PSI - Issue 78

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

1089

experiences no axial force, and the rotation θ 3LC caused by the axial deformation of columns Δ h is equal to half of that observed in the two-column configuration, i.e.

2

h



θ

(2)



3LC

2

e

a

d

b

c

Fig. 2. (a) modular configuration; (b) flexural and shear deformative contribution; (c) and (d) deformative contribution due to axial elongation or shortening of the columns in the case of two or three linked columns. 3. Summary of the design procedure The design procedure is iterative and is summarized as follows. At each step of the design procedure a modal response spectrum analysis is performed. The design spectrum corresponds to seismic events with a probability of exceedance of 10% in 50 years, and is reduced by means of a behavior factor that, at the first step of the design procedure, is equal to the maximum value allowed in Eurocode 8 for dual frames with eccentric bracings, i.e. q = q d × q r × q s = 3.3 × 1.3 × 1.5 = 6.5. Specifically, q d accounts for the deformation capacity and energy dissipation capacity of the system, q r accounts for the overstrength due to the redistribution of seismic action effects in redundant structures, q s accounts for the overstrength due to all other sources. Internal forces are amplified to considers second-order effects. If, at the end of the design procedure, the maximum interstory drift determined by the design method of analysis and amplified by q d exceeds the limit value reported in the code (2.0%), the behavior factor component accounting for the deformation capacity is reduced, and the cross-sections sizes of structural members are increased accordingly. 3.1. Deign of the primary system Cross-sections of links are selected so that shear and flexural resistances ( V p , M p ) exceed the corresponding internal forces, determined by the response spectrum analysis ( V Ed , M Ed ). The overstrength factor Ω d of links is calculated as the minimum of the overstrength in shear and flexure. With the exception of the top-storey links, the average overstrength factor of links belonging to the same story is computed and the ratio of the maximum to minimum average overstrength factors is verified to be smaller than 1.25. This requirement is intended to promote the exploitation of a global collapse mechanism. The internal forces in linked columns ( N Ed , M Ed , V Ed ) are calculated as the sum of the effects due to gravity loads in the seismic design situation and those due to seismic actions. The seismic contribution is amplified by a coefficient that accounts for: (1) the steel overstrength factor (ω r m ), the minimum link overstrength factor (Ω d ) and the hardening factor (ω sh ) of links. In accordance with the recommendations of the upcoming version of Eurocode 8, ω rm depends on the steel grade, and ω sh is a function of the link mechanical length ( eV p / M p ). Resistance, stability, and lateral torsional stability checks are performed to select the required column cross-section size. Further, the resistance of the panel zone is verified. Further details can be found in Bosco et al. (2024a).