The course aims to offer an analysis of the most important realizations, in the field of space structures, large span roofs and shells, regarding, at the same time, the buildings of the 50-70s, and the most important realizations with respect to nowadays architectures in Italy and all over the World. Through a detailed analysis of the modeling and verification methods, the course purposes to explain, the different approaches, progressively proposed, for the calculation of shell and spatial structures. For this motivation, the form-finding and the successively validation phase, for structures of this type, are presented. The course, in addition, aims to provide a critical point of view of the different methods introduced for the design of lightweight structures, firstly, considering the models employed for the realizations using traditional materials and successively evaluating atypical and futuristic prototypes. In these last cases, the use of sustainable and eco-friendly materials (timber and bamboo) and the design of transportable structures in the aerospace applications will be explored. The form-finding processes (FFp), such as the dynamic relaxation method, the particle spring model, the truss network analysis, etc. are illustrated together with their principles and their differences for the FFp of vaults, grid shells and active bending structures (FFp will be implemented by Rhinoceros, Grasshopper, Visual-Nastran 4D, etc.). The calculation methods and the shape generating procedures for tensegrity and origami structures will be also addressed in their fundamental outlines. The structural optimization of shells and spatial structures will be evaluated by investigating the main and most innovative methods based on the parametric and topological approaches, also by the use of NURBS surfaces. The course, finally, get the scope of identifying the most important validation procedures for these structures with respect to the criteria of local and non-local instability analysis of shells and vaults. The possible instability and coupled instability phenomenon will be studied through the application of linear and non-linear FEM models. In particular, the course will also provide an overview on the current retrofitting techniques and permanent monitoring systems, currently in use, in spatial and shell structures normally employed to cover public spaces such as squares and airports.

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Course Highlights and Short Programme: • Shell and spatial structures: Light-weight structures: origins and developments. Iconic and emblematic cases in the European and American schools. • Form finding approaches: dynamic relaxation method (DRM), particle spring model (PSM), thrust network analysis (TNA), multibody rope approach (MRA), R-funicularity. Theory and applications. • Tensile and tension-compression lightweight structures: Tent structures, tensegrity and origami. Theory and fundament al features; Local and Non-local stability analysis. Snap-through instability and collapse of shell structures, instability for tensegrities. • Structural optimization of shell and spatial structures: traditional and innovative approaches. • Monitoring of shell and spatial structures: main technologies and applications. Language: English Notes: The course will be online by the Zoom Platform. The link will be sent some before the beginning of the lessons. To participate please contact: amedeo.manuellobertetto@polito.it

On line synchronous mode

Written report presentation

P.D.2-2 - May

Coordinator: Prof. Amedeo Manuello Bertetto Invited Lecturers: Proff. Stefano Gabriele, Francesco Marmo, Ornella Iuorio, Andrea Micheletti, Giuseppe Carlo Marano. COURSE CALENDAR: First Week May, 14th 2021 Friday Virt.Room (VR) Zoom platform (ZP) 10:00 am - 01:00 pm (GMT+1) Coord.: Prof. Amedeo Manuello • Space and Shell Structures: Origin and Development: Emblematic Cases of European and American Schools (3 hours); May, 21th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Coord: Prof. Amedeo Manuello • Focus on "The Stuttgart School" and the "Italian School". Kenzo Tange, Frei Otto, Pier Luigi Nervi and Riccardo Morandi. Calculation models and their evolution up to the Parametric Design. (3 hours); Second Week May, 28th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Coord.: Prof. Amedeo Manuello & Prof. Ornella Iuorio • Local and non-local buckling analysis. Snap-through of shell structures. • Theory and interpretation of famous collapses; • Form-finding methods: The Multi-Body Rope Approach (MRA) and imperfections sensitivity. (2 hours); • Embodied carbon of shells and spatial structures (3 hours); June, 4th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Inv. Lecturer: Prof. Stefano Gabriele • R-Funicularity of form found shell structures (3 hours); Third Week June,11th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Inv. Lecturer: Prof. Francesco Marmo • Form-Finding by membrane Theory; • Force density method; • Thrust Network Analysis (TNA). (3 hours); June, 18th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Inv. Lecturer: Prof. Andrea Micheletti • Modelling and design of Tensegrity and Origami Structures. (3 hours); Fourth Week June, 25th 2021 Friday (VR) (ZP) 10:00 am - 01:00 pm (GMT+1) Coord.: Prof. Amedeo Manuello. Inv. Lecturer: Prof. G. C. Marano • Instability for Grid-shell and Tensegrities. Monitoring techniques of existing vaults. • Interaction phenomena and Structural Optimization. (3 hours) ------------------------------------------------------------------------------