Issue 29

L. Facchini et alii, Frattura ed Integrità Strutturale, 29 (2014) 139-149; DOI: 10.3221/IGF-ESIS.29.13 147 By means of the integration of Eq. (10)-(11)-(12), that constitute a set of coupled deterministic nonlinear equations, it is possible to obtains the sensitivity vectors and to estimate: i) the response   x t evaluated for   k E k  (Fig. 9); ii) the sensitivity of the response   k x t (Fig. 10) and iii) the derivative of the sensitivity   kk x t (Fig. 11). Figure 11: Derivative of the sensitivity   kk t x . And eventually, the approximations for the expected value of the response and its standard deviation are obtained considering a second-order expansion for the mean displacement and a first-order expansion for the variance, by:           2 1/ 2  σ σ σ kk k x k k x x E x t t t t x t        (13) The expected response, together with the 3σ bounds, is shown in Fig. 12. Figure 12: Expected response and bounds of the disordered BW system. C ONCLUSIONS he paper showed the application of a simplified methodology for the seismic analysis of masonry towers. The method is based on the assumption that such response is mainly due to the first modal shape of the tower, and takes into account the randomness of the tower parameters. With this assumption, the behavior of the first modal T