PSI - Issue 44

Elena Michelini et al. / Procedia Structural Integrity 44 (2023) 1530–1537 Elena Michelini et al / Structural Integrity Procedia 00 (2022) 000 – 000

1534

5

The MAC index can assume values between 0 and 1, respectively in the case of perfect orthogonality and perfect parallelism between the modes to which it refers. As can be seen in Table 2, the elements out of diagonal are very close to zero, a sign of the orthogonality between identified modes which in turn confirms that the measured points are sufficient to spatially distinguish the different mode shapes. The MAC of modes 1 and 5 is slightly higher than others, but, in any case, less than 10% and therefore more than acceptable in the context of experimental measurements.

Table 1. Identified modal parameters: frequencies, damping and modal masses. Mode f [Hz] ζ [%] Mx

My

1 2 3 4 5

3.38 3.55 4.08 4.44 5.24

1.00 0.95 1.07 0.75 0.97

0.83 0.06 0.00 0.01 0.03

0.05 0.57 0.09 0.02 0.04

1 st mode

2 nd mode

3 rd mode

4 th mode

5 th mode

Fig. 4. Identified mode shapes.

Table 2. MAC indices of identified mode shapes. Mode 1 2

3

4

5

1 2 3 4 5

1

0.007

0.026 0.005

0.028 0.030 0.022

0.093 0.027 0.010 0.001

0.007 0.026 0.028 0.093

1

0.005 0.030 0.027

1

0.022 0.010

1

0.001

1

4. Finite element modelling A numerical 3D model of the building was realized by using the FE software MIDAS FEA NX (Midas FEA NX Analysis Manual, 2020). The geometry of the model was deduced from the available geometric survey, which was subjected to additional local checks during on-site inspections. Masonry walls were modelled through 2D shell elements, with variable thickness both in plan and along the building height, according to the available drawings (Fig. 5a, different colors correspond to different wall thickness). 2D shell elements were also used for modelling the different types of masonry vaults in the building (barrel vaults, as well as cross and pavilion vaults, see Fig. 5b relative to the 2 nd floor), and for the stairs. Composite floors realized with RC joists and interposed hollow clay blocks were inserted as rigid diaphragms – due to the presence of the RC topping slab – by using rigid links, while main timber beams were modelled through beam elements. Due to the complex geometry and only partial accessibility of the roof, the corresponding elements were not directly inserted in the model, but they were applied as loads only.