Prestress and its application to shell, fabric, and cable net structures

Doctoral thesis, 2021

Prestressing and shells provide means to create material-efficient and well-functioning structures, as do their combination, offering opportunities for increased material efficiency within the built environment. Prestressing introduces stresses in an object to enhance its performance, and shells include concrete shells, masonry vaults, fabric structures, cable nets, and timber or steel gridshells. Both prestressing and shell structures come with technical and practical considerations that need attention during the design, or there is a risk of wasted opportunity. However, successful attention to and combination of these aspects, resulting in a material-efficient prestressed shell, is not enough to make a high-quality architecture. There is a need for additional project-specific considerations, requiring ways to study design choices' impact on structural and architectural aspects.

This thesis aims for an increased understanding of prestressing and its application to shell, fabric, and cable net structures and improved means for their design. It provides a broad overview of prestressing, expanding beyond the common perception of prestress being limited to concrete structures, and shell structures, focusing on applications within architecture. The scope is the combination of prestressing and shells, and it addresses three main research questions: (1) Can any shell be prestressed? For those that can, what is the meaning and influence of prestressing?; (2) How can prestressed shells be form-found using analytical and numerical approaches?; and (3) How can prestress in shells be represented and chosen, aspiring for efficient structural performance?

Appended papers A-F help answer these questions, and the thesis contributes to architectural and structural design and structural optimisation and applies differential geometry. It provides approaches for the form-finding of gridshells containing both tension and compression elements (Paper A) and of minimal surfaces (Paper C and D). Paper B concludes that a sphere cannot be prestressed, but a torus can. Paper E extends the Williams and McRobie (2016) discontinuous Airy stress function from flat structures to curved shells, allowing moments and shear forces in edge beams of shell structures to be quantified and appropriate prestressing chosen. Paper D uses a discrete Airy stress function and discusses the structural behaviour of shells with negative Gaussian curvature loaded with patch loads. Paper D studies Eduardo Torroja's prestressed concrete Alloz aqueduct, concluding that longitudinal prestressing may reduce the wall bending moments and that, at the limit, the channel act as a cylindrical membrane-action shell rather than of an Euler-Bernoulli beam, enabling thinner cross-sections.