Keywords: aerodynamic, hyperbolic parabolic, computational fluid dynamics, proper orthogonal decomposition.

The purpose of this research is to evaluate aerodynamic loads on medium to large span hyperbolic paraboloid shaped roofs. This geometrical shape is often used in the design of tension roofs with a cable structure. These kinds of structures are light and characterized by innovative construction materials and technical elements such as air conditioning, lighting, etc. The design of tension roofs is always striving towards technological and structural innovation in order to build ever lighter structures to cover equally ever larger spans. They also meet the demand for structures that only need basic planned maintenance and can also withstand seismic activity too. In Europe, this constructive typology has so far been largely neglected and to a certain extent 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. There is also a lack of information about wind action on hyperbolic paraboloid shapes. While there are precise indications for shells, slopes and domes, there are currently no wind regulations for this shape in Italy. This research followed three consecutive steps: the first was aimed at developing an optimized procedure for preliminary design for a cable structure; the second focussed on the study of the wind action on these structures. The procedure of preliminary design consists of evaluating prefixed cable spans and sags, the minimum values of pretensions and areas of the two series of cables so as to maintain the cable stress within the limiting values under the two opposite simplified load configurations: maximum snow load and maximum wind suction. By using the procedure for a set of values of spans and sags, a statistical sample of different roof shapes has been produced. Having in mind the design of sporting arenas swimming-pools and meeting rooms, we have taken into account another geometrical parameter measuring the distance between the roof and the ground floor. In the second phase of the research, experimental tests were performed in order to assess the wind action on tension roofs with a hyperbolic paraboloid shape. From the statistical sample of different geometrical shapes under study, certain configurations were selected to be tested in the wind tunnel in order to highlight their aerodynamic behaviour and calculate the pressure coefficients. Three different building shapes were chosen: square, circular and rectangular, i.e. the most common shapes for sporting areas. The proper orthogonal decomposition method and a computational fluid dynamics analysis are used in order to order to assess wind tunnel data and study three- dimensional vortex shedding.

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