PSI- Issue 9

Riccardo Fincato et al. / Procedia Structural Integrity 9 (2018) 136–150 Author name / Structural Integrity Procedia 00 (2018) 000 – 0 0

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e) f) Figure 8 a) and b) Normalized force vs normalized displacement along x and y for the SQ path; c) and d) normalized force vs normalized displacement along x and y for the CR path; e) and f) normalized force vs normalized displacement along x and y for the BA path.

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Figure 9 Cumulative inelastic strain H i of Eq. (8); a) SQ path ( H i max ≈ 1.2), a) CR path ( H i max ≈ 1.37), a) BA path ( H i max ≈ 1.0), a) Uniaxial path ( H i max ≈ 1.14). The reason for this behaviour might be duplex. First, the tangential contribution is a function of the similarity ratio R through the Eq. (9), which is constantly maximized in the CR path compared to the SQ and BA paths. Secondly, the CR path induces a constant rotation of the principal stress and strain axis, constantly triggering a tangential component of the stress rate. The comparison of the maximum damage level between the unidirectional and bidirectional loadings reveals that the paths SQ and BA have a slightly higher damage at the ninth cycle compared to the uniaxial loading, D = 0.615 and D = 0.66 respectively. The crack is potentially formed at the beginning of the eight cycle in the circular path. Figure 8 reports the normalized lateral force vs the normalized displacement along the x and y axes for the three bidirectional loading paths. Compared with the unidirectional loading the force peaks for the SQ path are slightly higher and the CR and BA paths showed lower values of the normalized force. Figure 9 shows the cumulative inelastic strain H i of Eq. (8) for the three bidirectional paths and the unidirectional path of section 3.3. As it can be seen the inelastic strains of the unidirectional path are localized at the base of the pier along the loading direction. The three bidirectional paths show a distribution of the inelastic strain along the circumference of the column. In particular, the path CR displays higher values of H i with a peak of 1.37, and this may explain the damage evolution of Figure 7.