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Going to the limits: structural basics

Continuing Education | September 1, 2010 | By:

To achieve the freedom of form that a fabric roof promises, strict rules must be obeyed if pitfalls and problems are to be avoided.

No type of structure—whether it uses steel, wood, concrete, masonry or some more exotic material—conveys such an image of freedom of form as the fabric tension structure. This image is at once fabric’s best selling point and the bane of fabric structure engineers.

Closer examination of fabric structure design reveals that the dramatic and voluptuous forms of fabric roofs actually respond to strict rules of form and shaping. And the properties of structural fabrics make the range of shapes available in fabric in some ways more limited than those in more conventional materials.

In every type of construction, conflict exists between the abstract form-giving goals of the architect and the practical limitations of engineered design and economical construction. Because of the contrast between the freeform appearance of fabric roofs and the inherent restrictions in their form, these conflicts can be particularly acute in tension structure design.

By understanding a few simple principles of fabric roof behavior, however, architects and designers can begin to understand some of the constraints on their design and conceive ways of achieving key design goals with structures that are structurally stable and economical.

Principles of design

It is easiest to conceive the way that a fabric roof carries a load by first considering it as a grid of individual fabric threads. A single thread, primarily because of its extreme slenderness, has considerable strength when pulled from the ends (put into tension), but negligible strength when either pushed on the ends (compressed) or loaded transversely at some point along its length (bent). [Fig. 1] Conventional structural materials, such as steel, concrete and wood, by contrast, are typically configured with cross-sections stout enough that a single linear element (analogous to a thread) has significant resistance to tension, compression and bending loads. [Fig. 2]

Extrapolating these ideas into a woven fabric material, we see that a flat sheet of fabric also is strong when pulled along opposing edges (put into tension), but weak when either compressed or bent. Taking advantage of the tensile strength of fabric while circumventing weaknesses related to its low resistance in compression and bending is the primary motive underlying the principles of shaping fabric tension structures.

Resistance to compression and bending are achieved primarily through the introduction of curvature and pretensioning into the fabric. In the same manner that curvature in suspension cables supporting a bridge deck provides resistance to vertical loads acting perpendicular to the bridge deck, the curvature in fabric provides resistance to wind or live loads that act perpendicularly to the fabric’s plane. [Fig. 3]

Because the weight of a bridge deck is usually in excess of any upward suction caused by wind, a bridge suspension cable needs to resist loads only in a downward direction. A fabric roof, however, has a large exposed “sail” area and minimal weight. The fabric roof, therefore, must generally resist wind loads that both push inward and cause suction outward on the fabric, in addition to dead and live loads that act vertically downward.

Because of this potential for reversal of load, fabric roofs generally can be made stable only by providing curvatures both inward and outward at all points of the fabric surface. In practice, this is achieved by curving the fabric fibers around one axis of the fabric in a convex manner and those around the other axis in a concave manner. Fabric or other surfaces having such opposing curvature are said to have anticlastic shapes. [Fig. 4]

Generating anticlastic shapes

Without anticlastic curvature, no fabric roof of significant size can safely resist varying loads. The architect who is able to visualize and manipulate anticlastic forms, however, gains access to the range of subtly elegant to wildly dramatic forms possible in tensioned fabric structures. This range of forms is achieved by manipulating the varying elements that support or restrain the fabric, elements that include cables, arches, masts, trusses and ring beams.

The roof forms that result can generally be classified either as saddles or tents, and these two types can be manipulated and combined to create the entire range of fabric roof shapes.

In the saddle, anticlastic shapes are generated by point, linear or curving perimeter supporting elements that use elevation variance to generate the doubly-curved surface [Fig. 5] Combinations of saddle shapes are created by using arches or similar curving elements to subdivide a given perimeter shape. [Fig. 6]

In a saddle, fabric curvature is generated because the perimeter supports (point, linear or curving) do not all lie within the same plane.

In a tent, the perimeter supports may all lie within one plane, but curvature is induced by connecting the fabric to a point inside the perimeter that is out of the plane of the perimeter supports. A center mast, perpendicular to the perimeter plane, for example, would induce curvature in this manner. Cones or inverted cone shapes result. [Fig. 7]

The configuration of the perimeter supports may be varied and additional point supports may be added to vary the shape of tent roofs, or tents may be used in combination, in the same manner as saddles.

