316 E. Mola et al. beams and the slab. Due to the slenderness of the structure and of the slabs, no floor diaphragm constraint was applied for the floors, which can freely bend and deform out of plane. As for the eigenvalue analysis itself, the calculation of eigenvectors was carried out by the method of Lanczos and, for all the elements of the structure, the geometry of the gross cross section was considered, since the structure is expected to behave elastically under the low dynamic loads provided by the environmental excitation. The composite sections of the columns of the first floors was represented in the model with homogenized sections with respect to their bending moment stiffness (EI). Finally, an eigenvalue analysis was carried out for both the building with and without the struts and the dampers. . Due to the negligible effect of the struts on global stiffness and mass of the building, the results of the eigenvalue analysis, in terms of frequencies and mode shapes, were identical for both cases, as expected. The same model was used to carry out a dynamic response spectrum analysis (Fig. 32.4a). The spectra used for the analysis are specifically derived for slender building, i.e. for periods larger than 4 s, Fig. 32.4b and the damping values used were those compatible with a very streamlined tall building, i.e. 1 % for all the modes, instead of 5 %. The expected low values of inherent damping were then increased by introducing the additional damping contribution that the dampers were designed to provide, i.e. a nominal additional damping of 9 % on the first and on the third mode. As further detailed in the following, one of the results of the dynamic tests was to confirm the estimation both of the inherent and of the additional damping, thus validating the design and installation of the dampers themselves. 32.3.2 Eigenvalue Analysis Results In the following, the frequencies and mode shapes obtained from the numerical model are reported. In Fig. 32.3, the first 12 mode shapes are represented, whereas in Table 32.1, the modal masses, frequencies and periods are summarized. Only the results pertaining to the configuration without struts and dampers are reported, since, as discussed before, the results of the analysis on the final configurations are not affected by the presence of the struts and dampers, which provide only negligible contributions in terms of additional mass and stiffness. From Fig. 32.3 and Table 32.1, it can be noted that the first mode is mostly flexural along the weak axis of the building, the second mode is mostly flexural along the strong axis, whereas the third mode is mostly torsional. Since the building is very slender in the weak direction, it is particularly sensitive to the across-wind effects when the wind blows along the long side of the building; also, the sensitivity to wind loads along the weak axis is enhanced by torsional effects, which are evident already in the third mode. 32.4 Experimental Analysis 32.4.1 Description of the Tests The experimental tests were carried out according to the Operational Modal Analysis method, both before and after the installation of the viscous dampers. In both cases, the accelerations due to environmental excitation were continuously acquired for 3.5 days, with a sampling frequency of 20 Hz, and averaged over 3-h windows. The test set-up consisted of 30 horizontal accelerometers, measuring X- and Y-direction acceleration, according to the reference system in Fig. 32.5 vertical accelerometers, measuring Z-direction accelerations. The location of the sensors is reported in Fig. 32.5, represented the plan configuration of the typical instrumented floor. The same configuration was replicated for all the instrumented floors, i.s. Levels 12, 24, 33, 42, 49. The accelerometers used for the tests were PCP Piezotronics sensors having high sensitivity (10 V/g) and antialiasing filters. The wind speed was also measured by means of an anemometer directed along the X direction, according to the reference of Fig. 32.5. The data were analyzed by means of the Polymax algorithm, [3], implemented into an in-house software owned by the Company who carried out the tests, which automatically chooses the best averaging windows to minimize bias to the data due to the presence of workers or other accidental forcing sources. The PSD (Power Spectral Density) plots for some of the sensors are reported in Fig. 32.6a. In order to increase the reliability of the estimated modal properties, cross-correlation was checked between all the computed modes up to 5 Hz, by calculating the values of the AutoMAC index, as exemplified in Fig. 32.6b, showing the results for Mode 1.
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