Optimum structure to carry a uniform load between pinned supports

Research Paper


Since the time of Huygens in the 17th century it has been believed that, if the weight of the structural members themselves are negligible in comparison to the applied load, the optimum structure to carry a uniformly distributed load between pinned supports will take the form of a parabolic arch rib (or, equivalently, a suspended cable). In this study, numerical layout optimization techniques are used to demonstrate that when a standard material with equal tension and compressive strength is involved, a simple parabolic arch rib is not the true optimum structure. Instead, a considerably more complex structural form, comprising a central parabolic section and networks of truss bars in the haunch regions, is found to possess a lower structural volume.


Structural optimization Layout optimization Parabola Arch 


  1. Chan HSY (1975) Symmetric plane frameworks of least weight. In: Sawczuk A, Mroz Z (eds) Optimization in structural design, Proc. IUTAM symp., Warsaw, pp 313–326Google Scholar
  2. Chiandussi G, Codegone M, Ferrero S (2009) Topology optimization with optimality criteria and transmissible loads. Comput Math Appl 57(5):772–788CrossRefMathSciNetGoogle Scholar
  3. Darwich W, Gilbert M, Tyas A (2007) Optimum structure to carry a uniform load between two pinned supports. In: 7th world congress of structural and multidisciplinary optimization, Seoul, KoreaGoogle Scholar
  4. Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J de Mechanique 3:25–52Google Scholar
  5. Fuchs MB, Moses E (2000) Optimal structural topologies with transmissible loads. Struct Multidisc Optim 19:263–273CrossRefGoogle Scholar
  6. Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(7–8):1044–1064. doi:10.1108/02644400310503017 MATHGoogle Scholar
  7. Gilbert M, Darwich W, Tyas A, Shepherd P (2005) Application of large-scale layout optimization techniques in structural engineering practice. In: 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, BrazilGoogle Scholar
  8. Hemp WS (1974) Michell frameworks for uniform load between fixed supports. Eng Optim 1:61–69CrossRefGoogle Scholar
  9. Knuth D (1997) The art of computer programming, vol 2: seminumerical algorithms, 3rd edn. Addison-Wesley, ReadingGoogle Scholar
  10. Lockwood EH (1961) A book of curves. Cambridge University Press, CambridgeMATHGoogle Scholar
  11. McConnel RE (1974) Least-weight frameworks for loads across span. J Eng Mech ASCE 100:885–901Google Scholar
  12. Owen JBB (1965) The analysis and design of light structures. Edward Arnold, LondonGoogle Scholar
  13. Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37(3):217–237CrossRefMathSciNetGoogle Scholar
  14. Rozvany GIN, Prager W (1979) A new class of structural optimization problems—optimal archgrids. Comput Methods Appl Mech Eng 19(1):127–150MATHCrossRefMathSciNetGoogle Scholar
  15. Rozvany GIN, Wang CM (1983) On plane Prager-structures. Int J Mech Sci 25(7):519–527MATHCrossRefGoogle Scholar
  16. Rozvany GIN, Wang CM, Dow M (1982) Prager-structures: archgrids and cable networks of optimal layout. Comput Methods Appl Mech Eng 31:91–113MATHCrossRefMathSciNetGoogle Scholar
  17. Sylla ED (2003) Die werke von Jakob Bernoulli. Hist Math 30(3):378–380CrossRefMathSciNetGoogle Scholar
  18. Yang XY, Xie YM, Steven GP (2005) Evolutionary methods for topology optimisation of continuous structures with design dependent loads. Comput Struct 83(12–13):956–963CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Civil & Structural EngineeringUniversity of SheffieldSheffieldUK

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