3D interaction domains for unreinforced masonry panels subjected to eccentric compression and shear

Flexural strength of unreinforced masonry (URM) cross-sections is typically predicted by means of two-dimensional (2D) interaction domains. Alternatively, three-dimensional (3D) interaction domains can be used to include the balance of the whole masonry panel in the limit state equations of an extreme section. In this paper 3D domains are presented to describe the interaction between shear force, axial force and its eccentricity for prismatic URM panels with rectangular cross-section. For both elastic and ultimate limit states, sectional equilibrium equations corresponding to a given axial strain diagram are merged with those of the entire masonry panel for cracked and uncracked conditions separately. Such domains are defined in a dimensionless format in order to be independent of the compressive strength of masonry. Limit state equations were derived for five different stress-strain relationships, to investigate the influence of masonry behaviour in uniaxial compression under the assumption of zero tensile strength. In this paper the general formulation is specialised for a strength-degrading constitutive model to emphasise the effects of strain softening. Finally, the 3D domains were sectioned with planes corresponding to different levels of axial force and axial force eccentricity in order to derive 2D interaction domains expressed respectively in terms of shear force versus axial force eccentricity and shear force versus axial force. It is shown that any increase in the axial force eccentricity causes a rotation of the shear force versus axial force domain, resulting in an allowable axial force lower than that associated with concentric compression.