A theory-based simplified trilinear model for characterisation of the out-of-plane behaviour of URM walls

Observations recorded after recent earthquakes have shown that out-of-plane failure of unreinforced masonry elements on unreinforced masonry buildings and to reinforced concrete buildings constitutes a serious hazard to life. This has led to the development of a wide variety of models and approaches, from simple analytical to complex numerical simulations. Within this framework, the present paper proposes an analytical approach derived from theoretical considerations to characterise the complete out-of-plane seismic response curve of unreinforced masonry cantilever walls. Masonry parapets and historical façades fall within this scope, since it was not customary to firmly connect walls to the horizontal structural elements in the past. This research also provides a straightforward way of elaborating a simplified trilinear version of these curves by means of a series of non-dimensional mathematical expressions. Additionally, the characterisation of the oscillating periods and the kinetic energies of the walls are thoroughly discussed. Finally, the capability of the approach in terms of capturing linear and non-linear behaviour of masonry walls under horizontal loads is demonstrated via comparison with several tests reported in the literature. •Theory-based formulation for characterisation of the out-of-plane behaviour of walls.•Straightforward expressions for a simplified trilinear version of the capacity curves.•Formulae to characterise the walls’ fundamental periods and kinetic energies.•Analytical formulation validated by experimental data of masonry cantilever walls.