### Abstract

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 language | English |
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Pages | 34-45 |

Number of pages | 12 |

Publication status | Published - Oct 2015 |

Event | VII International Conference on Textile Composites and Inflatable Structures - Barcelona, Spain Duration: 19 Oct 2015 → 21 Oct 2015 |

### Conference

Conference | VII International Conference on Textile Composites and Inflatable Structures |
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Country | Spain |

City | Barcelona |

Period | 19/10/15 → 21/10/15 |

### Fingerprint

### Keywords

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

### Cite this

*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.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - The use of dynamic relaxation to solve the differential equation describing the shape of the tallest possible building

AU - Naicu, Dragos

AU - Williams, Christopher

PY - 2015/10

Y1 - 2015/10

N2 - 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.

AB - 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.

KW - Column buckling

KW - Non-linear material

KW - Self-weight

KW - Tallest column

KW - Dynamic Relaxation

KW - Optimal design

UR - http://congress.cimne.com/membranes2015/frontal/doc/Ebook2015.pdf

M3 - Paper

SP - 34

EP - 45

ER -