Applications of Michell’s Theory in Design of High-Rise Buildings, Large-Scale Roofs and Long-Span Bridges

  • Cezary Graczykowski Institute of Fundamental Technological Research, Polish Academy of Sciences
  • Tomasz Lewiński Warsaw University of Technology
DOI: http://dx.doi.org/10.24423/cames.288

Abstract

This paper analyzes the relations between the theory of Michell structures, which is one of the most important theories in structural optimization, and some remarkable engineering structures, including selected high-rise buildings, large-scale roof coverings and long-span bridges. The first part of this study briefly presents the development of Michell’s theory, its basic concepts, assumptions, and examples and fundamental features of Michell structures. Then, several untypical engineering structures that make use of said concepts are presented, including skyscrapers proposed by the Polish structural designer W. Zalewski and the international architectural office of Skidmore, Owings and Merill (SOM). Next, large-scale roof coverings of “Spodek” arena in Poland as well as selected bridges are thoroughly analyzed in the context of similarity to Michell structures. The conducted study reveals that considered structural forms of the analyzed structures follow some of the concepts known from Michell’s theory and thus possess many features of the optimal structural designs.

Keywords

topology optimization, Michell structures, high-rise buildings, large-scale roofs, long-span bridges,

References

1. A.G.M. Michell, The limits of economy of material in frame structures, The London, Edinburgh, and Dublin Philosophical Magazine Series 6, 8(47): 589–597, 1904, doi: 10.1080/14786440409463229.
2. H.S.Y. Chan, Minimum weight cantilever frames with specified reactions, June, No 1,010.66, 11pp, University of Oxford. Depart. of Eng. Sci. Eng. Laboratory, Oxford, 1966.
3. H.S.Y. Chan, Half-plane slip-line fields and Michell structures, The Quarterly Journal of Mechanics and Applied Mathematics, 20(4): 453–469, 1967.
4. H.L. Cox, The design of structures of least weight, Pergamon Press, Oxford, 1965.
5. W.S. Hemp, Optimum Structures, Clarendon Press, Oxford, 1973.
6. T. Lewinski, M. Zhou, G.I.N. Rozvany, Extended exact solutions for least-weight truss layouts – Part I: Cantilever with a horizontal axis of symmetry, International Journal of Mechanical Sciences, 36(5): 375–398, 1994.
7. T. Lewinski, M. Zhou, G.I.N. Rozvany, Extended exact solutions for least-weight truss layouts – Part II: Unsymmetric cantilevers, International Journal of Mechanical Sciences, 36(5): 399–419, 1994.
8. G.I.N. Rozvany, Some shortcomings in Michell’s truss theory, Structural Optimization, 12(4): 244–250, 1996.
9. G.I.N. Rozvany, T. Sokół, Exact truss topology optimization: allowance for support costs and different permissible stresses in tension and compression – extensions of a classical solution by Michell, Structural and Multidisciplinary Optimization, 45(3): 367–376, 2012.
10. M. Gilbert, A. Tyas, Layout optimization of large-scale pin-jointed frames, Engineering Computations, 20(8): 1044–1064, 2003.
11. T. Sokół, A 99 line code for discretized Michell truss optimization written in Mathematica, Structural and Multidisciplinary Optimization, 43(2): 181–190, 2011.
12. T. Sokół, T. Lewinski, On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight, Structural and Multidisciplinary Optimization, 42(6): 835–853, 2010.
13. A.V. Pichugin, A. Tyas, M. Gilbert, On the optimality of Hemp’s arch with vertical hangers. Structural and Multidisciplinary Optimization, 46: 17–25, 2012.
