Simple numerical model with second order effects for out-of-plane loaded masonry walls

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a simplified “homogenized” procedure. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry walls by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine where second order effects are suitably considered adding a further term, quadratic in the nodal displacements, within the total energy of the discretized system. The finite element model, applicable under general load and restraint conditions, incorporates material and geometric nonlinearity and may be used to analyze slender URM walls, having the capability of capturing post-cracking and post-buckling behavior in an approximate but suitable way. As validation of the approach proposed, the instability behavior of some existing experimental pre-compressed four-point bending tests is reproduced. Square panels in two-way bending, exhibiting classical Rondelet’s mechanisms, are also studied. Finally the results obtained are compared with those provided both by commercial FE programs and specifically developed analytical models.