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Published online by Cambridge University Press: 13 March 2025
Chapter One introduces the geometric principles of equilibrium for concurrent systems of forces both in 2D and Polyhedral Graphic Statics. It starts with a simple example of a tensile or a compression-only node and explains constructing a closed force diagram for the given geometry in 2D and 3D. The chapter describes the geometrical and topological properties of a single force polygon in 2D and a polyhedron in 3D and its relationship with the static equilibrium of forces in a single node as the form diagram. In addition, the static determinacy and indeterminacy of forces are explained by the number of independent edges in the force diagram, which is referred to as the Geometric Degrees of Freedom. Furthermore, the construction of an indeterminate force polyhedron for a general node with multiple members or applied loads is discussed by explaining the Extended Gaussian Image of a polyhedron. The final examples of this chapter show how the knowledge of this chapter can be applied in the conceptual design of simple bridges with both tension and compression members.
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