Are there unsolvable structural problems? An open question
DOI:
https://doi.org/10.3989/ic.10.061Keywords:
structural design, insuperable size, structural cost, structural scope, optimal shapesAbstract
Galileo is the first Western author who pointed out the impossibility of that a similar figure grows indefinitely, by defining the concept of an insuperable size for any structure subject to the mechanical action of self-weight. If such insuperable size exists for a structural problem, such a problem would be unsolvable for greater sizes. The matter has not been answered until date, despite multiple researches along two conflicting lines: firstly, the determination of forms of constant stress whit no limit in size, and secondly, the determination of insuperable sizes for well defined structural problems. Here two related hypotheses are presented which could guide the search for a definitive answer.
Downloads
References
(1) Cervera Bravo, J.: Tres teoremas fundamentales de la teoría del diseño de estructuras. Informes de la Construcción, vol. 40, num. 399, pp. 57-66, 1989.
(2) Cervera Bravo, J.: Las estructuras y el peso propio. Informes de la construcción, vol. 42, núm. 407, pp. 73-86, 1990.
(3) Kauffman, S.: Investigations. Oxford University Press, New York, 2000.
(4) Rankine, W. J. M.: A manual of civil engineering. 2ª edición, 1863.
(5) Michell, A. G. M.: The Limits of Economy of Material in Frame-structures. Philosophical Magazine, S.6, vol. 8, num. 47, pp. 589-597, 1904.
(6) Vázquez Espí, M.: Un nuevo algoritmo para la optimación de estructuras: el recocido simulado. Informes de la Construcción, vol. 46, núm. 436, pp. 46-¬69, 1995.
(7) Cervera Bravo, J.: Concebir y analizar estructuras. Universidad Politécnica de Madrid, V2.0, 218 pp.
(8) Cox, H. L.: The design of structures of least weight. Pergamon, Oxford, 1965.
(9) Hemp, W. S.: The theory of structural design. Cranfield: College of Aeronautics, Report 115. 1958.
(10) Cervera Bravo, J.: Diseño de estructuras en edificación. Instituto Juan de Herrera, Madrid, 1993. http://oa.upm.es/3785/
(11) Fernández Cabo, J. L.: Estructura: tamaño, forma y proporción. Tesis doctoral. Madrid: Universidad Politécnica de Madrid. 1998.
(12) Keller, J. B.: The shape of the strongest column. Arch. ration. Mech. Analysis. Vol. 5, pp. 275-285. 1960. http://dx.doi.org/10.1007/BF00252909
(13) Karihaloo, B. L.; Hemp, W. S.: Maximum stregth/stiffness design of structural members in presence of self-weight. Proc. R. Soc. Lond. A, vol. 389, pp. 119-32. 1983. http://dx.doi.org/10.1098/rspa.1983.0098
(14) Chai, Y. H.; Wang, C. M.: Approximate Solution for the Shape of Submerged Funicular Arches with Self-weight Journal of Structural Engineering, vol. 131, num. 3, pp. 399-404. 2005.
(15) Zheng, B.; Ching-jui Chang, C.; Hae Chang Gea, H. C.: Topology Optimization Considering Body Forces. International Journal for Simulation and Multidisciplinary Design Optimization. Vol. 3, pp. 316-320. 2009. http://dx.doi.org/10.1051/ijsmdo/2009004
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2012 Consejo Superior de Investigaciones Científicas (CSIC)
This work is licensed under a Creative Commons Attribution 4.0 International License.
© CSIC. Manuscripts published in both the print and online versions of this journal are the property of the Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence. You may read the basic information and the legal text of the licence. The indication of the CC BY 4.0 licence must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the final version of the work produced by the publisher, is not allowed.
