Membrane Structure Prestress Analysis

The core model treats the membrane as a flexible cable under combined tension. The total stress is the sum of the initial pretension stress and the additional bending-like stress caused by external loads (wind + snow).

Where:
\(\sigma\) = Total membrane stress (Pa or N/mm²).
\(T\) = Applied pretension force per unit width (N/m).
\(t\) = Membrane thickness (m).
\(q = q_w + q_s\) = Total distributed load from Wind and Snow (Pa or N/m²).
\(L\) = Span length (m).
\(f\) = Camber height, calculated as \(f = (f/L) \times L\) (m).

A key stability criterion is that the pretension must be sufficient to prevent the membrane from going slack under load. The minimum required pretension is derived from the equilibrium of a cable under uniform load.

Physical Meaning: This is the absolute minimum tension needed so that under the design load q, the net tension at the membrane's center is still positive (i.e., not slack). In the simulator, if your set T is close to or below this value, the structure risks instability and large deflections.

Stadium Roofs (like the Munich Allianz Arena): PTFE-coated fiberglass membranes are prestressed over long spans to create weatherproof covers. Engineers use analysis like this to balance snow load in winter with wind uplift forces, ensuring the iconic shapes remain stable and safe for decades.

Air-Supported Structures (Domestic Domes): These rely entirely on constant internal air pressure to provide the prestress. The same principles apply, where the "pretension" is analogous to the pressure, and the analysis ensures the fabric can handle external wind loads without excessive deformation.

ETFE Cushion Façades (like the Beijing Water Cube): Multi-layer ETFE foil cushions are prestressed by inflating them to a specific pressure. The analysis determines the optimal initial stress so that the cushions can withstand hail impact, snow accumulation, and significant wind pressure differentials.

Tensioned Fabric Canopies & Sunsails: Common in airports, shopping malls, and public plazas, these smaller-scale structures use the same physics. Engineers specify the pretension during installation so the canopy maintains its shape and drains rainwater properly under varying wind loads.

First, there is a misconception that "higher pretension is always better." While it's true that the shape stability index increases, it places excessive load on the tensile strength of the membrane material itself, the supporting masts and foundations, and the edge fixing hardware (edge cables or clamps). For example, applying excessively high pretension to a 20m span PVC membrane risks failure of the welded seams or bolts before the membrane stress reaches its allowable limit. In the tool, areas where the "Required Weld Strength" warning turns red indicate that, in a real structure, very costly reinforcements would be necessary.

Next, oversimplifying load combinations. The tool simply adds wind pressure and snow load, but actual design codes (like the Building Standards Act) set combination factors, considering the low probability of maximum snow and maximum wind occurring simultaneously. Simply summing all loads often leads to overdesign. On the other hand, the setting of "sag (rise)" is also an oversight. Taking an excessively large rise for aesthetic curvature, as seen from the formula for required minimum pretension \( T_{min} = \frac{qL^2}{8f} \), increases the denominator and thus reduces \( T_{min} \). You might be tempted to think "less tension is needed," but this actually means the structure becomes more susceptible to wind-induced vibration (flutter) and rainwater ponding. In practice, balancing shape and function is key.