The non-linear behaviour of masonry panels is typically defined through strength domains and bilinear, multilinear, or non-linear force-displacement relationships. Flexural strength domains are derived from ‘stress-based’ approaches in which limit states are defined by means of linear or uniform normal stress diagrams over cross-sections subjected to the maximum bending moment. Nonetheless, those approaches do not allow to account for some real characteristics of masonry, such as micro-cracking in the elastic range and strain softening in the plastic range. Masonry micro-cracking induces a non-linear stress-strain relationship even at small strain levels, while strain softening causes a strength degradation under inelastic strains.

In this paper the flexural strength of unreinforced masonry cross-sections is investigated through a closed-form integration of non-linear normal stress diagrams corresponding to different stress-strain relations of masonry and linear axial strain diagrams. Such a study includes the effects of sectional cracking due to tensile strains. Strength domains have been also derived by implementing non-linear stress-strain diagrams which are able to simulate compressive behaviour of regular masonry assemblages up to large inelastic strain levels. The comparison between strength domains corresponding to different stress-strain diagrams has shown that current simplified formulas lead to less conservative estimates of the ultimate bending moment, if the given axial force is not significantly greater than one-half of the ultimate axial force. The implementation of degrading constitutive laws has highlighted a dramatic influence of strain ductility on the strength domain evolution. To this regard, variations in the ultimate bending moment are less significant under low axial forces. Considering explicitly strain ductility in the equations that define the limit lines of the strength domains allows to simulate the flexural strength evolution in static pushover analysis of masonry buildings, as the sectional strain demands changes with the deformation demands on individual masonry panels. It is thus possible to assume different values of strain ductility depending on whether an existing masonry building is assessed or a new masonry building is designed.