The art of design

In tensioned fabric structures, the art of design lies in the skillful manipulation of supports to create shapes that are aesthetically and functionally satisfactory, economical, adequate in load-carrying ability and reliable. An inexperienced designer should be aware of some of the common pitfalls that make a design concept difficult or impossible to realize.

Inadequate fabric curvature

The additional stress fabric has under load is directly proportional to the curvature in the fabric. Flat shapes with large curvature radii in the fabric, therefore, will become overstressed or may require the addition of cable reinforcement to resist load safely. Flat fabric shapes often can have a clean-lined, elegant appearance, but they are generally practical only on small canopies.

Inadequate cable curvature

Like fabric, cables are sensitive to changes in curvature. If the “sag” in a cable along its length is halved, the increase in cable force under roof load will double. It is therefore impractical to design a fabric roof where the catenary cables along the free edge of a fabric roof pass straight from support to support without reasonable curvature. The curvature in ridge, valley and other cables that lie in the interior of the fabric roof varies with the curvature of the fabric roof itself and must be considered in conjunction with fabric curvature.

Inadequate mast termination

In the interest of achieving the simplest and most direct fabric roof form, it is inviting to try to terminate the fabric in a point at the top of a supporting mast. Unless a number of radiating cables are added to the structure to help distribute load into the mast top, however, the fabric must be terminated in a ring large enough to transfer the load from the entire fabric roof into the top of the mast without overstressing the fabric.

Excessive aspect ratio

Designing a roof with a large height difference between its peak and the perimeter supports results in a high “aspect ratio” between the height of the roof and its plan dimensions. Such a design tends to generate plenty of fabric curvature, but also increases the exposure of the roof to lateral wind loads and increases the area of fabric that must be used to cover a given plan area. A desire for a high profile shape with dramatic and voluptuous curves must be balanced against these considerations.

Long compression members

Long masts, arches or other compression members are prone to buckling and require large and heavy cross-sections to achieve adequate capacity. Excessive compression member length is generally related to excessive aspect ratio.

Reversals in curvature

I recently consulted on a project in which the architect desired a fabric roof shape akin to an eagle’s talon: nearly vertical at the base, curving inward to a section that is nearly horizontal, then sloping back upward to a peak that is again nearly vertical. The proposed shape is dramatic and probably achievable, but it required the development of rather heavy supporting trusses to achieve the doubly curved shape. And the structural design must address the fact that the fabric has no curvature at the “point of inflection” where the reversal of curvature occurs.

Unstable supporting structure

Because fabrics may be subject to rapid tearing and because rigid masts or arches present a significant threat to property and life safety in the event of their collapse, good practice requires that these supporting elements be stabilized by something other than the fabric itself. Rigid base connections can provide this, though typically at significant expense. In general, therefore, good designs make use of either cable nets in the plane of the fabric (common in European practice), guy cables connecting the top of the mast or arch down to grade, or crossed arch or A-frame designs in which the supporting elements are self-bracing.

Inadequate measures to prevent ponding

A significant problem can occur in fabric roofs that do not take into account the possibility of water accumulating in low spots of the roof. To prevent this “ponding” of surface water in the event of excess rain or accumulation of snow in colder climates, several points must be addressed:

  • Flat membranes should be avoided in long span applications where significant snow load may occur.
  • Analysis should demonstrate that there is minimal possibility for any area of the fabric to pass through zero slope before water reaches the edge of the fabric and ponding may occur.
  • Careful attention should be paid to the risk of stacking one roof or membrane above another in such a way that the upper canopy deposits substantial water or snow onto a lower canopy. Slopes may be reversed or gutters added to prevent this occurrence.

This list is both general and incomplete, and no effort has been made to quantify appropriate proportioning of the fabric roof. Through awareness of these potential design pitfalls, however, in combination with careful observation of successful built structures and consultation with an experienced fabric roof engineer, an architect or other designer can begin to conceive fabric roof forms that achieve aesthetic and functional excellence with forms that are safe, reliable and economical.

Craig Huntington is a practicing structural engineer, fabric structure designer and president of Huntington Design Associates, Oakland, Calif.

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