PSI - Issue 44

Giacomo Iovane et al. / Procedia Structural Integrity 44 (2023) 1864–1869 Giacomo Iovane et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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The behavior q-factor is determined according to the equation given in Figure 2 (Uang, 1991), where q Ω and q μ are the behaviour factor contributions related to overstrength and ductility, respectively; F 1 is the base shear at the first non-linear event, F h is the design base shear, F u is the maximum base shear, d y is the displacement corresponding to the conventional elastic limit and d u is the ultimate displacement. In this work, three different ultimate conditions have been assumed, depending on the ultimate limit state and the structural configuration considered. They correspond to the attainment of the inter-storey drift equal to 2.5% (for MRF) and 1.5% (for D-X V-CBF and EBF) at Life Safety limit state (LS), 5% (for MRF) and 2% (for CBF and EBF) at Collapse Prevention limit state (CP), as provided by FEMA 356 for steel structures, and at the Collapse Mechanism (CM), corresponding to the achievement of the plastic ultimate capacity in all the steel links (Fig. 2). The push-over curves and the q factor calculated for every seismic resistant structures, according to the different conditions for the ultimate displacement d u , are reported in Figure 2 , together with the Δq i ratio (Δq i = q i /q d ; i: LS, CP, CM conditions), which measures the variation of the calculated q-factors for every ultimate condition considered as respect to the design values assumed. 3.3. Analysis of results The seismic performances are analysed in terms of strength, considering the maximum base shear achieved (F ui , where i is the i-th structural type), the Δ Fu,i ratio (Δ Fu,i =F ui /F u,j [%]; F u,j : the greater strength among the structural types), the lateral stiffness (K i =F yi / δ yi , where F yi = yielding shear; δ yi = yielding displacement) and the Δ Ki ratio (Δ Ki =K i /K ,j [%]; K j : the lower stiffness among the structural types). In terms of strength, it is observed that the MRF (F u,MRF =224kN) has a greater strength as respect to the other structural types due to the overstrength derived by the DLS verification of horizontal displacement, followed by D CBF (Δ Fu,D-CBF =47%), X- CBF (Δ Fu,X-CBF =47%), EBF (Δ Fu,EBF =57%) and V-CBF ( Δ Fu,V-CBF =76%). In terms of lateral stiffness, the MRF has a lower stiffness (K MRF =75,07kN/m) as respect to the other structural types, followed by EBF (Δ K,EBF =273%), D- CBF (Δ K,D-CBF =387%), X- CBF (Δ K,X-CBF =631%) and V-CBF ( Δ K,V-CBF =720%). In Figure 2, the behavior factors q d are compared with the calculated q LS , q CP and q CM factors through the Δq i ratios. It is apparent that the calculated q-factors, for the LS limit state, are always larger than the design ones. In particular, it is worth noticing that this occurs also for braced structures, D-X-V-CBF (q LS =5.9-7.9-6.2), because the high ductile capacity of links in compression is not affected by buckling, as the same the timber diagonals are active both in tension and in compression. In particular, for this reason, V-CBFs show a large dissipative capacity with q>>q d . In fact the vertical force on the beam, due to the unbalanced tensile force of the diagonal in tension, which could be generated if the diagonal in compression is not active due to buckling, is null; thus the value of the d u is increased. If CP and CM ultimate conditions are considered, the calculated q factors are even larger. The results prove a high dissipation of seismic energy of the structural configuration studied. The potential of the system is also confirmed by some experimental monotonic and cyclic tests carried out on timber beam-to-column joints with steel link to evaluate the local behavior, showing large dissipative cycles and confirming the efficiency of the proposed design criteria (Iovane et al., 2021; Iovane and Faggiano, 2021). 4. Conclusive remarks The methodology applied for studying the dissipative timber seismic resistant structures with steel links, although referred to single-storey structures, is comprehensive, including the conception of the global structural system type, the definition of the design criteria, the analysis of the seismic performance of the structures by means of linear dynamic analysis and the evaluation of the seismic behaviour through non-linear static analysis, for determining the behaviour factor. It is possible to observe that the moment resisting and bracing framed systems with dissipative links, belonging to Medium Ductility Class, appear to be very promising, in fact they allow on one side to reduce the structural mass, on the other side to avoid the brittle failure modes of timber members and to improve the overall seismic performance in terms of stiffness, strength and ductility capabilities. In terms of weight, for the specific case studies, all seismic resistant structural types show a mass reduction from 19%, for V-CBF and MRF structures, to 43% for EBF. The mass reduction corresponds to low seismic design forces, smaller sizes of structural elements, low foundation forces and consequent cost savings that can potentially offset the higher cost of timber material. In