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1 Distance between centre of rotation and centre of gravity.

2 Maximum horizontal force divided by total weight.

3 Maximum vertical force divided by total weight.

1 Distance between centre of rotation and centre of gravity.

2 Maximum horizontal force divided by total weight.

3 Maximum vertical force divided by total weight.

Figure 9. 3D FEM of the tower. Connections with chapel and church. (a) North and west façades (b)East and south façades.

Figure 9. 3D FEM of the tower. Connections with chapel and church. (a) North and west façades (b)East and south façades.

Figure 9 shows the model of the soil with 10460 solid elements, 14312 nodes and 10.640 degrees of freedom. To simulate the tower 4312 solid elements and 6932 nodes are used.

After an iterative process an average elastic modulus for the structure of 1.500 N/mm2 was obtained. For the basement an average elastic modulus of 200 N/mm2 was obtained.

Table 3 shows the modal participating mass ratios of the structure. These mass modal ratios permit to identify the different modes.

Once the numerical model has been calibrated using the experimental results, the horizontal forces caused by the swinging bells are introduced in the model. From this analysis it has been obtained that the dynamic amplification factor is lower than 1 for all the bells, so no dynamic interaction is found between belltower and bells.

The first three modal frequencies of the horizontal force introduced by the swinging bells (Fig. 11)

Figure 10. 3D FEM of the tower, (a) First mode (N-S). (b) Second mode (W-E) (c) Third mode. Torsion.

Figure 10. 3D FEM of the tower, (a) First mode (N-S). (b) Second mode (W-E) (c) Third mode. Torsion.

are separated more than 20% (DIN 4078) from the first three natural frequencies of the structure, so the dynamic amplification factor due to this dynamic interaction is negligible in this case. (Fig. 12)

Table 3. 3D model. Modal participating mass ratios.

Axis Direction

Rotation-axis

Table 3. 3D model. Modal participating mass ratios.

Axis Direction

Rotation-axis

Mode classification

Natural

Freq.

(Hz)

N-S %

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