1. Structural systems

IntroductionThe development of the high-tensile steel cable has made it possible forman to transmit large axial forces in tension at a relatively low cost. Theever-increasing spans and elegance of the modern suspension and cablestayed bridges are the most obvious examples of the economical way inwhich large loads can be supported by the use of members in tension.

The use of steel cables in the design of long span roofs has onlyrelatively recently begun to interest architects and engineers. It isprobably true to say that the cable roof structure which first fired theirimagination was the building of the North Carolina State Fair Arena atRaleigh, USA. The arena was completed in 1953. The main structure ofthis building consists of a cable net supported between two intersectingconcrete arches, each inclined at approximately 21° to the horizontal(Fig. 1.1). Stiffness of the roof was achieved through curvature andpretensioning of the cables. The way in which the tensile forces in thecables are balanced by the compressive forces in the arches is shown inFig. 1.2. Since the completion of the Raleigh Arena different roofstructures using steel cables have been studied, developed and built invarious parts of the world.

Cable roofs have a wide field of application and have been used tocover such differing buildings as stadia and sports halls, swimming poolsand water reservoirs, concert halls and theatres, cooling towers, hangars,warehouses and factories. Experience has shown that cable roof struc-tures have considerable architectural, structural and economical poten-tial. Their use has often resulted in attractive buildings, with structuresthat are stable and efficient since a large proportion of the main load-carrying members are in tension.

The use of cable roof structures has in the past mainly been consideredfor buildings which require large column-free areas. One reason for this isundoubtedly the general belief that they are an economical propositiononly when used to bridge large spans. There is, however, a considerableamount of evidence that cable structures also can be competitive alter-natives for smaller span structures. With the continuing rise in the cost ofsteel, the use of cables is steadily becoming a more attractive economicalternative to conventional forms of structures such as portal and spaceframes.

1

Introduction to cable roof structures

Tension roofs can be divided into categories based on whether the roofcladding is supported by:

(a) simply suspended cables(b) pretensioned cable beams(c) pretensioned cable nets(d) pretensioned cable grids.

The total structure may be either self-balancing or non-self-balancing. Aself-balancing building is one in which the structure supporting the cableshas a geometry which permits the forces in the cables to be balancedinternally. A non-self-balancing building is one in which the geometry ofthe building supporting the roof structure is unable to resist the cableforces without the aid of ground anchors.

Simply suspended cable structuresThe cladding of roofs which are rectangular or trapezoidal in plan can besupported by a series of simply suspended cables hanging in vertical

Fig. 1.1. The North Carolina State Fair Arena at Raleigh, USA

Fig. 1.2. The action of the main balancing forces in the Arena at Raleigh, USA

Structural systems

planes (Fig. 1.3). In roofs which are circular or elliptical in plan the cablesare suspended radially and attached at the perimeter of the roof to acompression ring and at the centre to a tension ring (Fig. 1.4). For roofswhich, in plan, are ellipsoids or of similar shapes, a combination of theabove two geometrical patterns of suspension may be used. This isachieved by constructing the tension ring in two halves and connectingthese with two horizontal cables, as shown in Fig. 1.5. The result is anelongated form of tension ring which permits cables to be suspended inparallel planes in the central area of a roof and in radial planes at eitherend.

For basket-shaped roofs as described above, drainage must be pro-vided centrally. Systems of this type have no stiffness. To reduce themovements which will be caused by any form of applied loading the roofcladding must either be very heavy or act as a shell. Obviously, for simplysuspended cable roofs, concrete is the most suitable roofing material. The

Fig. 1.3. Simply suspended cable roof with the cables suspended in parallel planes

Fig. 1.4. Simply suspended cable roof with the cables suspended in radial planesbetween an inner tension ring and an outer compression ring

Introduction to cable roof structures

Fig. 1.5. Simply suspended cable roof with the central cables suspended in parallelplanes and the cables at either end suspended between an inner split tension ring andan outer curved beam

concrete may be placed either as prefabricated slabs or in situ. Bothmethods are used. If the concrete is placed in situ, plywood or insulatingpanels clamped underneath the cables may be used as shattering. In eithercase it is advisable to apply a certain amount of pretension to the cablesin order to stiffen the structure during construction and to prevent cracksforming in the finished roof. In the case of circular structures, this canand has been done by jacking the central tension ring downwards andreleasing it after the concrete has set. When prefabricated slabs are used,prevention of cracking can also be achieved by placing an overload onthe roof before inserting grout between the slabs, and then removing theload when the grout has set.

Pretensioned cable beam structuresLighter and stiffer systems than those above can be achieved if a secondset of cables with reverse curvature is connected to the suspension cables(Figs 1.6(a), (b) and (c)). The resulting systems or cable beams will bequite stiff if tensioned to a level which ensures that both cables remain intension under any combination of applied loading. For convenience weshall refer to the beams shown in Figs 1.6(a), (b) and (c) (and Fig. 1.7) asconvex, concave and convex concave beams respectively. In the first ofthese beams the connecting members are in compression, in the second intension and in the third the two outer members are in tension and theremainder in compression.

