3D homogenized limit analysis of masonry buildings under horizontal loads

The current confidence levels in the ability to provide buildings with adequate resistance to horizontal actions do not easily apply to historic and existing masonry structures. Limit analysis is often not sufficient for a full structural analysis under seismic loads, but it can be profitably used in order to obtain a simple and fast estimation of collapse loads. Often, the limit analysis of ancient masonry structures is used in the context of several simplifications, the assumptions about the collapse mechanisms being the most relevant. Aiming at a more general framework, a micro-mechanical model developed previously by the authors for the limit analysis of isolated in- and out-of-plane loaded masonry walls is extended here and utilized in the presence of coupled membrane and flexural effects. In the model, the elementary cell is subdivided along its thickness in several layers, where fully equilibrated stress fields adopting a polynomial expansion are assumed. The continuity of the stress vector on the interfaces between adjacent sub-domains and anti-periodicity conditions on the boundary surface are further imposed. Linearized homogenized surfaces for masonry in six dimensions are obtained and implemented in a FE limit analysis code, and two 3D case studies are analyzed making use of the kinematic theorem of limit analysis. From the results, the approach proposed is validated and its usefulness for solving engineering problems is demonstrated.