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

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

Geometry and Performance of Timber Gridshells

Timber gridshells are a very efficient way of covering large spaces while also providing a unique architectural and material quality. As this can still be considered an emergent technology, the design of such buildings has relied on a relatively substantial amount of experimental work. This thesis, upon reviewing the design and construction processes of previous timber gridshells, puts forward a structural model that aims to represent the true nature and specifics of single and double-layered timber gridshells. The parametrically determined geometry of a computational prototype is described and used as a basis for a non-linear elastic numerical analysis. Particular attention is given to modelling the connections between the timber laths that provide composite bending action in a double layer grid. The deformation behaviour and the imperfection sensitivity are assessed with a view to understanding how gridshells respond under different conditions. A new gridshell will inevitably be analysed with computer software, but the information presented in this dissertation will be useful for scheme design as well as the calibration of the computer analysis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

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

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