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Formula 1: Forces Due to Bending
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![Basic Shapes of Membrane Structures [1]](/en/webimage/009595/2419502/01-en-png-png.png?mw=512&hash=6ca63b32e8ca5da057de21c4f204d41103e6fe20)
This paper is focused on the specific aspects of designing membrane structures that have specific requirements, such as form-finding and cutting pattern generation. An integral part of the design of these structures is the process of finding suitable prestressed shapes and generating cutting patterns. The text briefly describes two basic processes in the design of membrane structures. The physical principles are explained and the individual theses illustrated by examples.
RFEM and RSTAB are able to cover a large number of branches in the building and construction industry with their generally usable structural frame analysis and FEM programs. Designing cable structures is thus also possible in both software solutions. Some assistance tools for modeling and design will be presented in the following text.
Cable and tensile membrane structures are regarded as very slender and aesthetic building structures. The partly very complex double-curved shapes can be found using suitable form-finding algorithms. One possible solution is to search for the form via the equilibrium between the surface stress (provided prestress and an additional load such as self-weight, pressure, and so on) and the given boundary conditions.
The RF-FORM-FINDING add-on module determines equilibrium shapes of membrane and cable elements in RFEM. In this calculation process, the program searches for a geometric position for the membrane and cable elements in which their surface stress/prestress is in equilibrium with the natural and geometric boundary conditions. This process is called form-finding (hereinafter referred to as FF).
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With the activated option 'Topology on Form-Finding Form' in Project Navigator - Display, the model display is optimized based on the form-finding geometry. For example, the loads are displayed in relation to the deformed system.
In RFEM, there is an option to couple surfaces with the stiffness types "Membrane" and "Membrane Orthotropic" with the material models "Isotropic Nonlinear Elastic 2D/3D" and "Isotropic Plastic 2D/3D" (add-on module RF-MAT NL Add-on Module for RFEM 5 erforderlich).
This functionality enables simulation of the nonlinear strain behavior of ETFE foils, for example.
The "Orthotropic | Fabric | Nonlinear Elastic (Surfaces)" material model allows you to define prestressed fabric membranes using the representative microstructure-solid element model – RVE.
By considering the fabric geometry in the microstructure model, the corresponding transversal strain effect can now be considered for all force conditions in the membrane.
The Ponding load type allows you to simulate rain actions on multi-curved surfaces, taking into account the displacements according to the large deformation analysis.
This numerical rainfall process examines the assigned surface geometry and determines which rainfall portions drain away and which rainfall portions accumulate in puddles (water pockets) on the surface. The puddle size then results in a corresponding vertical load for the structural analysis.
For example, you can use this feature in the analysis of approximately horizontal membrane roof geometries subjected to rain loading.
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