PSI - Issue 44

Gaetano Della Corte et al. / Procedia Structural Integrity 44 (2023) 472–479 Cantisani, Della Corte / Structural Integrity Procedia 00 (2022) 000–000

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4. Non-linear static analysis results Fig. 6(a) shows a plot of the relationship between the link shear force ( V ) and the link chord rotation ( θ ). The link shear force is normalized by means of the expected plastic resistance of the cross section, V l,Re , A comparison of the results obtained using SAP2000, Code_Aster and Ansys is provided in the figure. All the numerical models indicate that both the link and the brace stability are ensured up to chord rotations equal to θ u = 0.08 rad, which is a value typically assumed as the link rotation capacity prior to fracture in case of cyclic loading (e.g., NTC 2018). Figure 6(a) shows clearly that all the numerical models provided the same linear elastic response. Besides, the models implemented in SAP2000 and Code_Aster did also provide practically negligible differences in the non-linear responses. Those two numerical models were almost identical, because they differed only for the details of the mesh geometry while both models adopted the same steel stress-strain relationship. On the contrary, differences in the range of non-linear response due to a different stress-strain relationship can be large. In fact, the results obtained with SAP2000 clearly show that the KH material model, simulating the monotonic steel stress-strain response, significantly underestimates the inelastic link shear forces in comparison with the corresponding SH model, which takes into consideration the steel cyclic strain hardening. The SAP2000 results obtained using the SH model are also in good agreement with the more accurate simulation results obtained using Ansys . The SAP2000 with SH material model provides some underestimation of the link force resistance for a link chord rotation in the range of 0.01 rad through 0.08 rad. This is a consequence of the material model calibration against the experimental stress-strain response of the steel. In fact, the SH model implemented in SAP2000 does not allow to match the material response over the full range of inelastic strains. The calibration of the SH model was intentionally addressed to match the experimental response at the largest link chord rotations, to capture more accurately the peak value of the inelastic shear force developing in the link. According to the Ansys model, the ratio between the link peak shear force developed for θ = 0.08 rad and the expected plastic shear resistance of the cross section is equal to 1.77. A very similar result was obtained using the SH model implemented in SAP2000 . Eventually, one can also see that the KH model provides much smaller inelastic shear forces in the link. Eventually, the results obtained with Ansys clearly show that the effect of geometrical imperfections and residual stresses was almost negligible in the range of inelastic link rotations that have been examined. In fact, the imperfections introduced in the model produced some but limited out-of-plane displacements and rotations at the bottom section of the link (i.e., at the intersection between the link and the diagonal members). Therefore, these analysis results indicate that there were no stability issues, and that the link was able to fully develop its inelastic action up to the maximum chord rotation of 0.08 rad. This is an especially important result for the practical application of this system for seismic upgrading of existing RC frames, because no lateral-torsional bracings were included at the bottom section of the link. Any need for introducing such out-of-plane bracing would impair the possibility to mask the eccentric bracing system inside the masonry cladding or partitions, as well as posing significant additional structural problems for the connections of such bracing to the existing structure. Fig. 6(b) and Fig. 6(c) show the equivalent Von Mises stress contour plots for the link and the initial portions of the diagonal members. Two analysis steps were considered for those plots: (i) the initial condition i.e., with no lateral loads applied onto the system and, (ii) the step corresponding to a link chord rotation demand equal to 0.08 rad . The presence of the residual stresses can be seen in Fig. 6(b), while Fig. 6(c) shows that the plasticity developed essentially in the link with minor to negligible yielding at the ends of the diagonal brace members. The plot in Fig. 6(c) also demonstrates that the link flanges also yielded due to the link end moments at large chord rotations. The above results are further confirmed by examining contour plots of equivalent plastic strains, which are shown in Fig. 7. The three subplots (a), (b) and (c) are for three different analysis steps, corresponding to link chord rotations equal to 0.01 rad , 0.04 rad and 0.08 rad , respectively. The subplot (a) shows that plastic strains start to develop in the link web, with the link flanges remaining elastic. This confirms the validity of the link classification system (i.e., short link yielding in shear). For larger link chord rotations (subplots (b) and (c)), the plasticity spread through the whole link web, eventually also involving the link flanges. The larger spread of plasticity to the flanges at the top section of the link compared with the bottom section is easily explained as due to the boundary conditions. In fact, the model has some more rotational flexibility at the link-to-brace connection due to the flexural deformability of the brace members.