PSI - Issue 78

Ciro Canditone et al. / Procedia Structural Integrity 78 (2026) 1855–1862

1860

A first comparison between numerical outputs can be drawn in terms of natural frequencies and modal shapes, with reference to the first three vibration modes (see Figs. 4a-f)). These were found to be translational on X and Y axis, and torsional with respect to Z. The modal displacements of 24 selected points, that is, storey-level points at building’s corners and at mid-façade length, were compared amongst the two models in order to assess the Modal Assurance criterion (MAC). The translational modes along X and Y, albeit well correlated by a MAC equal to 0.79, were found to be mismatched amongst the two models. This can be explained as the effect of different modelling assumptions, which were nevertheless found to be remarkably close in terms of resonant frequencies ( f x FEM = 4.91 Hz; f x AEM = 4.70 Hz; f y FEM = 4.89 Hz; f y AEM = 4.89 Hz). Lower agreement was instead found with regards to Mode 3, torsional, with a 0.37 MAC and numerical frequencies equal to f t FEM = 5.11 Hz and f t AEM = 5.27 Hz, respectively. This poorer correlation can be attributed to the fact that torsional response is more sensitive to variations in stiffness distribution, mass eccentricities, and boundary condition idealisations. Small differences in these aspects, such as the discretisation of openings, can cause changes in the torsional mode shape even when the corresponding frequency remains close.

(a)

(b)

(c)

FEM

fx FEM =4.91 Hz

fy FEM =4.89 Hz

ft FEM = 5.11 Hz

(d)

(e)

(f)

AEM

ft AEM = 4.79 Hz

fx AEM = 4.18 Hz

fy AEM = 4.18 Hz

Figure 4. Modal shapes and frequencies obtained via FEM and AEM analysis.

Another comparison was drawn with regards to the stress and displacement states of the two models under dead and live loads, combined according to an exceptional loading condition (EC1, 2002). A good agreement is found between the two models, which yielded a maximum compressive stress at pier bases approximately ranging from 0.30 MPa to 0.50 MPa, depending on the pier cross-section; see Figure 5a, 5b. Hence, considering a maximum compressive strength fc equal to 2.00 MPa, the archetype seems to be in a relatively safe condition under gravity and live loads. With regards to structural performance under settlement loading, an analysis of principal compressive stresses and damage indexes in terms of principal tensile strains for the AEM and of damage accumulation due to tensile loading for the FEM was performed, with a maximum settlement d v max = 15 mm attainment. Settlement loading can be observed to have significantly affected both the AEM and the FEM model’s initial stress distribution, causing approximately 1.00 MPa local stress concentrations within piers’ bases, that is, almost doubling the initial compressive stress demand (Figs. 5c and 4d). It is thus reasonable to infer that, for higher settlement magnitudes, progressive localized crushing of masonry pier bases may be expected. On the other hand, the stress state and load transfer within the AEM URM vaults do not appear to have been significantly altered, despite the extensive cracking pattern observed. In the FEM model, the vault behaviour was instead kept within the linear elastic range to prevent the onset of severe local cracking. With regard to damage states, a maximum principal tensile strain of 0.01 and a maximum damage accumulation of 0.9 (on a scale where 1.0 represents complete damage) were found to yield AEM/FEM crack patterns in good qualitative agreement (Figs 5e and 5f). As can be appreciated from Figure 4f, significant cracking is found within the gooseneck rising vault and URM spandrel elements; shear failures can also be observed within the base piers closest to maximum settlement. The observed damage correlated with approximately 17%, 9%, and 16% frequency reductions for the first three vibration modes in the AEM model, whereas the corresponding FEM results