PSI - Issue 78

Melina Bosco et al. / Procedia Structural Integrity 78 (2026) 1087–1094

1090

3.2. Deign of the secondary system Yielding of MRF beams is expected to occur under seismic actions with intensity exceeding that causing yielding of links. For this reason, the design bending moments at the ends of beams of MRFs are determined by amplifying the internal forces due to the seismic actions by a factor Ω link that accounts for both the overstrength and the hardening of links. Specifically,   link rm d MRF sh ω 1 λ ω 1          (3) Here,  MRF is a coefficient, ranging from 0.0 to 1.0, where  MRF =0.0 corresponds to internal forces in beams associated with the first yielding of a link;  MRF =1.0 corresponds to internal forces in beams associated with the ultimate resistance of the first link that reaches failure. Previous studies have shown that a value of  MRF equal to 0.25 is sufficient to ensure the desired performance objective. The internal forces in columns are calculated as the sum of the contributions due to the gravity loads in the seismic design situation and seismic action. This latter contribution is determined by the design method of analysis and is amplified by a factor accounting for the overstrength of beams Ω beam All the other requirements specified in the upcoming version of Eurocode 8 for the design of beams, columns, and panel zones of MRFs are not reported here but have to be fulfilled. 4. Design of the case study The proposed design procedure is applied to a 6-story residential building. Linked columns and moment resisting frames are placed along the perimeter of the building. Pinned connections are used at the end of the beams adjacent to the linked columns, at beam-to-column joints if columns are oriented so as to provide the minimum flexural stiffness (i.e. the minimum moment of inertia), and at the base of such columns. Conversely, rigid connections are used at the ends of other perimeter beams and at the base of columns oriented so as to provide the maximum flexural stiffness. The interior frames are designed to carry gravity loads only; hence, pinned connections are considered at the beam ends and at the base of the first-storey columns. Two structural configurations are considered, as illustrated in Fig. 3a and Fig. 3b. In both cases, four replaceable links are used in each principal direction. However, in the first configuration, three linked columns are used, whereas in the second configuration two linked columns have been used. At each floor, replaceable links are placed both at floor level and at mid-storey height. The length of the link, from the centerline-to-centerline axis of the linked columns, is equal to 1.2 m; the span of the moment resisting frame is L 2 = 8m, and the interstorey height is h = 3.3 m. The building is located near Siracusa (Sicily) and stands on a deposit of very dense sand, with an average value of the shear wave velocity v s30 equal to 550 m/s. Based on this value, the site is classified as Soil Type B according to both Eurocode 8 and the Italian Seismic Code. With reference to rigid soil conditions (i.e., soil type A), the Italian Seismic Code provides the values of the peak ground acceleration ( a g ), of the maximum spectral amplification factor ( F 0 ), and of the period T c * corresponding to the beginning of the branch of the spectrum with a constant velocity. Specifically, for the site under investigation and for seismic events with a probability of exceedance of 10% in 50 years, the above values are equal to 0.279 g, 2.28, and 0.43 s, respectively. The characteristic values of the permanent ( g k ) and variable ( q k ) loads are as follows:  at intermediate floors (i-th floor) g k = 4.7 kN/m and q k =2.0 kN/m  at the top floor g k = 3.0 kN/m and q k = 2.0 kN/m. Finally, to account for the weight of the infills, a line load G k = 2.6 kN/m is applied to the beams of the perimetric bays. The structure with three linked columns has been designed considering a behavior factor equal to 6.5. Conversely, in the case of the configuration with two linked columns, the behavior factor has been reduced to 3.5 to increase the cross-section sizes and, consequently, the overall lateral stiffness of the structure, ensuring that the interstorey drift determined by the design method of analysis and amplified by q d remains lower than the 2.0%. The distribution of drifts determined within the design phase for the two considered structural configuration is shown in Fig. 4a and 4b.