A macro‐element with bidirectional interaction for seismic analysis of unreinforced masonry walls

Abstract

Prior to implementing retrofitting measures for seismic action, it is necessary to evaluate the global capacity of unreinforced masonry (URM) buildings. Even with simplified assumptions, equivalent frame (EF) modeling adequately captures global responses and failure mechanisms in existing buildings, making it a popular modeling strategy among structural engineers. However, macroelements employed in the EF modeling of URM walls consider in-plane (IP) and out-of-plane (OP) behaviors separately by decoupling their interaction and require independent verification for OP failure involving limit analysis. Such decoupling of interaction is justifiable if proper wall-wall/wall-floor connections and rigid-diaphragm action of slabs are ensured; however, OP failure is likely a result of inadequate connections. Multiple components of ground motion excitation and plan eccentricity in buildings can activate bidirectional interaction in such circumstances. Due to OP damage, the interaction reduces the full IP strength of a URM wall, resulting in overestimating its lateral capacity. This paper proposes a frame-like 3D macro-element incorporating the effect of OP action on the IP shear response of URM piers under static and monotonic lateral loads. Only two parameters modifying IP shear stiffness and capacity are required to account for the interaction. Analytical expressions for the interaction parameters are proposed from a detailed micro-modeling study. The paper also demonstrates, within the EF modeling, the applicability of the proposed macro-element for seismic analysis of regular URM shear walls with openings.

Towards Performance-Based Design of Masonry Buildings: Literature Review

“…Each component is represented with a phenomenological (e.g., from experimental data) or mechanical-based (e.g., from Euler Bernoulli beam formulation) material response. For instance, masonry shear walls are typically transformed into an assemblage of piers (i.e., principal vertical resistant elements to both dead and seismic forces), spandrels (i.e., secondary elements that couple piers), and diagonal connecting elements (i.e., shear crack elements) [188][189][190][191][192][193][194][195][196][197][198], as illustrated in Figure 17. At the building level, masonry buildings are discretized into several panel-scale deformable structural components (e.g., piers or spandrels) and/or rigid bodies (representing masonry portions that experience no/limited damage) [199][200][201][202][203][204][205][206][207][208][209].…”

“…In addition to macro continuum models, macro element models have wider applicability in practice-oriented assessments for URM shear walls. Examples include monotonic behavior estimation with a primary interest in the initial stiffness and peak strength [188,191,193,194,198,212,213], and cyclic response assessment focusing on more structural characteristics (e.g., stiffness degradation, energy dissipation capability) [195,202,203,205,206,214]. Based on the assumption that damage could be approximatively concentrated in particular sections of the structure, macro elements can be modeled through lumped plasticity behaviors at specified locations (e.g., at the end and/or midpoint of structural elements).…”

Effect of cross walls on the interaction curves of the unreinforced masonry walls

“…Further, the reduction in initial stiffness is considerable for a flexure‐controlled pier compared to a shear‐controlled pier. Kesavan and Menon 12 developed a macro‐based equivalent frame model to analyze the masonry piers under combined in‐plane and out‐of‐plane loadings. The proposed model was able to capture the interaction effect fairly accurately compared to the micro‐model.…”