Pucher's equation relies on a prescribed stress resultant throughout the structure, while the forcedensity method relies on prescribed force-to-length ratios in each bar or cable, leading to a single system of linear equations.
Advantages and disadvantages of both methods are discussed, as well as examples illustrating the types of structures that can be formed.
In this thesis, a method of designing these complex structures is proposed.
By an analytical approach, an efficient structural column can be made and multiple optimization strategies are proposed. In the final chapters of the thesis, an example of a design is made using this strategy.
Structures designed both as physical models and in simulation software can require several iterations of fine adjustments.
In this thesis, we develop a form-finding application to reduce the iterative adjustments required when designing a tensegrity structure.However, the design of these complex columns is often done by the computer and optimizing software.There is a missing link in the field of structural mechanics and these types of columns, the knowledge of forces flowing through these complex three-dimensional structures. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Inherently characterized by the interaction of geometry and forces, the unique nature of long span dome, shell, and membrane structures readily allows collaboration between architects and engineers in the examination of their optimal form.Unlike free forms which are defined mathematically, form-finding shapes rely on the structure and loads themselves for definition.A shape often used as a support of this free-form architecture is the tree-like column or branching column.A structure branching out and redirecting forces from a big roof surface to one single point. By minimizing the use of materials, a form that is economical, sustainable and aesthetically attractive emerges. Through the elimination of bending and shear forces in the structure, less material and reinforcement is needed.The report supporting the submission is given in two sections: an introduction reviewing the behaviour and analytical requirements of tension structures which relates subsequent chapters to other publications, and a conclusion correlating the papers into an overall context of interactive design and analysis.For the sake of completeness as a thesis, main appendices A-D have been included at the end of the thesis to give comprehensive reviews of published work relating respectively to static analysis, form: -finding, dynamic analy1sis, and the development and mathematical basis of dynamic relaxation.