On the Design Process of Tensile Structures 3 Shape of Generation of Reassembling Structural be- Evaluation equilibrium cutting pattern and preten- haviour sion Fig.2.Enhanced design process of membrane structures [11] 3.1 Shape of Equilibrium The development of Computer Aided Geometric Design (CAGD)marked the start of changes in geometry endorsing new and free forms.This generation of double curved 3-dimensional surfaces is restricted by few limitations.Theoretically there are an unlimited number of forms to be numerical generated and represented.How- ever,the manufacture and realization of such double curved surfaces are subject to numerous boundary conditions and restrictions.Using cables and membranes for the load transfer only tension forces can be carried,the cables and membranes can not withstand bending moments and compression forces in a global point of view. The structures have to be pretensioned activating the geometric stiffness or to be able carrying compression forces by reducing the pretension.The shape of equilib- rium defines a pretensioned geometry of a doubled curved surface for a cable net or a membrane structure.The relation between the tension stress,geometry and equilibrium allows three possibilities to introduce the tension into the membranes and influences the shape of equilibrium,see Fig.3. Pretension against rigi Pretension as res t o e ia Pretension as result internal o n aries tion or es ul 一u2 (soil-.fluid-or gas-)pressure p R2 S traig t ire tions osite r e ire tions Same direction of the curvature S1 is in e en ent o S2 兴-是=0 +器=p Fig.3.Relation between tension forces and curvature The pretension against rigid boundaries enables plain tension structures,ten- sion structures with single curvatures and double curved tension structures if the direction of the cables or yarns is along the evolution line of a hyper parabola.The tension forces are independent from each other in this case.On the Design Process of Tensile Structures 3 Fig. 2. Enhanced design process of membrane structures [11] 3.1 Shape of Equilibrium The development of Computer Aided Geometric Design (CAGD) marked the start of changes in geometry endorsing new and free forms. This generation of double curved 3-dimensional surfaces is restricted by few limitations. Theoretically there are an unlimited number of forms to be numerical generated and represented. How￾ever, the manufacture and realization of such double curved surfaces are subject to numerous boundary conditions and restrictions. Using cables and membranes for the load transfer only tension forces can be carried, the cables and membranes can not withstand bending moments and compression forces in a global point of view. The structures have to be pretensioned activating the geometric stiffness or to be able carrying compression forces by reducing the pretension. The shape of equilib￾rium defines a pretensioned geometry of a doubled curved surface for a cable net or a membrane structure. The relation between the tension stress, geometry and equilibrium allows three possibilities to introduce the tension into the membranes Pretension against rigi o n aries traig t ire tions S1 is in e en ent o S2 Pretension as res t o e ia tion or es u1 −u2 osite r e ire tions S1 R1 − S2 R2 = 0 Pretension as result internal (soil-, fluid- or gas-) pressure p Same direction of the curvature S1 R1 + S2 R2 = p Fig. 3. Relation between tension forces and curvature The pretension against rigid boundaries enables plain tension structures, ten￾sion structures with single curvatures and double curved tension structures if the direction of the cables or yarns is along the evolution line of a hyper parabola. The tension forces are independent from each other in this case. Shape of equilibrium Generation of cutting pattern Reassembling and preten￾sion Structural be￾haviour Evaluation and influences the shape of equilibrium, see Fig. 3. S1 S1 S1 S1 S2 S2 S2 S2 S1 S1 S1 S1 S2 S2 S2 S2 u1 = – u2 u2 R2 R1 S1 S1 S1 S1 S2 S2 S2 p S2 1 R2 R1 p2