PSI - Issue 64

Margherita Autiero et al. / Procedia Structural Integrity 64 (2024) 1798–1805 Author name / Structural Integrity Procedia 00 (2019) 000–000

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calculate the resulting effective cross-sectional resistance, instead of using the 0.2% proof strength (f 0.2p,θ ). The new expressions are temperature-dependent leading to a variation in the effective cross-section properties under fire situations. For this reason, a simplified proposal, not temperature dependent, was investigated by the authors, based on the assumption that the influence of the temperature on the range of the critical temperatures usually expected for steel members (from 350 °C to 750 °C) are negligible leading to a simpler yet accurate design. These expressions are proposed for the new drafts of the next generation of structural Eurocodes. This means that the design buckling resistance of a compressed member for the new Eurocode can by evaluated as follow:

(2)

Where in this case the effective cross-sectional area determined according to the new equations explained before. Moving in the context of a PBA, the absence of external consequences due to structural collapse must be demonstrated, which means that the designer must prove analytically that the collapse mechanism is inward, and implosive. Many authors pointed out how the study of the mechanism of collapse is related to the fire model adopted and the types of methodologies of analysis that the designer must adopt to properly interpret it. Zaharia and Franssen (2002) studied the case of a two-dimensional ARSW built in Belgium, affirming that a natural fire scenario might be more realistic, but under this fire curve, the progressive collapse of the structure cannot be avoided, in fact, the local collapse of rack uprights, causes the global collapse. Mei et al. (2023) provides a robustness evaluation and highlights some possible aspects to be considered in the structural design to avoid a progressive collapse in the event of a fire. 3. Fire modelling of ARSW structure As analyzed by Mei et al. (2023) fire scenarios for ARSW will consider primarily the chance of an electrical malfunction that causes the burning of the stacker crane, at the lower building level; this choice is made because rack uprights are more stressed at the lower level. Since they are large and high structures a fully developed fire seems unrealistic and for this reason the fire model that better fits in this case could be the localized fire model, therefore, ARSW single or double depth the fire scenario at the base within the aisles for stacker cranes can be modelled by considering the localized fire (LOCAFI model). On the other hand, in the case of multi-depth ARSW because of their configuration and the presence of the shuttle systems, the fire could start like a localized fire also within the load levels and could develop into a traveling fire both in horizontal and vertical directions. Fire design methods for vertically traveling fires are not as developed as for horizontal ones, indeed, in the last decade, vertically traveling fires have been analyzed like multi-floor fires in high-rise buildings Usmani et al. (2009), which represents a different condition than the ARSWs. For these reasons, to study the fire behavior of the ARSW, it was necessary to obtain a fire model that allowed the vertical and horizontal propagation of localized fires to be considered, for this purpose some experimental results were looked for in the scientific literature. The work used as principal references for validating the fire model was carried out by Lönnermark and Ingason (2005), which performed several scale fire tests, to investigate the fire spread from an initial fire in rack storage to adjacent racks without any suppression system. These tests were simulated by using the software CFAST (Jones et al. 2006) which is a two-zone fire model that predicts the thermal environment caused by a fire within a compartmented structure, and that allows the modelling of different compartments that can communicate to each other. The results of test series 1 (cone calorimeter tests of the cardboard boxes) allowed obtaining the Heat Release Rate (HRR) curves of a single cardboard box, and starting from these input curves, it was possible to model test series 2 (fire spread tests with one small rack) and validate the CFAST model for a single rack. In this way, it was possible to simulate test series 5, which consists of the study of the vertical and horizontal fire propagation in a group of 4 racks, modelling the propagation of a localized fire, indeed this test was the only one that provided the vertical and horizontal propagation times between levels of the racks. This propagation was considered in the CFAST model by assigning time delays to the HRR curves, starting from the HRR curve of a single level. Thanks to the simulation of these experimental tests, it was possible to find that: vertical time propagation is equal to the time for the flame to reach the upper level of the racks, calculated by using the flame lengths Lf proposed in EC1 part 1-2, moreover since the main assumption of the zone model is that the temperature is uniform in each compartment, to obtain different temperature distributions within the structure it was necessary to divide the whole