Wind action evaluation on tension roofs of hyperbolic paraboloid shape

Abstract

Within the Ph.D course in "design of structure" one of the authors is working on the design of tension roofs with medium to large span, with particular attention to their cable structure. This kind of structures are light and characterized by innovative construction materials and technical elements such as conditioning, lighting, etc. The design of tension roofs is always striving towards technological and structure innovation in order to build lighter and lighter structures to cover ever larger spans. Tension structures are in line with the new contemporary architectural concept of space, allowing for the construction of a large free space where the flexibility and the modifiability of structures are the most important prerequisites.[1] Tension structures meet the demand for structures that only need basic planned maintenance and have a good seismic performance, too. In Italy, this constructive typology has been neglected so far and even ignored by building regulations; in fact no mandatory standards have been set for the design and construction of these structures, except for temporary constructions. The shape selected for a parameterization leading to an optimized design of this kind of structures is the hyperbolic paraboloid. This research work followed two consecutive steps: the first was aimed at developing an optimized procedure of preliminary design for the cable structure [3]; the second was focussed on the study of the wind action on these structures. The procedure of preliminary design consists in evaluating prefixed cable spans and sags, the minimum values of pretensions and areas of the two series of cables (load bearing and stabilizing) so as to maintain the cable stress within the limit value under the two opposite load configurations: maximum snow load and maximum depression of wind. By using the procedure for a set of values of span and sags, a statistical sample of different roof shapes has been produced. Having in mind the design of sport palaces, swimming-pools, meeting rooms, we have taken into account another geometrical parameter (in the following Hb) measuring the distance between the roof and the ground floor. This parameter has been added to the span/sag ratio in the experimental tests in the wind tunnel. In fact, the model is built in two different heights. In the second phase of the work, experimental tests were performed in the CRIACIV's wind tunnel in Prato, in order to assess the wind action on tension roofs with a hyperbolic paraboloid shape. While there are precise indications for shells, slopes and domes, in Italy there are no wind regulations for this shape. No prescriptions are provided in the new CNR-2008 for the calculation of the wind action, either.

Tensile Structures of Cables Net, Guidelines to Design and Applications

“…In Figure 25 a view of the structure deformation under 90˚ wind action is shown; it is interesting to note that this direction is particularly critic for Hyperbolic paraboloid cables net because the suction is higher than the other angles (Rizzo et al, 2011), so it is particularly important that the suction not decreases too the load bearing cables strain. In this case, like is reported in Table 7, the ratio between load bearing cables strains with and without wind is equal to 0.85 (reduction equal to 15%).…”

“…With the same procedure 2 A is fixed updating the value of 1 A . In conclusion, fixed an initial condition of traction the cables areas are defined according to the initial geometry wanted.…”

“…Of course after this first preliminary phase some specific wind tunnel experiments are necessary to study aerodynamic and aeroelastic effects. The pressure coefficients maps (Rizzo et al, 2011 andRizzo, 2014) for two significant angles used to evaluate the wind action are shown in Figure 18. The wind direction of 0˚ are parallel to the stabilizing cables and at contrary, the wind direction of 90˚ are parallel to the load bearing cables.…”

“…Using the procedure 1 illustrated in Figure 3, the geometry variation of the load bearing cable (in this case C 1 ) is evaluated in order to obtain the H 2,1 defined by Equation (12). It's important to note that 2,1 f and 2,1 T are the deformed sag and the cable C 1 traction with the snow action.…”

“…The stiffness coefficients are considered, respectively for the load-bearing cable (C 1 ) and stabilizing one (C 2 ) defined as expressed in Equation (2) and Equation (3), where k 1 and k 2 represent, respectively, the stiffness of the load-bearing cable C 1 and the stiffness of the stabilizing cable C 2 , defined in Equation (4); A 1 and A 2 , f 1 and f 2 , L 1 and L 2 are, respectively, area, sag and span length of the cable C 1 and C 2 .…”