Masonry walls restrained by dissipative tie-rods. Part 2 - Non-linear kinematic analysis

This paper proposes a framework to design Dissipative Tie-rods (DT) based on the Non-Linear Kinematic Analysis (NLKA) commonly used for masonry walls subjected to out-of-plane (OOP) modes, where walls are unrestrained or restrained by traditional steel tie-rods. Although the Non-Linear Dynamic Analysis (NLDA) represents a rigorous approach to solve the dynamics of any wall restrained by tie-rods, NLKA is the tool mainly used by researchers and professional engineers. Unlike NLDA, in the literature a NLKA-based methodology is currently not available to design or to assess masonry walls restrained by DT. The paper presents it exploiting the concept of equivalent damping ratio, necessary to perform NLKA and conceiving a way to calculate the capacity curve. The equivalent damping ratio, a key parameter of the proposed methodology, has been obtained from experimental tests and numerical procedures described in detail in the companion paper, Part 1. The procedure is validated through a NLDA by means of its application to a masonry wall of an existing masonry building located in Central Italy. The NLKA here proposed shows a very good agreement with the NLDA results, as the outcomes in terms of safety are consistent and the maximum displacements differ by around 16 %. Moreover, it is demonstrated that the NLKA is always conservative in comparison with the NLDA, which is in line with results from literature.