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Indeterminacy of reciprocal diagrams: 4-valent primal grid

Last modified on 22.01.2014

Category: Advanced Graphic Statics techniques

Keywords:

Based on the assumption that all loading is vertical, two-dimensional diagrams can be used to describe and control the three-dimensional equilibrium of a network of branches and nodes. The horizontal projection of the network serves as a form diagram. The reciprocal force diagram describes the in-plane equilibrium of the form diagram and therefore the horizontal equilibrium of the three-dimensional network. In a 4-valent network, there is an infinite range of possible solutions, i.e. it is a statically indeterminate system. This is clearly visible in the force diagram: different distributions of the internal forces are possible. In order to determine all forces in such an indeterminate system of forces, either more than one force needs to be known or certain relations between them have to be given.