Detailed and simplified non-linear models for timber-framed masonry structures

The need for improved methodologies to describe the post-elastic behaviour of existing structures in the framework of seismic vulnerability assessment has long been recognised. The study presented herein deals with the non-linear seismic response of timber-framed (T-F) masonry structures, such as those found in traditional edifices of cultural heritage. T-F masonry generally consists of masonry walls reinforced with timber elements, including horizontal and vertical elements, as well as X-type diagonal braces. Since the Bronze Age T-F buildings were common in regions where moderate-to-strong earthquakes were frequent. There is ample historical evidence that the embodiment of timber elements in masonry walls is closely related to earthquakes. The paper focuses on the description of the seismic response of T-F structures by means of a detailed analytical model. Although elastic analysis can adequately identify regions with high stresses, it fails to capture the redistribution of stresses and the ensuing failure mechanism. The simulation of T-F masonry is made here using a plasticity model. Non-linear laws for the materials, such as a trilinear stress-strain curve for monotonic loading of timber and a Mohr-Coulomb contact law for wooden members, are used to express their behaviour under moderate and high stress levels. An associated flow rule is assumed and Hill's yield criterion is adopted with isotropic work-hardening. Masonry infills are not included in the model due to their insignificant contribution after the initial elastic stage of the response. The proposed finite element model is intended for a detailed non-linear static analysis of parts of a building. A simplified model using beam and link elements with non-linear axial springs is also developed, which is appropriate for 2D non-linear analysis of common buildings. Both models are validated using experimental results of three T-F masonry walls obtained from the literature. Finally a non-linear static analysis of the façade of an existing building situated in the island of Lefkas, Greece is performed.