Advanced frame element for seismic analysis of masonry structures: model formulation and validation

Abstract

SUMMARYThis paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force-based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber-section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi-floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box-like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation.

New Frontiers on Seismic Modeling of Masonry Structures

“…The first validation is relative to the case of a single panel which was investigated considering a comparison between the proposed approach and an equivalent frame model combined with a fiber section model recently proposed in Raka et al (2015). The considered example is made of a simple panel restrained at its base and at its top; a two phase analysis is here applied, considering a first force controlled phase with the application of a vertical load and a second displacement controlled phase with an increasing horizontal displacement at the top of the panel.…”

“…The adopted mechanical properties are reported in Table 3; however, for this first example, the shear failure is considered inhibited. Even though the model described in Raka et al (2015) is based on an equivalent frame approach, with regards to the combined flexural-axial behavior, both models are based on a direct fiber section analysis. For this reason, it is expected that the two considered models provide very close results in terms of ultimate load.…”

“…A second example of a single panel is reported in the following. In this case again, a comparison between the proposed approach with the equivalent frame model proposed in Raka et al (2015) is reported. Unlike the previous case, here the axial, bending, and shear forces interact all together.…”

“…On the other hand, structural engineers need simple and efficient numerical tools, whose complexity and computational demand should be appropriate for practical engineering purposes. For these reasons, in the last decades, many authors proposed simplified or alternative methodologies to predict the non-linear seismic behavior of unreinforced masonry (URM) structures, particularly oriented to buildings (D' Asdia and Viskovic, 1995;Braga et al, 1998;Brenchich et al, 1998;Magenes and La Fontana, 1998;Kappos et al, 2002;Caliò et al, 2005;Chen et al, 2008;Marques and Lourenço, 2011;Raka et al, 2015). Marques and Lourenço (2011) report a comparison between different simplified approaches currently used in academic research and engineering practice.…”

The effective stiffness of modern unreinforced masonry walls

“…In order to compute the shear force‐displacement curve of the equivalent frame subjected to a horizontal load, the behaviour of its constituents, ie, walls and spandrels, have to be known. For the analysis of URM buildings, beam and macro elements have been developed to be used in the equivalent frame method . In several of these models, walls and spandrels are approximated by Timoshenko beams.…”