PSI - Issue 78

Lorenzo Audisio et al. / Procedia Structural Integrity 78 (2026) 1277–1284

1279

In the first case, it is necessary to explicitly include the NSE within the global structural model. In the second case, the seismic demand can be assessed by assuming that the floor acceleration represents the seismic input acting on the NSE, provided that its mass is negligible compared to the main structure one and therefore the dynamic interaction effects can be disregarded. Whereas, the FRS method (Biggs, 1971; Chen, 1974) falls within the second case, based on the simplified assumption that the structure can be considered as a harmonic excitation on NSE. According to the Instructions for the application of the Italian Standards NTC 2018 (MIT - Italian Building Standard 2018), the seismic demand in acceleration on a NSE, located on the j-th floor and due to the contribution of the i-th mode, is given by the following expression: , = ( ; ) (1) where is the modal acceleration equal to: = ( ) (2) and is the i-th mode shape at the j-th floor, the modal partecipation factor, and ( ) is the spectral ordinate of the i-th mode with a vibration period T i (also reduced by the behavior factor). The term R is the element amplification factor, depending on the ratio between the natural period of the NSE, (T a ) and the period of the i-th mode of the structure (T i ), as well as on the damping of the NSE ξ a .

Fig. 2. Floor Response Spectrum

Figure 2 schematically illustrates the procedure for evaluating the acceleration demand on NSEs using the FRS approach, based on the combination of the structural modal response and the dynamic properties of the component. The total demand in acceleration of the NSE in a given direction at the j-th floor is obtained by combining the modal accelerations (Eq. 1), for example, by using the SRSS (Square Root of the Sum of the Squares) rule: , = √∑( , ) 2 (3)