PSI - Issue 44

D. Sivori et al. / Procedia Structural Integrity 44 (2023) 2090–2097 D. Sivori et al. / Structural Integrity Procedia 00 (2022) 000 – 000

2096

7

model and efficient NLSA, the evolution of the modal behaviour of masonry palaces for increasing levels of seismic damage, aiming at their employment together with the SHM system for conditions assessment (Section 4).

Fig. 4. NLSA results: (top) pushover curves along the two main directions of the palace, corresponding (middle) reduction of natural frequencies and (bottom) variations in the mode shape due to the damaging of structural elements.

Table 2. Reduction of natural frequencies and variations in mode shapes (MAC value) with respect to the undamaged state for significant damage steps, as generated by NLSA.

x

y

d r

d s

d u

d r

d s

d u

Mode Δf (%) MAC

Δf (%) MAC

Δf (%) MAC

Δf (%) MAC

Δf (%) MAC

Δf (%) MAC

-7.7 -0.7 -2.8 -0.2 -1.3

0.99 0.89 0.88 1.00 0.98

-24.8 -1.0 -11.1 -0.9 -3.2

0.97 0.87 0.79 0.87 0.80

-32.9 -1.6 -14.6 -1.2 -3.6

0.95 0.91 0.78 0.79 0.68

1 2 3 4 5

-1.6 -7.1 -3.5 -2.6 -1.2

1.00 0.85 0.86 0.98 0.99

-7.5 -33.9 -12.9 -5.1 -3.0

// //

-10.9 -65.4 -15.9 -6.6 -3.4

1.00 0.42 0.87 0.74 0.94

0.85 0.85 0.95

4. Conclusions The paper has outlined a methodology to support the seismic monitoring of monumental masonry palaces, exploiting the EF formulation and its nonlinear capabilities. The application to a real case study shows the possibility, with low computational power and short simulation time, to estimate the variations of the modal properties of the structure for increasing levels of seismic damage. Future steps of the research are aimed at the integration with real vibration-based SHM systems, seeking the implementation of a hybrid model-based and data-informed damage