PSI - Issue 44

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Francesco Morelli et al. / Procedia Structural Integrity 44 (2023) 574–581 Francesco Morelli, Agn e Natali, Gabriele oggi / Structural Integrity Procedia 00 (2022) 000–000

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Fig. 10. IDA curve vs “classical” Pushover curves.

The multimodal pushover analyses (Campbell et al. 2010) have the goal of considering the influence of different mode shapes. The load distributions are evaluated according to the “method of modal combination” (MMC) which inherently includes the interaction of different modes. The horizontal load distribution, determined in eq. (2), derives from a combination of the relevant mode shapes and spectral accelerations according to the natural frequencies. � F j � = Γ 1 ∙ [M] ∙ { Φ 1 } ∙ S a (T 1 , ζ ) ∓ … ∓ Γ n ∙ [M] ∙ { Φ n } ∙ S a (T n , ζ ) (2) where: � � is the load vector representing the horizontal force distribution [ ] is the mass matrix is the modal participation factor for the i th -mode { } is the modal shape for the i th -mode ( , ) is the spectral acceleration for period of the i th -mode In order to determine the main multimodal force distributions, the first three vibration modes are used (Table 1), resulting in 4 combinations, see Fig. 11. a b

Fig. 11. (a) Deformed modal shapes; (b) main modes’ combinations.

Fig. 12 shows the comparison between the IDA curves and the pushover curves, highlighting that the best match is obtained for the pushover curve obtained from the combination “1+2+3” and the IDA curve obtained by combining the maximum base shear and the maximum displacement at the top of the structure. The same figure, right part, shows the comparison between the IDA curve (Vmax - Dmax) and the selected multimodal pushover, highlighting the performance points. It can be seen that the performance points are in quite good agreement in terms of base shear, while the pushover analyses tend to underestimate the displacements, supplying consequently higher