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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the intersections of the link and the two diagonal members. Instead, for the Code_Aster and Ansys models, the mesh was generated automatically by selecting one of the algorithms already available in both software packages. Consequently, the number of triangular elements was automatically generated by the software in those cases, while the size and shape of the generated quadrilateral elements was checked to be not excessively distorted.

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α RC beam axis

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Fig. 3. EB model: (a) boundary conditions; (b) node-to-node brace model.

3.2. Material modelling The implemented stress-strain relationships are summarized in Fig. 4(a). First, a simple bilinear stress-strain relationship with kinematic hardening (KH) was considered. The yielding strength was assumed equal to the expected value ( f ym = 343.8 MPa), while the ultimate strength and ultimate strain were assumed equal to the design nominal values ( f u = 430 MPa, ε u = 0.20). Such bilinear relationship was implemented for all the brace geometries both in SAP2000 and Code_Aster . Additionally, the numerical data used by Della Corte et al. (2013) were adopted to fit a numerical stress-strain relationship to available stress-strain experimental data. The considered experimental stress-strain relationships are also shown in Fig. 4(a), where both monotonic (M, continuous line) and cyclic (C, dotted line) test data are reported according to Della Corte et al. (2013). To assess the response for a cyclic loading history, the numerical calibration of the stress-strain relationship was carried out using the cyclic test data. This is essential to correctly capture the effects of the steel cyclic hardening behavior. To model the strain-hardening in SAP2000 , the non-linear isotropic saturation hardening (SH) model was used. The result from the model calibration is shown in Fig. 4(a) with a continuous red line. As one can see, the implemented stress-strain relationship represented the observed test data for strains ranging from 0.3 through 0.6, approximately. Some underestimations of the initial strain hardening response is apparent from the plot. A more complete representation of the stress-strain relationship was possible using Ansys . As shown in the plot, the numerical stress-strain curve implemented into Ansys almost perfectly matched the test data. With these material stress-strain relationships, different numerical models were built to investigate the role of the material modelling in terms of global system response. 3.3. Residual stresses Ansys allows also to introduce residual stresses in the numerical finite element model, an aspect which might be important for stability issues. The assumed distribution of the residual stresses through the cross section is shown graphically in Fig. 4(b). The adopted residual stress distribution follows the recommendations by ECCS (1984), with a multilinear distribution in both the web and the flanges. Values of the residual stresses at significant points are also shown in Fig. 4(b), as percentages of the material yielding strength. As an example, Fig. 4(c) shows the longitudinal stress component distribution that is obtained when applying the residual stress distribution to a single plate. The residual stress value was considered constant into the generic shell element.