Parametrical design trends for a hyperbolic paraboloid shaped over a square plan: Vertical displacements and natural periods

Tensile structures are one of the most convenient solutions for covering large spans. For both temporary and permanent uses, they are optimal as sport arenas, meeting rooms or concert halls. However, codes and literature neglect these structures thus making it difficult to carry out preliminary designs for this structural typology in order to estimate the cost-benefit ratio compared to others. On the contrary, parametric equations used to preliminarily estimate the static and dynamic behavior of these structures are useful to designers. In order to give parametric information about some examples of these structures, this paper investigates the initial natural frequency and vertical displacements under dead and permeant loads of cable nets, with a hyperbolic paraboloid shape and square plan, depending on geometry. In total, two curvatures of a hyperbolic paraboloid surface and five different plan sizes are calculated with eight different cable tractions in order to give design trends. The trends are illustrated with an error bar resulting from the variation between different tractions considered for each geometry. The results are useful to preliminarily estimate the cost and the range of interference between wind and structure.