PSI - Issue 64

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Corrado Chisari et al. / Procedia Structural Integrity 64 (2024) 199–205 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. Force-displacement plots for the analyzed vaults.

The plots show the importance of the vault thickness on the overall strength, highlighted by the different y-scale between plots on the left ( t / s =0.15) and on the right ( t / s =0.2). In this regard, it should be highlighted that t/s =0.15 is close to the minimum geometrical ratio for a semi-circular arch to bear its sole self-weight under Heyman’s assumptions (i.e. t/s =1/9) (Heyman, 1982). Comparing top row with bottom row, it is noted that lancet arches ( e/s =1.5) have higher vulnerability, i.e., lower strength, with respect to the drop pointed arches ( e/s =0.5) with drops in strength which may exceed 50%. Lateral wall thickness has a role in the overall strength, with thicker walls (blue lines) consistently showing higher capacity than thinner ones (red lines). This effect is less important when ribs are thicker (as in solid lines in Fig. 2, compared to corresponding dashed lines). The overall displacement capacity and stiffness of the system seem to be influenced by the input parameters similarly to the strength. In all cases the maximum displacements of the system are very small (no more than 4 mm, equivalent to 0.067% of the net span). 3.2 Collapse modes In all cases investigated, the collapse mode is characterized by shear failure of one of the arch supports corresponding to the open side. Depending on the configuration, this is coupled to more or less extensive damage at intrados of the vault, in the ribs, at interface between walls and vault and at diagonal extrados. The damage contours predicted by the models are shown in Fig. 3. In particular, the analyses show a larger redistribution capacity of damage in shorter vaults (e/s = 0.5) compared to higher vaults (e/s = 1.5), where the damage is more concentrated at imposts. In perspective, this translates into a minor efficiency of retrofitting actions interesting the vault intrados or extrados. In either cases, thicker vaults (t/s = 0.2) show larger damage at the wall-vault interface. The rib thickness, although significantly influencing both stiffness and capacity of the system (Fig. 2), seems to have small influence on the overall damage pattern.