Calculation Of Pneumatic Structures Like Airhalls or Foil Cushions

 Key Principles

  • Internal Pressure: Pneumatic structures maintain their shape and stability through a slightly higher internal air pressure than the external atmosphere.
  • Membrane Behavior: The flexible membrane (single or multi layers) acts in tension, carrying the loads caused by internal pressurization, external loads (wind, snow), and its own weight.

Calculation Stages

  1. Form-Finding

    • Specialized Software: Programs designed for form-finding and membrane analysis are crucial (examples: Easy, NDN, etc.).
    • Input: Initial geometry (often basic shapes like spheres, arches, etc.), material properties, and target internal pressure are defined.
    • Output: Software determines the equilibrium shape of the inflated structure, providing the necessary geometric information for further analysis.

  2. Load Analysis

    • Static Loads:
      • Internal pressure
      • Self-weight of the membrane
      • Snow load (if applicable)
    • Dynamic Loads:
      • Wind loads (often the critical factor) determined per relevant codes.
      • Seismic loads (location-specific)

  3. Structural Analysis

    • Finite Element Analysis (FEA): Specialized FEA software can simulate the stresses and strains within the membrane as it deforms under different loading scenarios.
    • Nonlinear Analysis: Due to the membrane's nonlinear behavior, the software solves for the structure's behavior in an iterative manner as loads and geometry change.

  4. Detailing and Design

    • Cables and Anchorage: For larger structures, cables or nets may provide additional reinforcement. Calculations determine cable forces and proper anchorages to the ground.
    • Openings: Analysis of stresses and deformations around doors, vents, and connections to other structures.
    • Safety factors: Appropriate safety factors are applied to all calculations.

Specific Considerations for Pneumatic Structures

  • Material Properties: Accurate nonlinear stress-strain models for the specific membrane material are essential.
  • Pressure Control: Systems are needed to maintain a constant internal pressure differential, counteracting potential leaks or changes in environmental conditions.
  • Creep: Over time, some membrane materials may experience creep (deformation under sustained load), which needs to be factored into long-term performance calculations.
  • Wrinkling: The analysis should evaluate potential wrinkling areas, as this can lead to stress concentrations and potential failure.

Software Tools

  • Form-Finding: Easy, NDN, Rhino with Grasshopper plugins
  • FEA: Sofistik, Oasys GSA, Karamba 3D, RFEM (sometimes in conjunction with form-finding software)

Important Notes:

  • Standards: Adherence to relevant codes and safety standards is critical for pneumatic structures.
  • Collaboration between engineers, architects, and membrane specialists leads to successful designs.

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