A simple and user-friendly method for the design and structural analysis of singly-curved, reinforced tile vaults was presented in López López et al. (2019) . It was based on limit analysis but took into account the reinforcement´s contribution to the composite cross-section´s bending capacity. The method was called Extended Limit Analysis of Reinforced Masonry (ELARM) and it was validated through experimental research.
A three-dimensional approach to ELARM is presented in this paper. The theoretical framework to understand the implications and limitations of extending ELARM to fully 3D structures is described, together with the strategies to carry out the leap from 2D to 3D. This extension is a lower-bound approach for the design of composite, reinforced masonry and/or concrete shells and the assessment of their strength and stability against external loading.
The new, extended method is implemented computationally to speed up the iterative processes, provide quick structural feedback, offer immediate results and allow for user-interactive form-finding and optimisation procedures. Different applications of the developed tool are described through the presentation of examples, including reinforcement optimisation, a form-finding process and a non-compression-only case.