PSI - Issue 78

Mauro Mazzei et al. / Procedia Structural Integrity 78 (2026) 1649–1656

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dynamism. The geometry chosen for this structure is that of the hyperbolic paraboloid, a ribbed surface with double curvature that provides an optimal balance between mechanical strength and visual impact. The hyperbolic paraboloid, known for its unique geometric properties, is mathematically defined by an equation that describes its curvature and symmetry. This surface can be obtained as an affine transformation of other rotational surfaces, such as hyperboloids and elliptic paraboloids, and has hyperbolic intersections with horizontal planes and parabolic intersections with vertical planes. These characteristics confirm its ribbed nature, making it particularly suitable for realisation using rectilinear rods, an efficient and easily modulated construction solution. The structural modelling was performed using OpenSees software, which allowed the surface to be discretized into a regular nodal mesh. The structural elements were simulated using beam-columns with elastic behaviour, while the curvature of the roof was obtained by varying the heights of the nodes according to the generating function of the surface. The main nodes were constrained on perimeter pillars, ensuring stability and geometric consistency. The static analysis highlighted the ability of the hyperbolic shape to effectively distribute internal stresses under both permanent and accidental loads, confirming the validity of the geometric choice. The integration of mathematical form, natural inspiration and structural performance makes this roof an emblematic example of the synergy between engineering and architecture, where formal beauty is not only an aesthetic expression, but also the result of a rational, high-performance construction logic. 2. The focus on the proposed model The methodology adopted for the design and analysis of the lattice roof consists of three main phases: geometric definition, numerical modelling and structural analysis. Each phase was developed with the aim of integrating the architectural form inspired by nature with criteria of structural efficiency and constructive feasibility. The geometry of the roof was defined from a hyperbolic paraboloid, a rigid surface with double curvature that allows construction using rectilinear rods. The shape was mathematically described through the canonical equation of the hyperbolic paraboloid, which was subsequently adapted through affine transformations to obtain a configuration compatible with the architectural and structural constraints of the project. The preliminary geometric analysis made it possible to identify the main characteristics of the surface, such as intersections with horizontal and vertical planes, useful for the definition of the structural mesh. 2.1. Defining the form from a mathematical point of view The case study concerns the design of a large roof with a laminated wood lattice structure supporting a hyperbolic paraboloid structure through the nodes to form a hyperbolic paraboloid reminiscent of the wings of a seagull in flight. The idea was born in consideration of the following equations:

2.2. Single-pitch hyperboloid

2 2 + 2 2 − 2 2 −1=0 2 2 + 2 2 − 2 2 =−1 2 2 + 2 2 − 2 2 =0

2.3. Two-pitch hyperboloid

2.4. Second-order cone