The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building

Dragos Naicu, Christopher Williams

Research output: Contribution to conferencePaper

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Abstract

The problem of finding the tallest possible column that can be constructed from a given volume of material without buckling under its own weight was finally solved by Keller and Niordson in 1966. The cross-sectional size of the column reduces with height so that there is less weight near the top and more bending stiffness near the base. Their theory can also be applied to tall buildings if the weight is adjusted to include floors, live load, cladding and finishes.

In this paper we simplify the Keller and Niordson derivation and extend the theory to materials with non-linear elasticity, effectively limiting the stress in the vertical structure of the building. The result is one highly non-linear ordinary differential equation which we solve using dynamic relaxation.
Original languageEnglish
Pages34-45
Number of pages12
Publication statusPublished - Oct 2015
EventVII International Conference on Textile Composites and Inflatable Structures - Barcelona, Spain
Duration: 19 Oct 201521 Oct 2015

Conference

ConferenceVII International Conference on Textile Composites and Inflatable Structures
CountrySpain
CityBarcelona
Period19/10/1521/10/15

Fingerprint

Tall buildings
Differential equations
Ordinary differential equations
Buckling
Elasticity
Stiffness

Keywords

  • Column buckling
  • Non-linear material
  • Self-weight
  • Tallest column
  • Dynamic Relaxation
  • Optimal design

Cite this

Naicu, D., & Williams, C. (2015). The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building. 34-45. Paper presented at VII International Conference on Textile Composites and Inflatable Structures, Barcelona, Spain.

The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building. / Naicu, Dragos; Williams, Christopher.

2015. 34-45 Paper presented at VII International Conference on Textile Composites and Inflatable Structures, Barcelona, Spain.

Research output: Contribution to conferencePaper

Naicu, D & Williams, C 2015, 'The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building' Paper presented at VII International Conference on Textile Composites and Inflatable Structures, Barcelona, Spain, 19/10/15 - 21/10/15, pp. 34-45.
Naicu D, Williams C. The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building. 2015. Paper presented at VII International Conference on Textile Composites and Inflatable Structures, Barcelona, Spain.
Naicu, Dragos ; Williams, Christopher. / The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building. Paper presented at VII International Conference on Textile Composites and Inflatable Structures, Barcelona, Spain.12 p.
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