WIND ACTION EVALUATION ON TENSION ROOFS OF HYPERBOLIC PARABOLOID SHAPE

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1 BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications Milano, Italy, July, WIND ACTION EVALUATION ON TENSION ROOFS OF HYPERBOLIC PARABOLOID SHAPE Fabio Rizzo a, Piero D Asdia a,lorenzo Procino b a Università degli Studi G. D Annunzio, Chieti-Pescara b Università degli Studi di Firenze KEYWORD: Aerodynamic, hyperbolic paraboloid, cable. 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 for the calculation of the wind action, either. 1

2 From the statistical sample of different geometrical shapes that under study, (about one thousand different configurations) some configurations were selected to be tested in the wind tunnel in order to highlight their aerodynamic behaviour and calculate the pressure coefficients. Three different shape of buildings were chosen: square, circular and rectangular, i.e. the most common shapes for sport palaces. All wind tunnel wood models are constructed with two different roof heights (sum of the load bearing cable s sag and the stabilizing cable s sag) obtained by changing the height of the ground level with an additional base. The ratio between the two sags of the two sets of cables is 2. The stabilizing cable sag is twice the bearing cable sag. This ratio provides an optimized cables stress under extreme loads. The tests programme and an outline of the geometrical parameters used are presented below Tab. (1).[2] Aerodynamic tests performed: Square Mod. (L,max = 80.0 cm) p.7 f1+f2 = 1/6 Lmax Hb = 1/6 L p.8 f1+f2 = 1/6 Lmax; Hb = 1/3 L p.1 f1+f2 = 1/10 Lmax; Hb = 1/6 L p.2 f1+f2 = 1/10 Lmax; Hb = 1/3 L Rectangular Mod. (L1<L2) (L,max = 80.0 cm) p.3 f1+f2 = 1/6 Lmax Hb = 1/6 L p.4 f1+f2 = 1/6 Lmax; Hb = 1/3 L p.5 f1+f2 = 1/10 Lmax; Hb = 1/6 L p.6 f1+f2 = 1/10 Lmax; Hb = 1/3 L Circular Mod. (L,max = 80.0 cm) p.9 f1+f2 = 1/6 Lmax Hb = 1/6 L p.9 w.r. f1+f2 = 1/6 Lmax Hb = 1/6 L Reduced roughness p.10 f1+f2 = 1/6 Lmax; Hb = 1/3 L p.10 w.r. f1+f2 = 1/6 Lmax; Hb = 1/3 L Reduced roughness p.11 f1+f2 = 1/10 Lmax; Hb = 1/6 L p.12 f1+f2 = 1/10 Lmax; Hb = 1/3 L Square Mod. (L,max = 40.0 cm) p.13 f1+f2 = 1/6 Lmax Hb = 1/6 L Table 1: The tests programme and an outline of the geometrical parameters used All models have about pressure take-offs that are distributed on the roofs and on the four lateral surfaces. The dimensions of twelve models are equal to 80 cm (L1, L2) whereas the dimensions of only one are equal to half this size (40 cm) in order to assess the influence of the model scale factor on the vortex-shedding.[4] The wind tunnel test speed is 20 m/s and for each model the measures have been obtained for 16 angles of incidence of the wind. The boundary layers are developed with a city-configuration in the wind tunnel. Some pictures of the tests are (reported) shown below Fig. (1)-(7). 2

3 Figure 1: f1+f2 = 1/10 Lmax; Hb = 1/6 L Figure 2: f1+f2 = 1/10 Lmax; Hb = 1/3 L Figure 3: p.1 test f1+f2 = 1/10 Lmax; Hb = 1/6 L Figure 4: p.2 test f1+f2 = 1/10 Lmax; Hb = 1/3 L Figure 5: p.11 model f1+f2 = 1/10 Lmax; Hb = 1/6 L (Reduced roughness) Figure 6: p.11 test 6: f1+f2 = 1/10 Lmax; Hb = 1/6 L Figure 7: p.12 test f1+f2 = 1/10 Lmax; Hb = 1/3 L The roughness of the lateral surface in the circular model was increased in order to try to obtain the correct values (with a Reynolds number high) in wind tunnel where the Reynolds number is low Fig. (5) (7). However, two tests with a low Reynolds number were carried out in order to evaluate the influence of this variable. Another aerodynamic test was performed, the Particle image velocimetry tests (PIV) Tab. (2), in order to obtain data for the third phase of the work that consists in a fluid dynamic simulation. This simulation has a double purpose: to simulate the wind tunnel environment in order to evaluate other geometrical shapes and to study the vortex-shedding in the threedimensional space. The present work aim is to describe an approach to tension roof design, starting from geometry and a preliminary design, a numeric computation and an aerodynamic evaluation resulting in an optimized design. While needing some further processing, the findings already 3

4 First A. Author, Second B. Author and Third C. Author show that the aerodynamic behaviour varies considerably from one shape to another when the same curvature is maintained and also when a second curvature is introduced. Pictures of Particle image velocimetry tests Test data Measuring angles Frequency: 20 Hz Speed: 11 m/s Profile: city Acquisition: 15 Hz cross-correlation: interrogation area: 32x32 pixels overlap: 25% Low-pass Gaussian: With=1/k^2 = 0.3; k= angle up-wind middle 90 angle down-wind up-wind middle down-wind Table 2: Particle image velocimetry tests REFERENCES: [1] P. D Asdia, F. Rizzo, V. Sepe Wind action and optimezed shape of a tension roof: Pescara s roof stadium. Proceeding of INVENTO 2006, Pescara, Italy, June, (in Italian). [2] P. Biagini, C. Borri, M. Majowiecki, M. Orlando, L. Procino. BLWT tests and design loads on the roof of the New Olympic Stadium in Piraeus. Journal of Wind Engineering and Industrial Aerodynamics 94, , [3] W. D. Pilkey. Mechanics of structures variational and computazional methods. W. Wunderlich, CRC Press. 4

5 [4] G. Bartoli, C. Costanzo, F. Ricciardelli. Characterisation of pressure on build s surface with a separate flow Proceeding of INVENTO 2006, Pescara, Italy, June, (in Italian). 5