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

474

3

The design of connections was carried out according to CEN (2005b). Capacity design rules and strain hardening of the steel links, as well as uncertainties in the value of the link yield resistance, were considered according to CS.LL.PP. (2018) and CEN (2005c). The link-to-beam connections usually govern the design process (Mazzolani et al. (2022), Cantisani et al. (2021)), as it can be seen from the geometrical details of the case study shown in Fig. 1(c) and Fig. 1 (d). In fact, connections between the link and the RC beam were strongly affected by the concrete edge failure mode (Della Corte and Landolfo (2017), Sarracco et al. (2016), Della Corte et al. (2018)), thus resulting in the need to use several anchor bolts to allow for sufficient connection overstrength. The evaluation of the forces transmitted from the yielded and strain-hardened link was carried out according to the simple schemes drawn in Fig. 2, showing the design forces transmitted to the RC beam (Fig. 2(a)) and those used for the design of the diagonal members and relevant connections (Fig. 2(b)). As shown in the figure, the internal forces arising from the link shear yielding were increased to consider both the link steel strain hardening and the uncertainty of the steel yielding strength ( γ ov ), according to the current code prescriptions (CS.LL.PP. (2018), CEN (2005c)). For the brace end connections, the worst scenario was considered, assuming fixed ends of the diagonal members subjected to the link actions in the ultimate conditions.

e

1.1 1.5 ⋅ γ

M

V

= ⋅

⋅

⋅

2 l

, l Rd

Ed

ov

1.1 1.5 ⋅ γ

V

V

= ⋅

⋅

e





, l Rd

Ed

ov

1.1 1.5 ⋅ γ

M

V

2 l ⋅  +    c e

= ⋅

⋅

, l Rd

Ed

ov

1.1 1.5 ⋅ γ

V

V

= ⋅

⋅

, l Rd

Ed

ov

c e

l e

a)

b)

Fig. 2. Capacity design: (a) beam force demand; (b) brace force demand.

3. Numerical modelling 3.1. General issues

A 3D Finite Element (FE) model of a couple of braces and the corresponding vertical link was built to investigate the out-of-plane (OOP) stability of the bracing system and the effects of various models for the steel strain hardening response in terms of global force-deformation demand parameters. The models were built by using non linear shell elements with three FE software packages, which were adopted to perform the analysis and compare the results: (i) the commercial software SAP2000 (CSI (2011)); (ii) the open-source software Code_Aster (EDF (1989)); (iii) the commercial software Ansys (Thompson and Thompson (2017)). The three software packages were used to perform linear elastic, linear buckling, as well as general geometric and material non-linear analyses. For the discussion presented in this paper, the boundary conditions were assumed as shown in Fig. 3(a) and with reference to nominal lengths of members as described in Fig. 3(b). All out-of-plane displacements and rotations were considered as fully restrained at the brace ends. A horizontal displacement ( ∆ ) and corresponding force ( V ) applied to the link end simulated the seismic interaction with the RC building (Fig. 3(a)). Each I -shaped steel member was represented by means of shell elements discretizing the plates comprising the members. Two different meshing strategies were considered for the SAP2000 and Code_Aster/Ansys models. The mesh for the SAP2000 model was generated by hands, on purpose, to minimize the number of triangular elements needed to discretize the geometry at