PSI - Issue 64

Patrick Covi et al. / Procedia Structural Integrity 64 (2024) 1774–1781 Patrick Covi and Nicola Tondini/ Structural Integrity Procedia 00 (2019) 000 – 000

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Different limit states, following EN 1363-1, are defined to identify failure in the structural members: • Beams — Limit state 1 (LS1): o deflection exceeding L 2 /400d and rate of deflection exceeding L 2 /(9000d) mm/min. • Columns — Limit state 2 (LS2): o vertical contraction exceeding C=h/100 mm and rate exceeding dC/dt = 3 h/1000 mm/min. where h is the initial column height in mm, L is the beam length, and d is the depth of the beam. Despite the fact that LS1 and LS2 are derived from the standard fire tests, they provide a measure about the extent of damage that the structural members may undergo. Among the 189 simulations, 167 analyses did lead to an FFE event because either the PFA and IDR satisfied the three thresholds for an ignition to occur, as explained in the previous section. It is also worth noting that about 22 simulations did not lead to an FFE event because either the ground motion was not strong enough to ignite a fire in a compartment or the ground motion was too strong that caused the collapse of the structure owing to the seismic action. In 103 analyses, the beams were the first element to fail (LS1), while in 6 analyses, the columns were the first element to fail (LS2), as illustrated in Fig. 8. In 11 analyses, the structure survived the FFE event without any partial/total collapse and without any failure of the structural elements. Finally, 47 of 189 analyses were discarded because they were interrupted due to numerical problems in an early stage of the FFE simulation.

Fig. 8 . Classification of the 189 analysis results.

4. Fragility functions This section developed FFE fragility functions based on the results of the FFE simulations. A fragility function expresses the probability P of a given engineering demand parameter (EDP), such as IDR exceeding a specific limit state (LS), conditioned on an intensity measure (IM), such as peak ground acceleration or fire load density. Using the Akaike information criterion (AIC) method on the results of the comparative analysis, the Generalized Extreme Value (GEV) distribution was selected to derive the fragility functions. Not only does the distribution provide the best fit, but it can also be represented in a simple and closed-form function with three parameters. The cumulative probability distribution function f or the GEV distribution has the form of Eq 1, where σ denotes the scale parameter (variability of the distribution), μ is the location parameter (shift of the distribution), and k is the shape parameter. ( > | = ) = {exp {− [1 + ( − )] −1/ } ≠ 0 exp{− [−( − )]} = 0 (1) Fig. 9a-b show the fragility curves and surfaces, respectively, for the beam failure conditioned on the time to failure and grouped as a function of the spectral acceleration (Sa) at the first period of the structure. Fig. 9a illustrates different slices of Fig. 9b. As expected, the higher the spectral acceleration, the higher the impact of the FFE on the structure, because of the higher number of ignitions and failure of the compartment measures. In fact, for values of less than 0.55 g, there is a 90% probability of exceedance of reaching the beam limit state in 50 min, whereas the limit state is reached in 35-40 min for the same probability target at larger Sa values. In the major of the cases of this analyzed frame, the failure of the FFE occurred in the beam of the 1 st or 5 th beams due to the fact its double lenght compared to the internal ones.