The aim of the study is to develop an original, methodical, and practical approach to the early stages of parametric design of roof shells formed by repetitive modules of Catalan surfaces. It is presented on the example of designing the roof shells compound of four concrete elements. The designing process proposed by us consists in linking geometric shaping of roofs' models with their structural analysis and optimization. Contrary to other methods, which use optimization process in order to find free roof forms, we apply it in order to explore and improve design alternatives. It is realized with the application of designing tools working in Rhinoceros 3D software. The flexible scripts elaborated by us, in order to achieve roofs' models of regular and symmetrical shapes, are converted into simulation models to perform structural analysis. It is mainly focused on how the roof shells perform dependently on their geometric characteristics. The simulation enables one to evaluate various roof shells' shapes, as well as to select an optimal design solution. The proposed approach to the conceptual design process may drive the designing to achieve geometric and structural forms which not only follow the design intentions but also target better results.

The paper concerns shaping curvilinear steel bar structures that are hyperbolic paraboloid canopy roofs by means of parametric design software Rhinoceros/Grasshopper and Karamba 3D. Hyperbolic paraboloid shape has found applications in various solutions of building roofs, mainly as reinforced concrete or steel coverings made of bent sheets. The hyperbolic paraboloid as a ruled surface can be a good base surface for forming bar grids. However, there are few studies on the effect of its division and the obtained topology of bar structures on their load-bearing capacity. In order to fill this gap, the aim of the presented research was to compare the effectiveness of various curvilinear steel bar structures of hyperbolic paraboloid canopy roofs covering the same plane, as well as defining both the most effective pattern of their structural grids and the optimal supporting system. This analysis was carried out thanks to the application of genetic algorithms enabling the free flow of information between geometrical and structural models, as well as thanks to the obtained result of multi-objective optimizations of the shaped structures for given boundary conditions. Minimal mass of the structure as well as minimal deflection of the structural members were assumed as the optimization criteria.

The correlation of the architectural form and the structural system should be the basis for rational shaping. This paper presents algorithmic-aided shaping curvilinear steel bar structures for roofs, using modern digital tools, working in the environment of Rhinoceros 3D. The proposed method consists of placing the structural nodes of the shaped bar structure on the so-called base surface. As the base surface, the minimal surfaces with favorable mechanical properties were used. These surfaces were obtained in two optimization methods, due to both the structural and functional requirements. One of the methods used was the so-called form-finding method. It wasalso analyzed the amount of shadow produced by the roof and the adjacent building complex, during a certain research period, to find the roof’s optimal shape. The structure of the optimal shape was then subjected to structural analysis and its members were dimensioned. The dimensioning was carried out for two bar cross-sections, and as the optimization criterion, the smallest structure’s mass was used. The presented research aims to show how it is possible to use generative shaping tools, so as not to block the creative process, to obtain effective, responsive structural forms, that meet both architectural and structural requirements.

The paper addresses the problem of the efficient shaping of curved steel rod structures conducted based on the enneper surface. The proposed parametric design process consists in linking the geometric shaping of grid models with their structural analysis and optimization, which is realized through the application of design tools working in the rhinoceros 3D software. The mechanical performance of lattices covered with glass panels is evaluated and the structures are pre-dimensioned. The presented aesthetic grid shells with good structural characteristics may constitute original coverings. however, the analysis, which targets an early stage of the design, aims at providing design guidelines to facilitate communication between architects and civil engineers.

SummaryThe aim of the study was to develop a practical approach to parametric shaping of spatial steel rod structures formed based on a hyperbolic paraboloid. This design approach was realized by application of designing tools working in environment of Rhinoceros 3D, that is its plug-in Grasshopper for geometric modelling and Karamba 3D for structural analysis. The goal of this research was to elaborate an universal scripts in order to create rod structures’ models of various forms and grid patterns, as well as evaluating their structural behaviour dependently on various boundary conditions. The optimisation criterion was the minimum mass and deflection. Several proposals of coverings by means of single layer grid structures were presented and analysed to choose the best solution. The rod structures generated based on a hyperbolic paraboloid turned out to be structures with good static properties, so may be an interesting proposals to cover large areas.