Figure 1.8 shows a cable truss which was developed by the Swedishengineer, David Jawerth. Here the ties are inclined and connected in sucha way that they, together with the suspension and pretensioning cables,form a system of pretensioned triangles. Thus, after having been preten-sioned, this truss is a structure, as opposed to the beams shown in Fig. 1.6

Structural systems

(a) Convex cable beam

(b) Concave cable beam

(c) Convex-concave cable beam

Fig. 1.6. Pretensioned cable beams: (a) convex cable beam; (b) concave cablebeam; (c) convex concave cable beam

which are structural mechanisms. The level of pretension is usually suchthat the ties remain in tension when subjected to dead load only. Theapplication of increasing live load, however, will cause some of thediagonals to go slack until only half of them remain in tension. Thetruss changes to a structural mechanism at the stage when one or more ofthe ties go slack. The Jawerth truss has been successfully used in a largenumber of buildings with spans ranging from approximately 15 to 100 m.

For roofs which are rectangular, trapezoidal, circular or elliptical inplan, cable beams may be arranged in geometrical patterns similar tothose described for simply suspended cable structures. Examples of sucharrangements are shown in Figs 1.9(a), (b) and (c).

Multi-span cable beam constructions such as those shown in Figs1.10(a), (b) and (c) can be used with advantage either where a number oflarge spans can be interconnected or where column-free interiors are notrequired. The advantage of multi-span constructions lies in the fact thatthe anchor forces are a function only of the size of the individualmaximum span and not of the number of spans. In cases where interiorcolumns can be permitted, the use of multi-span constructions not onlyreduces the size and thence the cost of the anchors required, but also

Introduction to cable roof structures

Fig. 1.7. Concave cable beam with diagonal ties: the beam was developed byD. Jawerth and has been used in a large number of constructions

Fig. 1.8. (a) Convex cable beam structure with corrugated metal roof decking;(b) concave cable beam structure with corrugated metal roof decking; (c) convexconcave cable beam structure with corrugated metal roof decking

Structural systems

(c)

Fig. 1.9. (a) Radial convex cable beam structure with inner tension rings and anouter compression ring; (b) radial concave cable beam structure with inner tensionrings and outer compression rings; (c) radial convex concave cable beam structurewith inner tension rings and outer compression rings

decreases the height, dimensions and foundation loads of the externalcolumns.

The reduction in height results in a saving in cladding costs and reducesthe internal volume which needs to be heated. For large buildings thetotal savings in cost can be considerable.

Pretensioned cable net structuresThe third type of cable roof structure is that in which the suspension andpretension cables all lie in one surface and form a large net. As with cablebeams, for a net to be stiff the cables must be in tension and it followsthat the geometry of a net must be such that all the surface is anticlasticor saddle-shaped. Local 'baskets' will result in areas where the cablescannot be properly tensioned, and the roof will be soft and subjected tomovements which may damage the cladding. In large roofs, even flatareas ought to be avoided, as such parts of a roof may be subjected toflutter. If, for architectural reasons, basket-formed or flat areas cannot beavoided, internal or external ties or some other means of stiffening theroof will have to be considered.

Flat nets are not very stiff and therefore not a practical proposition forlarge roofs. They may, however, be used for smaller roofs provided theboundary makes it possible to provide a high level of pretension andarrangements can be made for adequate drainage. The latter can be

Introduction to cable roof structures

-r^cxn\

(a)

K(b)

K(c)

Fig. 1.10. Multi-span cable beam structures

ensured by having a sloping roof surface, or in the case of flat horizontalroofs by central drainage.

The geometries of cable nets are functions of their points of supportand the tensions in the cables. They may be designed to resemble tent-likestructures with masts and edge cables as shown in Figs 1.11 (a) and (b), orwith stiff boundary members such as beams, arches and space rings as inFigs 1.12(a), (b), (c) and (d). Nets like that shown in Fig. 1.11 (a) may alsobe used in multi-net constructions, see Fig. 1.13. Cable nets with mastsand edge cables tend to be less stiff and require more complicated detailsthan those with stiff boundaries. For the general contractor they are alsolikely to be more difficult to erect.

As in the case of cable beams, the clamps connecting the cables mustexert sufficient pressure on them to prevent slipping. Any movement ofthe clamps will result in losses of cable tension which again will result inreduced stiffness. It is therefore advisable to arrange the geometry of thesuspension and pretension cables so that the resulting forces along thecables due to the action of clamps are minimized. This will also reducethe size and the cost of the clamps.

Pretensioned cable grid structuresCable grids may be considered as double-layer nets or as multi-direc-tional systems of intersecting cable beams. Several different types havebeen proposed. However, from the point of view of structural efficiencyand practical and geometrical considerations, only those which can beconstructed as two-, or possibly three-directional convex, concave andconvex concave systems are practical possibilities. Because of the geo-metries of cable beams the use of grids is limited to roofs which are eithercircular or elliptical in plan. The construction of cable grids leads to thesame shapes as those created using the radial cable beam systems (Figs1.14(a), (b) and (c)). They are therefore best suited for self-balancingstructures.

