Issue 47

R. Fincato et alii, Frattura ed Integrità Strutturale, 47 (2019) 231-246; DOI: 10.3221/IGF-ESIS.47.18 242 a) b) c) d) Figure 8: cumulative tangential plastic strain at a) the end of the 5 th cycle, b) the end of the 6 th cycle, c) the end of the 7 th cycle, d) the end of the 8 th cycle. On a local scale, the damage has been investigated along the three circumferential cross sections schematically illustrated in Fig. 7a. The three cross sections indicated with the marks A-A’, B-B’ and C-C’ are located at 45 mm, 105, and 165 mm from the base of the pier, respectively. Fig. 7b, c and d report the corresponding ductile damage level at the end of the 8 th loading cycle. One first observation is that the effect of the tangential plasticity on the damage seems to be more relevant around half of the circumferential length for smaller distances from the pier base. In fact, the two solutions NP-D and P-D in Fig. 7b show a complete difference tendency at the 0.5 value on the x-axis. The more the distance increases from the base of the column the more the effect becomes small. a) b) Figure 9: lateral displacements at the loading points for the prescribed displacements amplitudes ±3δ y , ±6δ y and ±8δ y for a) SIDE A and b) SIDE B of Fig. 3a. A second conclusion is that the damage is maximized for the points located along the loading direction in the graphs of Fig. 7d and c (i.e. the points B, C, B’ and C’). Here, both the solutions NP-D and P-D have peaks in the damage accumulation in correspondence of the points B’ and C’. In detail, the point B’ shows the highest absolute peak with a value of D ≈ 0.54. Van Do et al. [36] obtained a similar peak value, using a different damage accumulation law for the same study case.