PSI - Issue 78

Gennaro Vesce et al. / Procedia Structural Integrity 78 (2026) 936–943

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3. Seismic demand assessment Based on the results summarized in Section 2, this paper investigates the role of the mass ratio on the dynamic design parameters used into evaluating the seismic demand for masonry buildings with CLT vertical additions. The mass ratio is defined as  = m U /m L , where m U and m L are the total masses of the upper and lower structure respectively. The parameter  was considered as variable in the present investigation, assuming values in the range  = [0.1 - 0.4], whereas the stiffness ratio was assumed constant. The use case building adopted to perform the structural analyses is that represented in Fig. 1, where a single top vertical CLT addition was considered (supposed to have different mass ratios). 3.1. Dynamic modal analysis Fig. 2a compares the vibration periods associated with the three vibration modes of the investigated structure derived from the modal analysis, as a function of the mass ratios  . Focusing on the first vibration periods, they elongate about 20-22% for a mass ratio increment equal to 10%. Independently from the mass ratio  , the first periods belong to the plateau of the response spectrum adopted in this study and reported in Fig. 1; whereas the periods relative to the second and third mode are significantly lower than the first (for each considered mass ratio) ranging into the ascending branch of the response spectrum. The fact that the first period belongs to the plateau of the spectrum, can represent a first guiding criterion to adopt in the seismic designing of such a type of structure, because allows to select a suitable magnitude of the expected spectral acceleration. As far as the participating masses (M * ) is concerned, Fig. 2b shows that the excited masses associated with the first vibration mode decreases as the mass ratio increases and that they are lower than the limit value associated with the first vibration mode, set equal to 85% by the codes to consider the structure with a ‘regular’ behavior. The reduction of the first modal contribution due to the introduction of additional masses was expected, being the masses at upper storey are lower than those at the lower structure. This produces an irregularity in elevation of the building and makes the effect of the vibration modes other than the first more relevant from a dynamic standpoint. Note that, by considering the lower structure only (i.e., without CLT vertical additions), the participating mass of the first mode is greater than 90%, thus resulting the lower masonry structure categorized with a ‘regular’ behavior. On the other side, also in the context of nonlinear static analysis - basically adopted by engineers to assess the seismic capacity of existing buildings - IBC and Eurocode 8 set the participating masses of the first vibration mode equal to 75% as a limit value to assume a lateral seismic actions profile characterized by a linear distribution along the building height. On the contrary, they clarify that the lateral seismic action profile must be determined by means of a combination of the modal contributions, cumulating a number of vibration modes exciting a mass greater than 85% with respect the total one.

a) b) Fig. 2. Comparison among the modal parameters: a) first vibration periods (expressed in seconds), b) participating masses