The construction industry is responsible for nearly half of the UK's carbon emissions, and the use of an extremely large volume of concrete, the world's most widely used man-made material, accounts for more than 7% of global CO2 emissions. The scale of this problem spawned research that explored the potential for structurally efficient non-prismatic geometries to substantially reduce the amount of concrete in building elements, thus also reducing their embodied carbon footprint. In particular, the research focused on segmented thin concrete shells as floor slabs, leveraging computational design and digital fabrication methodologies to automate their production off-site. An important part of this research was the development of a computational framework for the design of thin concrete shells, to make such construction methodology accessible to building designers in practice. The framework combined solutions for parametric modelling, finite element analysis, isogeometric analysis, form finding and optimisation, and also embedded fabrication constraints specific to the project's automated manufacturing system. This paper documents the application of the developed computational framework in the design of a 4.5m x 4.5m prototype, illustrating how automating concrete construction can transform the industry towards net-zero.