318 E. Mola et al. Table 32.1 Frequencies, periods and modal mass values for the first 20 vibration modes of the Allianz Tower Frequency Period TRAN-X TRAN-Y TRAN-Z Mode no (rad/s) (cycle/s) (sec) MASS (%) SUM (%) MASS (%) SUM (%) MASS (%) SUM (%) 1 1.26 0.20 5.00 66.28 66.28 0.01 0.01 0.00 0.00 2 1.39 0.22 4.51 0.01 66.29 57.85 57.86 0.00 0.00 3 2.79 0.44 2.25 0.00 66.29 0.00 57.86 0.00 0.00 4 4.39 0.70 1.43 10.21 76.49 0.00 57.86 0.00 0.00 5 7.00 1.11 0.90 0.00 76.49 19.03 76.89 0.00 0.00 6 9.86 1.57 0.64 5.26 81.76 0.00 76.89 0.00 0.00 7 9.96 1.58 0.63 0.00 81.76 0.00 76.89 0.00 0.00 8 15.90 2.53 0.40 2.53 84.29 0.02 76.91 0.00 0.00 9 16.47 2.61 0.38 0.01 84.30 6.59 83.50 0.00 0.00 10 17.67 2.81 0.36 0.00 84.30 0.00 83.50 58.53 58.54 11 21.32 3.39 0.29 0.00 84.30 0.00 83.51 0.00 58.54 12 21.52 3.43 0.29 0.37 84.67 0.00 83.51 0.00 58.54 13 23.77 3.78 0.26 1.93 86.60 0.00 83.51 0.01 58.54 14 24.38 3.88 0.26 0.00 86.60 0.00 83.51 15.49 74.03 15 26.03 4.14 0.24 0.00 86.60 0.00 83.51 0.02 74.05 16 27.01 4.30 0.23 0.00 86.60 3.18 86.69 0.00 74.05 17 27.49 4.38 0.23 0.00 86.60 0.01 86.70 0.01 74.06 18 29.99 4.77 0.21 0.66 87.26 0.00 86.70 0.00 74.06 19 31.19 4.96 0.20 0.00 87.26 0.00 86.70 0.00 74.06 20 31.25 4.97 0.20 0.00 87.26 0.00 86.70 0.00 74.06 Fig. 32.4 (a) Finite element model of the Allianz Tower for eigenvalue and response spectrum analysis; (b) Site-specific, long-period response spectrum used for the analysis 32.4.2 Test Results and Comparison with Numerical Analysis The experimentally derived frequencies and modal damping values are reported in Table 32.2, together with the frequencies derived from the numerical model, for the modes that were identified: the numbering of the mode sequence is that of the experimental measures, but in brackets the numbering corresponding to the sequence of the eigenvalue analysis is also provided. In Figs. 32.7, 32.8 and 32.9, the experimental mode shapes of the identified modes are plotted together with the
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