PSI - Issue 84

Siro Casolo et al. / Procedia Structural Integrity 84 (2026) 1214–1221

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strength under cyclic loading is then assumed, and the curve loses its initial symmetry. A specific numerical procedure has been implemented to update the skeleton curve based on the normal stress value recorded on the bond-spring, increasing the shear strength due to internal friction and numerically reproducing a Coulomb-like behavior. The internal friction coefficients ( ) adopted are: 0.80 for “Masonry 1” and “Masonry 2”; 0.40 for “Masonry 3”; 0.10 for “Infill” and “Contact”.

Fig. 3. Stress-strain laws adopted for the bond-springs.

5. Discussion of results 5.1. Modal analysis

The first six modal shapes of the case study are shown in Figure 4. The first natural mode, with a frequency of 3.4973 Hz, is characterized by longitudinal oscillation of the central arch, with contraction and expansion of the side arches. The second and third natural modes, with frequencies of 5.4530 Hz and 7.4215 Hz respectively, are basically characterized by the vertical oscillation of the central arch. The fourth vibration mode, with a frequency of 8.0561 Hz, is characterized by the rotation of the upper part of the central arch around the out-of-plane Z-axis. The fifth and sixth vibration modes, with frequencies of 10.5649 Hz and 10.9436 Hz respectively, are centered on the longitudinal and vertical oscillation of both the central arch and the two lateral arches.

Fig. 4. In-plane modal shapes and frequencies obtained for San Marcello Pistoiese bridge by RBSM.

5.2. Non-linear Dynamic Analysis This section analyses the results obtained from non-linear dynamic analyses in the 5 impact scenarios with variable position and inclination angle, named Test A, B, C, D, E (according to the symbols of Figure 1). Test A (Figure 5, left) involves almost exclusively damage to the infill at the abutment. Only with an angle of 45° the impact also affects