Prestress in Nature and Technics

To direct the forces of nature is a central task in the creation of spaces and load-carrying structures for architecture. This research investigates how prestress can be used as a design tool for the creation of material efficient and well-functioning structures, and in early design stages contribute to sustainable, functional and beautiful architecture.The thesis begins with a discussion about central concepts such as stress and stiffness. Stiffness can be understood as the sum of elastic stiffness and geometric stiffness and the latter is differently influenced by the presence of tensile or compressive stresses. Only structures that are statically indeterminate are possible to prestress so that the stress pattern is affected. The terms externally-equilibrated and auto-equilibrated prestressed structures are introduced.The design of load-bearing structures for architecture requires a collaboration between architects and engineers and the conditions for a successful collaboration is reflected upon. Prominent design cultures are highlighted and the one this research is linked to is described.A collection of historic and contemporary examples of prestressed structures is presented. The focus is architectural applications but examples from other realms are also included. From this collection, a framework for prestressed structures is proposed and discussed which considers five perspectives. The first explores the historical knowledge development. The second is devoted to structural mechanical modes of actions where material behaviour, member actions and structural systems are discussed. The third highlights computational strategies and those appropriate for early stage design are distinguished from those suitable for late stage verification. The fourth perspective seeks to establish objectives for why prestress is used. The fifth perspective leads to suggestions for strategies for how the prestress is achieved.Three papers are included. Paper A presents a numerical method for the form finding of prestressed gridshells consisting of both compressed and tensioned members. Paper B describes a structural design process where methods usually applied by architects are used by structural engineers. The work resulted in the construction of a temporary pavilion consisting of a post-tensioned wooden gridshell called the Wood Fusion Pavilion. Paper C explores under what conditions an unloaded shell formed of a closed surface unattached to any supports can contain a state of membrane stress which can be induced by prestressing. It is concluded that a torus can be prestressed, but there must almost certainly be more to explore

Bi-directional algebraic graphic statics

A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized

Bi-directional Algebraic Graphic Statics : On Force Diagram Constraints

This paper presents a study exploring the capabilities of a new method, described by Åkesson and Alic [1], which extends the capabilities of the algebraic graphic statics method, by Van Mele and Block [11]. The new method extends the algebraic graphic statics method by making it bi-directional i.e. allowing for determination of an updated form diagram by making direct interactive manipulations of the force diagram. In the new method, Newton’s method is used for solving a set of non-linear equations, to find an updated form diagram from given changes in the force diagram. Additional geometric constraints are introduced on the form diagram to obtain desired solutions. The implementation of the method as a back-end to an interactive application is discussed, and the usability of the method is shown in examples where the qualities of directly manipulating the force diagram are discussed. The main part of this paper will supplement Åkesson and Alic [1] by presenting further studies of the application of constraints to the force diagram, and which shapes this leads to in the form diagram. Further, the paper will present how to adapt force and form diagrams for interactive graphical representations suitable for computers