PSI- Issue 9

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

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The local damage behavior of the pier was analyzed at three points around the base of the column as schematically indicated in Figure 5d. It has to be said that the authors could not find any experimental data to compare with the FE simulation and the local ductile damage evolution is reported as a consequence of the calibration on the global response of the structure. However, it is interesting to notice how the contribution of the inelastic tangential stretch accelerates the damage accumulation which can explain why the ductility seems to be higher when the load is proportional. For example, the point B is completely undamaged in the solid red line but it shows some damage evolution whenever the tangential inelastic stretch is considered. Moreover, due to the asymmetry of the MC failure envelope, the different damage accumulation in compression and tension can be appreciated. All the three points A, B and C refer to the centroid values of the elements located in the internal wall of the pier, where the numerical simulation showed the maximum damage contribution. This last set of analyses aims to investigate which kind of non-proportional loading represents the most critical scenario for the steel column. Three different bidirectional loading conditions were applied with increasing amplitude, similarly to the previous unidirectional case. The first load is a squared type loading SQ, the second one is a circular type loading CR and the last one is butterfly type loading BA. Figure 6 schematically displays these new boundary conditions that have been also investigated in a previous work of the authors Momii et al. (2015). All the numerical analyses in this section were conducted considering the whole cylindrical section, and not half as in the previous case, due to the bidirectional nature of the load. However, the body was modeled with linear hexahedral elements with reduced integration (Abaqus C3D8R elements) up to a height equal to 2D from the base of the column, the remaining part was modeled with a beam element as in Figure 2a. 3.4. Bidirectional loading

a)

b)

c)

Figure 6 a) Square type loading SQ, b) circular type loading CR, c) butterfly type loading BA.

The following Figure 7a reports the damage evolutions at the most damaged element (element centroid) for the different loading paths. The solid lines refer to the solutions obtained neglecting the contribution of the tangential inelastic stretch, instead the dotted lines refer to the solution obtained using the damage evolution law in Eq. (8) and setting the material parameter T 3 = 0.6. As it can be seen the solid lines display almost the same level of damage at the end of the analyses, which is, more or less the same damage level of the unidirectional loading analysis in Figure 5d. A different trend is shown for the NP-D laws where the CR loading path generate the highest damage, followed by the butterfly type and the squared type. The SQ loading path manifest a marked effect of the non-proportionality of the load at the beginning of the damage evolution (i.e. third and fourth cycles). In the BA type of loading the contribution of the inelastic stretch seems less relevant at the beginning, however the damage grows with a higher rate than in the SQ case, and the two dotted lines cross each other at the beginning of the eight cycle. A different tendency was observed in the circular path, where the red line shows a non- linear increase until rapture (i.e. D ≈ 1) .