High strength steel cables have been used extensively over the past twenty five years for space roof structures. There are two different possibilities when using steel cables in roof structures.The first possibility, consists of using the cables only for suspension of the main roof structure, which can be either conventional, e.g. beams, cantilevers, etc., or a space frame. In this case, the main roof structure, instead of being supported, is actually suspended from steel cables above the roof, which transmit the tensile forces to appropriate anchorages (Figure 1). They are cable-stayed roofs.
Fig: 1. Cable-stayed roofs
There are many examples of this type of construction used as industrial buildings where the roof structure, either as a single or as a double cantilever, is suspended from cables, which in turn are anchored on robust pylons above the roof level.
In this type of construction, the cables behave as simple suspension elements, while the roof structure itself behaves like a normal load resisting unit, subject to moments, shears, and other kinds of action effect. It is expected that the suspending elements remain in tension, even under wind uplift, due to the dead weight of the roof.
The second possibility is represented by those roof structures where the steel cables are effective members of the roof structure itself, and not just conveyors of forces from the structure to the anchorages. In this type of construction (tension structures), the cables themselves resist the various external loads. Their particular behavior has deeply influenced the structural forms used and has imposed new methods of execution.
Tension structures may be categorized as:
(a) Single-layer cable systems (Figure 2a)
Fig: 2. Single and double cable systems
(b) Double-layer prestressed cable truss systems (Figure 2b)
(c) Prestressed tensile membrane systems (Figure 3)
Fig: 3. Prestressed tensile membrane system
Tension structures are used to cover stadia, arenas, swimming pools, recreation halls and other buildings where a large area for public assembly and exceptional aesthetic effect are required simultaneously.
There are some particular problems associated with these cable-stayed and tension roof structures.
A first problem derives from the fact that the cable is flexible. It assumes a shape compatible with the applied loads whilst architectural and building requirements demand that the structure has a definite form. Any deviations from that form due to the action of the applied loads, must be kept to a minimum. To meet this requirement, a pretension must be introduced into the structure, which must be compatible with the desired shape, and when combined with the applied loads, must maintain the deformation between specified limits. Design may therefore involve use of mathematical 'form-finding' procedures, implemented by appropriate software.
Another feature of these structures is their geometrically non-linear behaviour. Deformations play an essential role in the analysis and the principle of superposition of effects is not valid.
Finally, an important problem associated with these structures is their sensitivity to aerodynamic instability, e.g. flutter. This sensitivity imposes special requirements on the design and the constructional details of these systems, particularly those which use membranes made of lightweight fabric as cladding.
The requirements of stiffness under transverse loading and anchorage are major form determinants for cable structures, and these are examined in the following sections.
Single cable structures are characterized by their flexibility, Figure 3. They require stiffening to prevent a change of shape with each variation in load and to make them capable of resisting uplift due to wind, Figure 5. Gusty winds can produce oscillations, unless damping is provided to the structure.
Fig: 4. Single cable: Load/shape relations
Fig: 5. Cable stability: Plane systems
The principal methods of providing stability are the following:
i. Additional permanent load supported on, or suspended from, the roof, sufficient to neutralize the effects of asymmetrical variable actions or uplift Figure 5a).
This arrangement has the drawback that it eliminates the lightweight nature of the structure, adding significant cost to the entire structure.
ii. Rigid members acting as beams, where permanent load may not be adequate to counteract uplift forces completely, but where there is sufficient flexural rigidity to deal with the net uplift forces, whilst availing of cables to help resist effects of gravity loading (Figure 5b).
Fig: 5. Cable stability: Plane systems
iii. Rigid surfaces behaving as inverted shells or vaults, where uplift forces are countered by the in-plane compressive rigidity of the structure (Figure 5c).
iv. Secondary cables prestressing the main cables so that these remain in tension under all conditions of load. Such prestressing can take a variety of forms:
· a stayed (guyed) arrangement, wherein the main cable is stayed to other elements or to the ground, as in the case of guyed trusses (Figure 5d).
· A planar arrangement of suspension and stabilising cables, with opposite curvatures cables, Figure 4e. This structure reacts elastically to all changes of shape provoked by the externally applied loads. This principle can be extended to permit creation of space trusses, or structures of revolution.
· An orthogonal or diagonal arrangement of suspension and stabilising cables, with opposite curvatures, forming an anticlastic (saddle-shaped) surface, Figure 5f and 6.
Fig: 6. Cable stability: anticlastic cable
Figures 4 and 5 shows the application of these general principles to cable and cable-stayed systems, whilst Figure 6 details the structural actions of pre stressed cable truss systems. Accurately defined, a cable truss system has a triangulated structural form which increases stiffness, particularly under non-symmetric loading. However, the term is also frequently applied to the cables with opposite curvature shown in Figure 5e.
Fig: 7. Cable stability: cable trusses
The orthogonal or diagonal arrangement of anticlastic cables shown in Figure 6 can also be extended to the conical form shown in Figure 7. The increasing use of horizontal ring cables, from Figure 8 to 8c enhances stiffness against asymmetric loading. Because of the difficulty of anchoring a large number of cables at a point, the top is usually flattened as shown in Figure 8d.
Fig: 8. conical membrane
Fig: 9. Complex tent system with multiple interior supports and internal anchorages
Cable stayed structures generate a requirement for the anchoring of tension forces. Some of the commoner solutions are:
i. Vertical and horizontal reactions provided by axially loaded elements - stayed columns used with ground anchors (Figure 10a).
Fig: 10. Cable anchorage systems
ii. Vertical and horizontal reactions provided by flexural elements i.e. cantilever columns (Figure 10b) or legged columns (Figure 10c).
iii. Vertical columns acting with horizontally loaded edge beams which transfer horizontal reactions to rigid diaphragms (Figure 10d).
iv. Inclined walls, or vertical cylindrically curved walls (Figure 11a).
Fig: 11. Cable anchorage system-2
v. Form-related boundary shapes, creating, in some cases, a closed self-equilibrating system of tension and compressive forces and requiring no tension ground anchors (Figure 11b).
The magnitude of forces in stayed columns and in diagonal stay restraining cables is reduced by inclining the columns. In some symmetrical structures lateral thrust is balanced by means of struts at foundation level.