14 Rosemarie Wagner net with triangle meshes.The net with hexagonal meshes is the one with the highest flexibility;the flexibility of the net with triangle meshes is in direction normal to the net surface nearly the same compared to the net with square meshes.The in plane stiffness reduces theses deformation of the net with triangle meshes. Net with hexagonal meshes Net with spare meshes Net with triangle meshes Fig.16.Flexibility ellipsoids of pretensioned nets with different meshes Redundancy A common definition of redundancy is the availability of more functional system components than necessary for meeting the requirements.For example the statically indeterminacy is a measure for redundancy of structures by the meaning of safety against failure.In cinematic structures such as cable nets this definition has to be extended by taking into account the geometrical stiffness.Well known is the fact that each node has 3 independent possibilities of movement in space structure,the normal force of each element and the boundary forces are giving the necessary equations for equilibrium.If the number of independent movements of the nodes is equal to the number of equations resulting from the element forces and boundary forces the structure is statically determined. Redundancy is more than the statically indeterminacy,which can be shown by the considerations of Dieter Stroebel [23]The number of indeterminacy is distributed among all elements in relation the geometry of the structure,the stiffness of the elements and the relatively elongation of each element within the structure.The elastic elongation of each element is influenced by stiffness of the connected elements. Focusing on one element means an extremely stiff surrounding structure compared to the element the change of length causes directly an increase of the force.The opposite is a very flexible structure which allows the elongation of the element without influencing the forces. This behaviour can be described by the elastic redundancy in terms between 0 and 1.An elastic redundancy of 0 means no forces arise if the length an single element is changed.An elastic redundancy of 1 says changing the length leads to a force depending on the elastic stiffness. Cinematic structures can be stabilised by tension forces.The tension forces built up a resistance if the structure is deformed under load known as geometrical stiff- ness.The three components of the stabilising tension forces lead to three additional14 Rosemarie Wagner net with triangle meshes. The net with hexagonal meshes is the one with the highest flexibility; the flexibility of the net with triangle meshes is in direction normal to the net surface nearly the same compared to the net with square meshes. The in plane stiffness reduces theses deformation of the net with triangle meshes. Fig. 16. Flexibility ellipsoids of pretensioned nets with different meshes Redundancy A common definition of redundancy is the availability of more functional system components than necessary for meeting the requirements. For example the statically indeterminacy is a measure for redundancy of structures by the meaning of safety against failure. In cinematic structures such as cable nets this definition has to be extended by taking into account the geometrical stiffness. Well known is the fact that each node has 3 independent possibilities of movement in space structure, the normal force of each element and the boundary forces are giving the necessary equations for equilibrium. If the number of independent movements of the nodes is equal to the number of equations resulting from the element forces and boundary forces the structure is statically determined. Redundancy is more than the statically indeterminacy, which can be shown by the considerations of Dieter Stroebel [23] The number of indeterminacy is distributed among all elements in relation the geometry of the structure, the stiffness of the elements and the relatively elongation of each element within the structure. The elastic elongation of each element is influenced by stiffness of the connected elements. Focusing on one element means an extremely stiff surrounding structure compared to the element the change of length causes directly an increase of the force. The opposite is a very flexible structure which allows the elongation of the element without influencing the forces. This behaviour can be described by the elastic redundancy in terms between 0 and 1. An elastic redundancy of 0 means no forces arise if the length an single element is changed. An elastic redundancy of 1 says changing the length leads to a force depending on the elastic stiffness. Cinematic structures can be stabilised by tension forces. The tension forces built up a resistance if the structure is deformed under load known as geometrical stiff- ness. The three components of the stabilising tension forces lead to three additional Net with hexagonal meshes Net with spare meshes Net with triangle meshes