Practical Aspects of the Design and Construction of a Small Cable Roof Structure

Cable roof structure s ha ve only become widespread in large span structures in the latter part of the twentieth century. However, they still represent a relatively new form of roof construction, especially as in the present case of a small span innovative structural solution. The contribution of this text to the structural engineering community lies in the increased interest in building simple cable roof structure s . Since its completion in September 1996, this small cable roof structure has been recognized as an interesting architectural and structural example. The text describes aspects of the design and construction of a small cable roof that was designed as a roof for an open-air theater stage for the city of Sao Jose do Rio Pardo, Sao Paulo, Brazil. A cable network, in the shape of a hyperbolic paraboloid surface, is anchored in a reinforced concrete edge ring. The projection of the ring’s axis onto the ground plane is an ellipse. Workers with specialized training were employed in the various stages of the construction, which was completed in September 1996.

• Cable Roofs
• Hypar Roofs
• Tension Structures

1. Introduction

The cable roof network, initially in the form of a hyperbolic paraboloid surface, is anchored in a ring of reinforced concrete whose axis projects an ellipse in the horizontal plan. The larger and smaller axes of the ellipse measure 20.00 m and 13.00 m, respectively. The network is formed by an orthogonal mesh 10 by 6, which is parallel to the ellipse axes. Both end points of the larger axis are 1.75 m below the surface center, while both end points of the smaller axis are 1.00 m above the surface center. The center of the surface is 4.50 m above the ground. A wire rope with diameter of 1 inch (25.4 mm) and composed of galvanized steel wires of high resistance was specified for the cables. Cable clamps were used at the intersection of two cables and purlins were fixed over the cable clamps in the direction parallel to the ellipse’s smaller axis. A pre-painted steel sinusoidal sheet was used for roof cladding. The cross section of the edge ring is rectangular measuring 1.00 m wide by 0.45 m high. The edge ring axis follows the form of the hyperbolic paraboloid surface. The ring is sustained by four identical reinforced concrete columns with 3.71 m high and rectangular cross section measuring 0.25 m by 0.50 m. The axis of the smaller moment of inertia of the rectangle is tangent to the ellipse equation. The structure is shown in Figure 1. Notice the rotation of the cross section of the edge ring.

2. The Hyperbolic Paraboloid Surface Equation

The hyperbolic paraboloid surface, which is necessary for the description of the undeformed configuration of the cable network, can be written as:

The value of A is equal to −1.75 m, the value of B is equal to 1.00 m, the value of a is equal to 10.00 m and the value of b is equal to 6.50 m.

3. Finite Element Discretization of the Structure

The finite element discretization of the structure is shown in Figure 2. The cable network was discretized with 96 cable elements. Reference [1] describes this element and explains a procedure to tension the cable network. The edge ring was discretized with 72 beam elements, of the type often used in the linear analysis of structures. This element is suitable because small displacements are expected for the edge ring. The discretized edge ring is defined by a closed poly-

Figure 1

Structure

Figure 2

Structural model

gonal line, whose vertexes belong to the hyperbolic paraboloid surface. Only one beam element was used for the discretization of each column. Reference [2] is a public domain 3D finite element program for the design and analysis of light structures. The program element library includes cable elements, membrane element, frame element and spring element. The computer source code written in Ada95, the executable code for Windows and examples is available for download. The input files used to analyze this structure are included as example number 2.

Figure 3 shows the node numbering of the structural model. Column 1 is linked to nodes 6 and 73, column 2 is linked to nodes 30 and 74, column 3 is linked to nodes 42 and 75 and column 4 is linked to nodes 66 and 76. The connection between the edge ring and the column can obstruct the ring’s rotation about its axis, favoring the appearance of torsional moment in the ring. To minimize this torsional moment, the columns were hinged at the ring connection and clamped at its the base. Moreover, the axis of the smaller moment of inertia of the column’s cross-section was placed tangentially to the ellipse equation, because the pinned hypothesis for the connection will not be verified perfectly in the real structure.

4. Material Specifications

A wire rope with a diameter of 1 inch (25.4 mm) and composed by 37 galvanized steel wires of high resistance was specified for the cables. The metallic area is equal to 3.829170 cm², the elastic modulus is equal to 14710 kN/cm², the break force is equal to 456 kN, and the thermal coefficient is equal to 0.0000115/C. Reference [3] discusses the benefits of structural cables previously submitted to tensioning to eliminate the initial lengthening caused by the helical configure-

Figure 3

Binding cable connected to the edge ring

tion of the wires. The specification for the concrete is given by an elastic modulus equal to 2746 kN/cm², transverse elastic modulus equal to 1144 kN/cm², and a specific weight equal to 24.5 kN/m³.

5. Loading Cases

At the time of the construction, no wind loads guidelines were available for this roof shape. In the absence of guidelines and considering the characteristics of the region where the structure was built, an ad hoc estimate for the design wind loads was a downward pressure of 470 Pa and an upward pressure of 706 Pa. For the cable network, the wind load was considered acting orthogonal to the hyperbolic paraboloid surface, which is the undeformed configuration of the cable network. Reference [4] provides guidelines for loading cases and corresponding safety factors for structural applications of steel cables for buildings. Notice that a deformed configuration of the cable network does not define a hyperbolic paraboloid surface. For the edge ring, the load of the lateral wind was considered acting orthogonal to its faces. The eight loading cases considered for the design of the structure are shown in Table 1, where L is the loading case number, SF is the safety factor for the cable force, DT is the temperature change, (1) is the vertical pressure applied to the cable network due to the permanent or live load, (2) is the orthogonal pressure applied to the cable network due to the wind load and (3) is the orthogonal pressure applied to the edge ring due to the lateral wind load. The direction of the lateral wind is horizontal and is further determined by an angle specified in degrees in relation to the X-axis.

6. Cable Network

Reference [1] describes the cable element. The cable element has three states:

Table 1

Loading cases

References

1. Arcaro, V. (2002) A Simple Procedure for Analysis of Cable Network Structures, Proceedings of the Fifth International Conference on Space Structures, Surrey, 19-21 August, Thomas, Telford, 585-592. https://doi.org/10.1680/ss5v1.31739.0063

2. LIGHTS Computer Code (1996) https://www.arcaro.org/tension/

3. Buchholdt, H.A. (1985) Introduction to Cable Roof Structures. Cambridge University Press, Cambridge.

4. American Society of Civil Engineers (1996) Structural Applications of Steel Cables for Buildings (ASCE 19-96). American Society of Civil Engineers, Reston.

5. Nocedal, J. and Wright, S.J. (2006) Numerical Optimization. 2nd Edition, Springer-Verlag, Berlin.

6. ABNT-NBR 6118 (1993) Design of Concrete Structures—Procedure. Associacao Brasileira de Normas Tecnicas, Rio de Janeiro.

7. Leonhardt, F. and Monnig, E. (1986) Vorlesungen über Massivbau: Teil 2 Sonderfalle der Bemessung im Stahlbetonbau (in Portuguese, Rio de Janeiro, Interciencia).

8. Structurae (2017) https://structurae.net/

9. Tensinet (2017) http://www.tensinet.com/