The URM buildings designed to be conforming with the Italian building code, as illustrated in the companion paper by Manzini et al. (2018), were analyzed by performing time-history analyses on models realized using an equivalent frame approach and by adopting two different constitutive laws. Both the effect of record-to-record variability and of epistemic and aleatory uncertainties in modelling were explored. The achieved results constitute the basis for the evaluation of the risk level implicit in Italian code-conforming buildings (Iervolino et al. 2018). Two main performance conditions are considered, namely usability-preventing damage and global collapse limit states.

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Several building codes propose methodologies to account for epistemic uncertainties in the seismic assessment of masonry buildings by selecting a knowledge level and reducing material strengths by means of the associated value of the confidence factor. Previous works showed that, in the case of masonry structures, this approach has various limitations, such as the lack of proper consideration of experimental tests performed. This article focuses on the issue of imperfect knowledge on material properties of existing masonry buildings and proposes a probabilistic methodology for the assessment, based on Bayesian updating of mechanical properties. The use of a Bayesian approach allows to update the values of the material properties assumed a priori as knowledge on the building increases, by taking into account all the experimental information gathered during the assessment process. A large number of simulated assessments is carried out and the values of the confidence factors on material properties are defined through the comparison between the obtained results and those of the reference structure, assumed to be perfectly known. These factors are useful in a more general framework for the assessment of masonry buildings accounting for different sources of uncertainty.

In the numerical modelling of the nonlinear response of masonry buildings by equivalent-frame models based on macroelements representative of the in-plane response of structural members, it is important to correctly capture compressive behavior, lateral stiffness, and strength of the structure. The macroelement model currently implemented in the TREMURI computer program, thanks to the presence of nonlinear interfaces lumped at the element extremities, allows studying the coupled axial and in-plane bending response, with the inherent limitation of approximating the stiffness associated with at least one of these behaviors. The simplified compressive law does not capture the displacement accumulation during cyclic loads; moreover, second-order effects are not modelled. The article presents an improved macroelement model, able to simulate the in-plane cyclic response of masonry walls. The model overcomes some of the limitations of the currently available macroelement. As regards the compressive and flexural behavior, a new compressive law is introduced, together with a methodology to capture the correct flexural stiffness of the panel and to model the secondorder effects. The improved model was then implemented in the TREMURI program and validations of the new features are shown, together with a simulation of an experimental test on a single wall characterized by flexural behavior. A companion article presents the shear formulation and shows the ability of the new macroelement of accurately predicting the nonlinear response of masonry structures at the building scale through the simulation of a larger number of experimental tests.

Macroelement models are widely recognized to be particularly suitable to model the nonlinear behavior of masonry buildings. This article, together with the companion article, presents a new macroelement model, able to solve the limitations of the macroelement model currently implemented in the TREMURI computer program. Whereas the companion article deals with the axial and flexural behavior, this article presents the formulation regarding the shear behavior. In the macroelement currently implemented in the TREMURI program, the shear strength and deformability of an element can be captured only if a manual calibration of equivalent material properties and shear deformation parameters is performed before the analysis. On the contrary, the proposed new macroelement is able to predict the cyclic response of a wall failing in shear, considering multiple strength criteria, directly starting from experimentally measured or code prescribed mechanical properties and automatically calculating the equivalent shear parameters. Furthermore, a procedure to calculate the deformability parameters governing the nonlinear shear response starting from experimentally measured or code prescribed parameters is also included. Therefore, calibrations of material properties and shear deformation parameters at the beginning of the analysis are no longer required. The improved model was then implemented in the TREMURI program and its ability of accurately predicting the nonlinear response of masonry structures is verified through the simulation of experimental tests at different scales.