PSI - Issue 44

Maria Maglio et al. / Procedia Structural Integrity 44 (2023) 550–557 M. Maglio, R. Montuori, E. Nastri, V. Piluso / Structural Integrity Procedia 00 (2022) 000–000 ( ) = ( ) ( ) ≥ , 475 where: 0 ≤ ≤ : ( ) = 0 = ≤ ≤ : ( ) = 0 + � − 0 � ( − )/( − ) ≤ : ( ) = (8) It is important observing that is the lower bound factor for the horizontal reduced spectrum, the new Eurocode 8 introduces for the factor the 0.08 value to be applied to the PGA for buildings (prEN1998-1-2, 2021). The value of the PGA has been computed as the ratio between , 475 and . This lower bound value applies only to forces, displacement demands should still be evaluated from the displacement spectrum or the elastic response spectrum, for very soft structures. It means that the checking in terms of resistance must be made with the lower bound modified spectrum while the drift and second order effects checking must be done with the spectrum without the lower bound limit. The reduced horizontal response spectra for SD, DL and OP are shown in the following figure and the lower bound limit applied to the SD spectrum is also reported. 553 4 (7)

Fig. 2. Horizontal reduced response spectra for DC2 ductility class

3. Design approach aligned with prEN1998-1-2 (2021) 3.1. Second order effects The evaluation of second order effects exploits the sensitivity coefficient θ which is revised by Plumier (2022) and inserted in the new prEN1998-1-2 (2021) version as follows: = , ℎ (9) where is the total gravity load at and above the storey, due to the masses considered in the seismic analysis of the structure; , is the design interstorey drift, defined as the difference of the average lateral displacement at the top and bottom of the storey under consideration and calculated according to the prEN1998-1-1 (2021) for the SD limit state by the analysis for the displacement-based approach; is the total storey shear in the seismic design situation for the force-based approach; ℎ is the interstorey height; and are the behaviour factor components. Second-order effects may be neglected if the condition ≤ 0.10 is fulfilled in all the storeys. If 0.10 < ≤ 0.20 , the second-order effects may approximately be considered by multiplying the relevant seismic action effects by a factor equal to 1/ (1- θ ). If 0.20 < ≤ 0.30 at any storey, the second-order effects should be taken into account directly by using the established methods of second-order analysis which take account of geometric non-linearity, i.e., consider the equilibrium conditions on the deformed structure. The value of θ should not exceed 0,30. The novelty point of Eq. (9) is the presence at the denominator of and with the scope of reducing the possible structural oversizing coming from the limitations in terms of second order effects.