Membrane structures rely on double curvature to effectively resist applied loads. Imagine being on a flat cloth where the applied snow can only be resisted by the tension in the horizontal fibers, it's kind of like keeping the catenaries on a suspension bridge level and they still carry the weight of the road deck.

In the classical hyperbolic paraboloid (Figure 1), any point on the membrane surface can be constrained by the corner points. The flatter the membrane structure, ie the smaller the height difference between the high and low points, the greater the aggregate load on the corners. The inflatable fabric structure is a synchronous elastic form in which a constant air pressure causes the membrane structure to expand into a shape with double curvature. Other common ballistic forms are conical (Figure 2) and domed (Figure 3).                                                                                                    

Almost all tensile membrane structures come from one or both of these three shapes. The surface is derived from one or a combination of two of these three shapes, and the surface of the membrane adopts a similar characteristic double curvature.

Prestress is the tensile force introduced into the canopy during installation. The shape of the membrane surface is determined by the ratio of the prestress in the two principal directions of curvature. These are established during computer form generation and the absolute value of the calculated prestress is sufficient to keep all parts of the membrane under tension under any load condition.

Any applied live load will be taken up by redistributing the stress within the membrane. If this causes any part to go into compression, i.e. relax, a crease will appear. Also, if the prestress is not high, snow loads may cause water accumulation etc.