# Cutting Pattern of Membranes and Cable Elements

### Technical Article

001484

10/09/2017

Cable and tensile membrane structures are regarded as very slender and aesthetic building constructions. The partly very complex double-curved shapes can be found using suitable form-finding algorithms. A possible solution is, for example, to search the form via the equilibrium between the surface stress (provided prestress and an additional load such as self-weight, pressure, etc.) and the given boundary conditions.

The preparation or work preparation of structural components for assembly on the construction site is, in addition to the development of shape, a key process. This is where the engineer becomes a tailor. The big task is to model the double-curved membrane envelope as a whole under the given prestress from many small planar sections. The difficulty of this task becomes clear when you try to create the processing for half an orange in the thought model. Due to the radial and tangential curvature of the membrane skin, half of the orange can not be assembled from a planar part. Only the division into planar sections helps.

In addition to the actual pattern development, this decomposition is also highly demanding. In the assembly, the intersection lines are to be selected in such a way that the respective section has as uniform a prestress state as possible over the surface in the 3D geometry and no irregular loading is added due to the flattening. The smaller the division, the more homogeneous are the prestress distributions and the strain surcharges. This approach requires a free setting of the cutting lines for the subunits independent of any initial input and the global membrane geometry. The following aspects must be considered when plotting intersection lines for surface units:

• Homogeneous prestress state in 3D geometry
• Homogeneous strainal allowance due to flattening
• Limit width of the cast steel roller
• Material Location Photograph
• Joint
• Architecture
• Damage to the semi-finished product due to segments that are too large
• Assembly

After segmentation, the segmented 3D surface section then yields the desired single component for the assembly. The following aspects must be considered in the oscillation process:

• Material Location Photograph
• Compensation / relaxation over the surface and at the edges
• Surcharges at the edges
• have the same limit lengths between adjacent elements

Both steps regarding the definition of the section line guidance and the subsequent flattening of the surface components are referred to as cutting in practice.

In addition to the development of the design parameters for the membrane casing, there is also the assembly of the cable elements. The initially mentioned form-finding process searches for a geometry that balances the given surface tension of the membrane and the given cable force or resulting force of the given cable sag with the boundary reactions. This algorithm finally results in a new geometry with applied forces.

The cable length for the manufacture can thus not be tapped from the geometry found in its pure form, but results from the geometry found minus the cable extension from the acting prestress.

$${\mathrm L}_{\mathrm{unbelastete}\;\mathrm{Länge}}\;=\;\frac{\mathrm A\;\cdot\;\mathrm E\;\cdot\;{\mathrm L}_{\mathrm{belastete}\;\mathrm{Länge}}}{\mathrm N\;+\;\mathrm A\;\cdot\;\mathrm E}$$
where
A ... cross-sectional area
E ... modulus of elasticity
N ... cable force