Lateral Stiffness of Masonry Walls with Steel Frame–Reinforced Openings

The reduction in stiffness caused by a new opening in a masonry wall must remain below a prescribed threshold, lest overall seismic performance be compromised, a requirement that practitioners attempt to meet by installing a steel frame anchored to the surrounding masonry. This paper presents a closed-form analytical model to determine the lateral stiffness of a masonry wall that features a new opening reinforced with a steel frame under both coupled and uncoupled top-spandrel conditions. The model explicitly captures the anchor-mediated frame–masonry interaction and yields all principal response quantities, including the peak shear force in the anchors. The model is directly applicable to both symmetric frame-reinforced perforated masonry walls and asymmetric configurations in which the contribution of the smaller masonry pier is negligible. For configurations requiring numerical analysis, the model offers an analytical benchmark for validating computational tools.