Analytical formulation describing the behaviour of URM walls seismically strengthened using timber strong-backs

Unreinforced masonry structures are vulnerable to seismic actions and frequently exhibit partial or global out-of-plane wall collapse when subjected to large intensity earthquake shaking. The installation of timber strong-backs connected to the masonry surface with mechanical fasteners is a reversible and effective strengthening solution that considerably improves the out-of-plane response of masonry walls. An analytical formulation is presented that enables the out-of-plane behaviour of unreinforced masonry walls seismically retrofitted with timber strong-backs to be described, with limit analysis theorems being utilised to establish the lateral capacity curve and the demands on the masonry wall, on the timber strong-backs, and on the fastener components of the retrofitted walls, thereby enabling the design of retrofit interventions. These analytical predictions were validated using experimentally derived data from five full-scale masonry wall tests and were also compared with simulations obtained from a numerical model developed using the software SAP2000 and adopting a simplified micro-modelling approach. Analytically derived load actions were consistent with experimental values (errors < 5 %) and were compatible with the numerical deformation results (errors < 10 %). The expected performance of various retrofitted wall configurations is then reported as support for general considerations regarding the retrofit solution.