8

Structural systems

Fig. 1.11. (a) Saddle-shaped cable net structure with edge cables; (b) cable netstructure with edge cables and an internal column

Introduction to cable roof structures

Fig. 1.12 (above and facing), (a) Saddle-shaped net with edge beams. Because ofthe bending moments in the edge beams this form of construction is suitable only forrelatively small spans, (b) Saddle-shaped cable net supported between two verticallyerected arches. This is a diagram of the Ice Hockey Stadium in Tampere, Finland.Because the arches are vertical, back-stays with anchors had to be provided tobalance the tensile forces in the suspension cables, (c) Saddle-shaped cable netsupported by a space ring. This form of construction should be designed with arelatively flexible ring beam to permit redistribution of the forces in the cablescaused by dead and live loads. The curvature of the net should be relatively small inorder to avoid excessive horizontal displacements of the ring beam, (d) Cable netstructure with four outward leaning arches

10

Structural systems

Fig. 12—continued(d)

Compared with the radial systems, the absence of a tension ring leadsto a more even distribution of cables and the use of longer cable units.This again reduces the number of cable terminals required. Because thecable beams in grid systems are self-aligning, the forces required to beexerted by any clamps are small. In practice the use of clamps mayprobably be omitted. Against the above advantages must be set theslightly greater difficulties in detailing the ring beams at the points ofcable attachments.

General structural characteristicsBecause most pretensioned cable structures are structural mechanismsand not true structures, and the high-tensile steel used in cables cansustain strains which are approximately six times those permitted inordinary constructional steel, cable roofs are classified as nonlinearstructures. Their stiffness tends to increase with an increase in displace-ment as long as all the cables remain in tension. In consequence, the useof linear methods of analysis tends to overestimate both displacementsand forces.

Initially the analysis of pretensioned cable structures was carried outby developing nonlinear membrane theories. However, with the devel-opment of high-speed computers this method of approach was soonovertaken by developments of nonlinear finite element methods whichimplicitly or explicitly are based on minimization of the total potentialwork. Methods for predicting the static and dynamic response of linearand nonlinear skeletal structures based on the explicit minimization ofthe total potential work are given in Chapters 4 and 5.

The stiffness of cable structures is mainly a function of:

(a) the curvature of the cables(b) the cross-sectional areas of the cables(c) the level of pretension(d) the stiffness of the boundary and support structure.

11

Introduction to cable roof structures

Fig. 1.13. Multi-span cable net structure: each net is of the type shown inFig. 1.11 (a)

Fig. 1.14. (a) Circular convex cable grid supported by a horizontal ring beam;(b) circular concave cable grid supported by two horizontal ring beams; (c) circularconvex concave cable grid supported by two horizontal ring beams

12

Structural systems

The cladding will not, unless it is in the form of a concrete shell,significantly increase the stiffness of a roof. It is, however, the majorsource of structural damping.

As a general rule, cable sags between 4% and 6% of the span will givesatisfactory structural behaviour, provided the factor of safety for thecables is not less than two and the level of pretension is such that no cablegoes slack under any combination of loading. Cables going slack willcause a softening of the structure which may lead to deformations whichmay damage the cladding. In general, increasing pretension appears tohave a greater stiffening effect on net structures than on beam and gridstructures. Pretensioned cable structures are not, unlike many other typesof structure, subject to instability problems. Experience has also shownthat they are dynamically stable provided the degree of curvature andlevel of pretension are sufficiently high.

The effect of any fire, with consequent increase in temperature, is toreduce the tension in the cables and hence also the forces in the boundarystructure. Since the forces in the cables due to pretension will be lost at atemperature well below that at which the strength of steel is impaired, thesafety against collapse is initially increased.

The effects of variations in curvature, cable dimensions and pre-tensions may be studied by referring to the nondimensional graphs givenin Chapters 8 and 9. Cable roof structures are inherently economicalstructures because the main load-carrying members which support theroof loading are subjected to tensile forces only; they are relatively simpleto construct and can in most cases be built by small teams of erectors. Asthe cost of material, labour and transport increases, their cost effective-ness, compared with alternative forms of structure, is likely to improve.

Bibliography1.1 Otto, F. Tensile structures. MIT Press, Cambridge, MA, 1962.1.2 Esquillan, N. and Saillard, Y. (eds). Hanging roofs. {Proc. I ASS

Colloquium on Hanging Roofs, Continuous Metallic Shell Roofs andSuperficial Lattice Roofs, Paris, July 1962.) North-Holland Publish-ing Co., Amsterdam, 1963.

1.3 Glaeser, L. The work ofFrei Otto. New York Graphic Society, 1972.1.4 Mollmann, H. Analysis of hanging roofs by means of the displacement

method. Polyteknisk Forlag, Lyngby, 1974.1.5 Kullmann, E. Nets in nature and technics. Institute for Lightweight

Structures, University of Stuttgart, 1975.1.6 Krishna, P. Cable suspended roofs. McGraw-Hill, 1978.1.7 Kollar, L. and Szabo, K. Structural design of cable-suspended roofs.

Ellis Horwood (in press).

13