Digital archive of theses discussed at the University of Pisa


Thesis etd-03062019-163928

Thesis type
Tesi di dottorato di ricerca
Thesis title
Reinforced and post-tensioned structural glass shells: Concept, morphogenesis and analysis
Academic discipline
Course of study
tutor Prof. Froli, Maurizio
tutor Dott. Cignoni, Paolo
  • Reverse Engineering
  • Post-tensioning
  • Post-breakage behaviour
  • Membrane forces
  • Hybridism
  • Hybrid structure
  • Funicular
  • Finite Element Model
  • Fail Safe Design
  • Damage Avoidance Design
  • Computational Design
  • Architectural Geometry
  • Shell
  • Structural glass
  • Triangular glass panel
Graduation session start date
The constant architectural request for transparency and de-materialization of primary structures and building skins appointed glass as structural material in contemporary buildings. Structures made of glass are essential from the material usage point of view because they constitute not only a transparent and fascinating building separation but also they can bear loads. However, the design and realization of large glass structures rely on two significant requirements. The first one is to assure adequate safety levels. Theoretical formulations concerning the remaining life-time of a glass pane submitted to a given load history are very complex and their predictions can not exclude brittle failures, so are not yet reliable enough for practical purposes. As a consequence, it is always necessary to assume the occurrence of a brittle failure in one or more glass components and to design consequently the whole construction to assure a residual safety level even in those accidental scenarios. Such a result can be reached by following the principles of the Fail-Safe Design and by adopting the concept of hybridism to relieve the glass material lacks.
The second requirement is to guarantee limited rehabilitation costs in case of glass cracking. Indeed, although a fail-safe glass structure dismisses the global collapse of the construction, the only occurrence of just a single crack produces economic damages comparable to global collapses, especially for monolithic or splice-laminated glass elements, since for aesthetic and psychological reasons, cracks are not tolerable, and the complete substitution of the damaged structure is unavoidable. Based on Damage Avoidance Design, glass segmentation and reciprocal diffuse post-tensioning by steel tendons, may be implemented as a cost-saving strategy where the replacing is limited to the only collapsed elements.
Inspired by these principles, this research explores a new design concept for hybrid glass-steel post-tensioned long-span shells to tackle both requirements. This concept is established on the developmental chain of the Travi Vitree Tensegrity (TVT) structural system, introduced by Froli (Froli and Lani, 2010; Froli and Mamone, 2014) and patented by the University of Pisa (Froli, 2006, 2014).
Hybrid glass-metal systems are up to now limited to mono-dimensional elements (such as beams and columns) or simple bi-dimensional elements (arches, domes, barrel vaults). On the other hand, only few albeit seductive shells made of glass have been built in statically or geometrically favourable cases while; when the lattice surface is submitted to limited or diffuse positive stresses, grid shells are preferred as alternatives. In grid shells, apart from supporting its own weight, glass plays the role of simple cladding, and the load bearing function is delivered to the metal grid.
The approach proposed and discussed in this thesis is based on the collaboration of multiple laminated triangular glass panels with a filigree steel truss, which constitutes the unbonded reinforcement of each panel edge. The panels are further post-tensioned by means of cables in order to add a beneficial compressive stress on their surfaces preventing crack initiation. In the development of this challenging long spanned shells, redundancy is an essential requirement and should be designed properly in severe scenarios, accounting glass cracking. Thus, the reinforcement cross area can be sized in a performance-based design approach to support all panels supposed collapsed in the limit extreme case, defined as ‘worst case scenario’. Being unable to fulfil safely any load-bearing task, the cracked panes are considered as a dead load, approaching the grid shell behaviour.
The conceptual design phase of such shells is managed automatically using an innovative approach, developed in collaboration with the Institute of Information Science and Technologies (ISTI), National Research Council of Italy (CNR) in Pisa, that tackles geometric and manufacture constraints as well as structural requirements. The main components of the structure are thus generated starting from the remeshing of a continuous shell surface, assigned its loading and boundary conditions. The approach is able to place the cables on the shell to install a favourable static regime on the surface, exploiting the best structural feature of the glass material that is the compression strength. This automatic cable-placement capability consists in the most challenging part of the work and, at the meantime, brought to one of the most significant innovation in the state-of-the-art of pre-stressed structures and of the static-aware algorithms. In particular, such morphogenesis procedure derives an optimized cable net, with the relative pre-load, such that the traction on the resulting hybrid shell is minimized. Cables are aligned to the edges of the mesh to maximize the transparency and for constructional reasons.
The quality of the results produced and the significance of the proposed strategy is demonstrated with global nonlinear analyses produced on several datasets. The shells show good static performances, high stiffness and redundancy rate with respect to the worst case scenario. Moreover, glass panes are prevalently and almost-uniformly loaded in compression. Also visual and structural lightness are substantially improved with respect to their grid shells competitors.
The structural behaviour of these structures is further investigated by means of analyses on a local plan to confirm their feasibility. The two most relevant components are investigated: the node and the glass panel. Experimental cyclic tests and their numerical description lead on a six-way node attest the node load-bearing capacity and stiffness, which make it suitable for the statically-relevant task assigned to it. The finite element models are generated with a Reverse Engineering procedure. Triangular laminated glass panels are a novel and unexplored research field, their Ultimate Limit State performances, in the case of in-plane and out-of-plane loading, are deduced by parametric nonlinear analyses, calibrated on the failure tests of the TVT prototype.