PSI - Issue 78

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

1093

5.3. Response parameters and fragility curves The seismic response of the structure is evaluated in terms of several performance parameters, including: maximum interstorey drifts (δ max ), residual interstorey drifts (δ res ), damage indices (DI) for ductile members (i.e. links, beams and columns of MRFs), resistance index (RI) for fragile members (linked columns), and stability (SI) index for columns. The DI is calculated as the ratio of plastic rotation demand to the plastic rotation capacity at the Near Collapse limit state. To this end, the rotation capacity of links (γ NC ) is assumed equal to 4/3 of the rotation capacity defined in Eurocode 8 for the Significant Damage limit state. The rotation capacity (θ NC ) of beams of the MRFs and of columns with an axial load ratio not higher than 0.3 is defined as a multiple of the chord rotation at yield (θ y ). Specifically, θ NC is equal to 8θ y and 6θ y for class-1 and class-2 cross-sections, respectively. The rotation capacity of columns with an axial load ratio larger than 0.5 is assumed to be null, whereas the rotation capacity of columns with an axial load ratio ranging from 0.3 to 0.5 is determined by linear interpolation the two limit cases. The Resistance Index and a Stability Index for fragile members are determined based on the resistance and stability checks provided by Eurocode 3 for members subjected to combined axial forces and bending moments. The aforementioned response parameters are used to compute the fragility curves for the Damage Limitation (DL), Significant Damage (SD), and Near Collapse (NC) limit states. Table 1 summarizes (1) the limit values associated with each response parameter at the respective limit state, and (2) the probability of exceedance PVR in 50 years (and the associated return period) of the seismic event for which the fulfilment of the limit state is expected. Fragility curves shown in Fig. 5a-b, derived based on the maximum interstorey drifts, indicate that the structural solution with 3 linked columns (black curve) exhibits probabilities of exceedance of the limit values of δ max similar to those obtained with the structural solution with 2 linked columns, despite the higher costs associated with the latter solution. At spectral accelerations corresponding to seismic events with T R equal to 475 years, the probabilities of exceedance of a residual interstorey drift equal to 0.5% for the system with 3 LC are slightly larger than those obtained in the case of 2 LC (Fig. 5c). This difference arises because the members in the three-column system undergo a more significant nonlinear response, as they are designed with a higher behavior factor. Nonetheless, these exceedance probabilities remain very low, reaching at most about 6%.

Table 1. Limit values of the response parameters for the selected limit states. δ max (%) δ res (%) DI links DI

RI

SI

PVR in 50 yrs.

T R years

beams/columns

Damage Limitation Significant Damage

0.75% 2.00%

‒

‒

‒

‒

‒

35% 10%

115 475

0.5%

0.75 1.00

0.01

1.00 1.00

1.00 1.00

Near Collapse

‒

‒

3%

1600

P LS

P LS

P LS

T R 115 (3LC)

T R 475 (3LC)

T R 475 (3LC)

0.00 0.25 0.50 0.75 1.00

0.00 0.25 0.50 0.75 1.00

0.00 0.25 0.50 0.75 1.00

T R 475 (2LC)

T R 115 (2LC)

3LC - x 3LC - y 2LC - x 2LC - y

3LC - x 3LC - y 2LC - x 2LC - y

3LC - x 3LC - y 2LC - x 2LC - y

T R 475 (2LC)

T a,50%

T a,50%

T a,50%

R S

R S

R S

0.00 0.05 0.10 0.15 0.20

0.00 0.30 0.60 0.90 1.20

0.00 0.30 0.60 0.90 1.20

a

b

c

Fig. 5. Fragility curves in terms of (a) δ max at DL limit state; (b) δ max at SD limit state; (c) δ res at SD limit state.