On the Design Process of Tensile Structures 13 with (4),(5)and (6)in (2)follows naBsTbsubaB+uie.=p Assuming only vertical loads,allows setting the 2.term to zero and the vertical displacement is 1 boBb 一·p In both equations,the change of the stresses and the vertical displacement,the denominator is the same and a product of the elastic stiffness and the curvature of the surface.The lower this product is the higher the vertical deformations will be. Therefore this term describes the stiffness of the surface and is named as D naB67.ba8.b57 Expanded and the orientation of the coordinate system in direction of the prin- ciple stresses (2=1=0)or principle curvature (b12=b21=0)leads to: D=111 n2222 形n111+.n222 + 脱· Flexibility ellipsoids Two aspects have to be mentioned considering the load bearing behaviour of ca- ble nets or membrane structures,the stiffness of a three-dimensional shape and the possibility of pretensioning the structure in relation to the material behaviour and the stiffness.There exists an analogy between net calculation in geodesy and the analysis of membranes [22,23]and leads to new aspects describing the load carry- ing capacity of structures.Flexibility can be seen as the deformation of each node loaded by a rotating unit load and leads to flexibility ellipsoids showing the three dimensional deformation of the node. The in plane stiffness of the cable net or membranes has a large influence to the possibility of pretension because this allows to change plane two dimensional flat strips into a three dimensional surface without wrinkles.The advantage of cinematic cable nets and membranes is the ability to distribute the forces during the process of pretensioning nearly homogeneous by tensioning only boundary cables or lifting high points.The ability of a double curved cable net distributing forces which are acting at the edges or boundaries homogeneous through the net can be described by redundancy. The comparison between three different types of cable nets will give an example for the application of flexibility ellipsoids in evaluation of the structural behaviour. In geometry three homogeneous nets are exiting which can be transformed in double curved cable nets.Each net has the same tension forces and the stiffness per meter. The net with hexagonal meshes has only nodes with three links and leads to an equilibrium of each node under pretension only if the forces in all links are the same. The shape is then comparable with a minimal surface.The high degree of kinematics makes these nets very flexible and the stiffness can be mostly influenced by the height of the pretension forces.The net with square meshes has still no in plane shear stiffness but if the cables are arranged in the direction of the main curvature this net has even less deformation for a uniformly distributed load compared to theOn the Design Process of Tensile Structures 13 with (4), (5) and (6) in (2) follows nαβδγbδγ u3 bαβ + u3 |α,β · σαβ = p3 Assuming only vertical loads, allows setting the 2. term to zero and the vertical displacement is u3 = 1 nαβδγ · bαβ · bδγ · p3 In both equations, the change of the stresses and the vertical displacement, the denominator is the same and a product of the elastic stiffness and the curvature of the surface. The lower this product is the higher the vertical deformations will be. Therefore this term describes the stiffness of the surface and is named as D = nαβδγ · bαβ · bδγ Expanded and the orientation of the coordinate system in direction of the prin￾ciple stresses (σ12 = σ21 = 0) or principle curvature (b12 = b21 = 0) leads to: D = n1111 R2 1 + n2222 R2 2 = R2 2 · n1111 + R2 1 · n2222 R2 1 · R2 2 Flexibility ellipsoids Two aspects have to be mentioned considering the load bearing behaviour of ca￾ble nets or membrane structures, the stiffness of a three-dimensional shape and the possibility of pretensioning the structure in relation to the material behaviour and the stiffness. There exists an analogy between net calculation in geodesy and the analysis of membranes [22,23] and leads to new aspects describing the load carry￾ing capacity of structures. Flexibility can be seen as the deformation of each node loaded by a rotating unit load and leads to flexibility ellipsoids showing the three dimensional deformation of the node. The in plane stiffness of the cable net or membranes has a large influence to the possibility of pretension because this allows to change plane two dimensional flat strips into a three dimensional surface without wrinkles. The advantage of cinematic cable nets and membranes is the ability to distribute the forces during the process of pretensioning nearly homogeneous by tensioning only boundary cables or lifting high points. The ability of a double curved cable net distributing forces which are acting at the edges or boundaries homogeneous through the net can be described by redundancy. The comparison between three different types of cable nets will give an example for the application of flexibility ellipsoids in evaluation of the structural behaviour. In geometry three homogeneous nets are exiting which can be transformed in double curved cable nets. Each net has the same tension forces and the stiffness per meter. The net with hexagonal meshes has only nodes with three links and leads to an equilibrium of each node under pretension only if the forces in all links are the same. The shape is then comparable with a minimal surface. The high degree of kinematics makes these nets very flexible and the stiffness can be mostly influenced by the height of the pretension forces. The net with square meshes has still no in plane shear stiffness but if the cables are arranged in the direction of the main curvature this net has even less deformation for a uniformly distributed load compared to the