A three-dimensional approach to the Extended Limit Analysis of Reinforced Masonry

The Extended Limit Analysis of Reinforced Masonry (ELARM) is a simple and user-friendly method for the design and structural analysis of singly-curved, reinforced tile vaults [1]. It is based on limit analysis but takes into account the reinforcement's contribution to the composite cross-section's bending capacity. 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 reinforced masonry, reinforced concrete and concrete-masonry composite 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 case with a shape beyond funicular geometry. © 2021 The Author(s)