, S., Winslow, P., and Martin, B. (2011). “Experimental investigation of a double layer ‘tensegrity’ space frame.” 52nd Annual Symp. IASS/6th Int. Conf. on Space Structures, London.
Motro, R. (1987). “Tensegrity systems for double layer space structures.” Proc., Int. Conf. Design and Construct. Non-conventional Struct., Civil-Comp, Edinburgh, U.K., 43–51.
Motro, R. (2003). Tensegrity: Structural systems for the future, Kogan, London.
Panigrahi, R., Gupta, A., and Bhalla, S. (2009). “Dismountable steel tensegrity grids as alternate roof structures.” Steel Compos. Struct., 9(3), 239–253.
Pars, M. (2008). “Tensegriteit.” 〈http://www.tensegriteit.nl/〉 (Jan. 10, 2009).
Pellegrino, S. (1993). “Structural computations with the singular value decomposition of the equilibrium matrix.” Int. J. Solids Struct., 30(21), 3025–3035.
Pellegrino, S., and Calladine, C. R. (1986). “Matrix analysis of statically and kinematically indeterminate frameworks.” Int. J. Solids Struct., 22(4), 409–428.
Raducanu, V. (2001). “Architecture et système constructif: Case de systémes de tenségrité.” Ph.D. thesis, Université de Montpellier II, Montpellier, France.
Rhode-Barbarigos, L., Hadj Ali, N. B., Motro, R., and Smith, I. F. C. (2010). “Designing tensegrity modules for pedestrian bridges.” Eng. Struct., 32(4), 1158–1167.
Skelton, R. E., Adhikari, R., and Helton, J. W. (1998). “Mechanics of tensegrity beams.” Rep. No. 1998-1, Structural Systems and Control Laboratory, Univ. of California, San Diego, CA.
Stucchi, S., Micheletti, A., Santangelo, F., and Totaro, A. (2006). “Tensegrity units for a movable settlement.” Proc., Adaptables, Int. Conf. On Adaptable Building Structures, Eindhoven, Netherlands, 95–99.
Tran, H. C., and Lee, J. (2010). “Initial self-stress design of tensegrity grid structures.” Comp. Struct., 88(9–10), 558–566.
Zhang, J. Y., and Ohsaki, M. (2007). “Stability conditions for tensegrity structures.” Int. J. Solids Struct., 44(11–12), 3875–3886.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 139 • Issue 9 • September 2013
Pages: 1618 - 1636
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 15, 2012
Accepted: Sep 12, 2012
Published online: Sep 17, 2012
Published in print: Sep 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.