A Practice-Oriented Proposal to Consider the Flange Effect in Equivalent Frame Modeling of Masonry Buildings

This paper focuses on the so-called "flange effect" in unreinforced masonry buildings when the connection among walls is good, thus forming a 3D assembly of intersecting piers (with L-, C-, T-, or I-shaped cross-sections). Given the direction of the horizontal seismic action, the presence of such flanges (the piers loaded out-of-plane) can influence the response of the in-plane loaded pier (the web) in terms of failure modes, maximum strength, and displacement capacity. Specific rules are proposed in codes to evaluate the effective width of the flange, for the in-plane verification of a single masonry wall. However, in the case of 3D equivalent frame (EF) modeling of the whole building, all the intersecting piers should be considered entirely, to model the response in both the orthogonal directions as well as the torsional behavior, but this may lead to overestimating the flange effect if a perfect connection is assumed. This paper investigates the capability of simulating the actual behavior in EF models by introducing an elastic shear connection at the intersection between two piers using an "equivalent beam", coupling the nodes at the top of piers. A practice-oriented analytical formulation is proposed to calibrate such a flange effect on the basis of the geometric features and material properties of the web and the flange. Its reliability is tested at the scale of simple 3D assemblies and entire buildings as well. Finite element parametric analyses on masonry panels with symmetrical I- and T-shaped cross-sections have been performed to investigate the axial load redistribution between the flanges and the web and the consequent repercussion on the overall performance of the web. The results have proven that, after a calibration of the shear connection, the variation of axial force between the web and the flanges is correctly reproduced and the strength criteria for 2D panels provide reliable results. Finally, in the conclusions, some practical hints for simulating an imperfect wall-to-wall connection are also provided, since this case is relevant in historic masonry buildings, which are characterized by different masonry types, transformations over time, and already-cracked conditions.