Geometric curvature in the out-of-plane flexural design of unreinforced masonry walls

Abstract Unreinforced masonry (URM) walls are highly susceptible to out-of-plane (OOP) loading, often failing in brittle flexure. Existing analytical formulations and design provisions are largely tailored for planar walls that do not apply to curved masonry walls, which offer an underexplored opportunity to enhance lateral resistance through architectural form. This study investigates the coupled influence of geometrical curvature and material properties on the flexural capacity of URM walls subjected to out-of-plane loading. Experimental characterization of clay bricks and selected mortar mixes revealed significant variability in elastic stiffness relative to compressive strength, highlighting the heterogeneous nature of masonry materials. These properties were incorporated into a nonlinear finite element model developed in ABAQUS using simplified micro-modelling and traction-separation interface laws, which successfully reproduced crack initiation, stiffness degradation, and ultimate failure mechanisms reported in experimental studies. Parametric analyses showed that planar walls exhibited bending-dominated behaviour governed by tensile cracking, with increased mortar strength improving load capacity without significantly altering failure mode. In contrast, curved walls, as indicated by moment-curvature relationships, developed compressive thrust paths and arching mechanisms that increased stiffness and flexural capacity through stress redistribution and geometric stiffening. An effective section modulus relationship based on wall projection is proposed to estimate the flexural capacity of curved URM walls. The results demonstrate that geometric curvature has a greater influence on out-of-plane flexural capacity than material strength, highlighting the need to incorporate curvature effects into the analysis and design of masonry walls where planar assumptions may underestimate structural performance.