14. A.V. Pichugin, A. Tyas, M. Gilbert, L. He, Optimum structure for a uniform load over multiple spans, Structural and Multidisciplinary Optimization, 52: 1041–1050, 2015.
15. T. Sokół, T. Lewinski, Michell Cantilever on Circular Support for Unequal Permissible Stresses in Tension and Compression, Proceedings of the SOLMECH 2018 Conference, Warsaw, Poland, 2018.
16. T. Lewinski, T. Sokół, C. Graczykowski, Michell Structures, Springer, 2019.
17. L.L. Beghini, J. Carrion, A. Beghini, A. Mazurek, W.F. Baker, Structural optimization using graphic statics, Structural and Multidisciplinary Optimization, 49: 351–366, 2014.
18. T. Sokół, A new adaptive ground structure method for multi-load spatial Michell structures, [in:] M. Kleiber, T. Burczynski, K. Wilde, J. Górski, K. Winkelmann, Ł. Smakosz [Eds], Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, pp. 525–528, CRC Press, 2016.
19. G.I.N Rozvany, W. Prager, A new class of structural optimization problems: optimal archgrids, Computer Methods in Applied Mechanics and Engineering, 19(1): 127–150, 1979.
20. R. Czubacki, T. Lewinski, Optimal archgrids: a variational setting, Structural and Multidisciplinary Optimization, 2020, doi: 10.1007/s00158-020-02562-y.
21. W. Zalewski, W. Zabłocki, Engineering inspirations in shaping tall buildings, [in:] Lightweight Structures in Civil Engineering, Proceedings of the International Symposium, Warsaw, Poland, 24–28 June, pp. 109–118, 2002.
22. W. Zalewski, Strength and lightness – The muses of a structural designer [in Polish: Moc i lekkość: muzy projektanta konstrukcji], Architektura, 74(11): 94–95, 2000.
23. W. Zabłocki, Optimization of structures and new forms of tall buildings [in Polish: Optymalizacja konstrukcji a nowe formy architektoniczne budynków wysokościowych], Architektura, 74(11): 96–98, 2000.
24. E. Allen, W. Zalewski, Boston Structures Group, Form and forces. Designing efficient expressive structures, Wiley, New Jersey, 2010.
25. T. Zegard, C. Hartz, A. Mazurek, W.F. Baker, Advancing building engineering through structural and topology optimization, Structural and Multidisciplinary Optimization, 2020, doi: 10.1007/s00158-020-02506-6.
26. W. Zalewski, Construction of the supermarket roof in Warsaw [in French: Construction de la toiture du supermarket a Varsovie], [in:] N. Esquillan, Y. Saillard [Eds], Hanging roofs: Proceedings of the IASS Colloquium on Hanging Roofs, Continuous Metallic Shell Roofs and Superficial Lattice Roofs, Paris 9–11 July, 1962.
27. W. Zalewski, Constancy of force as a criterion of the rational form of a construction [in French: Constance de la force comme critere de la forme ationelle d’une construction], 1963.
28. W. Zalewski, Some new structural forms created in the period 1950–60 [in Polish], 1964.
29. W. Zalewski, E. Allen, Shaping structures: Statics, Wiley, New York, 1998.
30. M. Pelczarski, Considerations from interviews with W. Zalewski, Architectus, 2(34): 69–82, 2013.
31. H.E. Fairclough, M. Gilbert, A.V. Pichugin, A. Tyas, I. Firth, Theoretically optimal forms for very long-span bridges under gravity loading, Proceeding of the Royal Society A, 474(2217): 20170726, 2018, doi: 10.1098/rspa.2017.0726.
Published
Sep 17, 2020
How to Cite
GRACZYKOWSKI, Cezary; LEWIŃSKI, Tomasz. Applications of Michell’s Theory in Design of High-Rise Buildings, Large-Scale Roofs and Long-Span Bridges. Computer Assisted Methods in Engineering and Science, [S.l.], v. 27, n. 2–3, p. 133–154, sep. 2020. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/288>. Date accessed: 23 dec. 2024. doi: http://dx.doi.org/10.24423/cames.288.
Citation Formats
Issue
Vol 27 No 2–3 (2020)
Section
[CLOSED] Engineering Optimization