The widespread presence and seismic vulnerability of unreinforced masonry (URM) structures have prompted extensive research into their assessment and retrofit. Even when local vulnerabilities are mitigated and a global three-dimensional behavior is promoted, the seismic performance under horizontal excitations might still be insufficient. To address this limitation, strengthening interventions using composite materials, such as Fabric-Reinforced Cementitious Matrices (FRCM) or Composite-Reinforced Mortars (CRM), as well as retrofitting systems based on steel or timber exoskeletons, are often applied to one or both sides of the masonry walls.

This paper introduces a novel three-dimensional macroelement developed to effectively capture the coupled in-plane and out-of-plane response of unstrengthened and strengthened masonry elements, balancing computational efficiency with constitutive law versatility through a stripe or fiber discretization of the cross-section. Indeed, the proposed formulation facilitates the introduction of additional reinforcement, enabling the explicit modeling of a wide range of strengthening solutions.

The effectiveness of the proposed macroelement in reproducing the lateral response of masonry piers are proved through the numerical simulation of experimental quasi-static cyclic shear-compression tests.