Anticlastic

The necessity of adequate local curvature in tensile membranes is axiomatic. In the tent-form structures this generally means finding an anticlastic prestressed form with appropriately small radii of curvature.

Horst Berger expresses a similar sentiment even more bluntly in "Light Structures - Structures of Light" - on page 50:

All tensile structures must have anticlastic shapes.

It certainly seems as though the tensile structure industry's products are dominated by structures which put their membranes into configurations which exhibit anticlastic curvature.

Some pleated designs which use parallel ridge and valley cables make use of classical anticlastic surfaces with small radii - e.g.:

Matrix Marquee

However, looking at many of the existing deployed pleated designs, the extent of the anticlastic curves is often very slight - sometimes practically to the point of being non-existent.

Consider, for example the surface of the Komatsu dome.

Komatsu Dome

There may be a case to be made that the membrane surface has a slight curvature in one direction - but the tension in the cables seems to do a pretty good job of eliminating any doubly-curved surfaces.

Use of an anticlastic surface is an effective way of stabilising a membrane in space.

Pleating takes another approach to stabilisation - it ensures that the membrane is always close to a steel cable.

By regularly supporting the fabric, the importance of ensuring that the fabric itself forms anticlastic surfaces declines.

In fact the combination of regular membrane stabilisation and the fact that no membrane is parallel to the ground means that prestressing the membrane is not so much of an issue as it would be if the membrane were playing more of a structural role.

In pleated designs, the membrane acts a bit like a guitar string - pulled between two adjacent cables. Like a guitar string, it offers little resistance to small perturbations perpendicular to its surface - and can be expected to oscillate up and down. It lacks what engineers call linear stability: to a first order approximation, there is no restoring force opposing such small deflections.

However, unlike a guitar string, the membrane faces considerable damping from air resistance. In fact, such motion is nothing to be concerned about. The membrane is never very far from a cable - and so non-linear restoring forces kick in quickly.

Increasing anticlastic curvature

The following diagram shows one approach - involving the ridge cables not lying parallel to the valley cables.

Dallas Fort Worth Airport Terminal D

Anticlastic curvature and pleating

If the use of anticlasitic curved surfaces is considered to be axiomatic, it isn't hard to understand why pleated designs - that often hardly use that type of curvature at all - have been relatively overlooked.