PSI - Issue 84

Fabio Mazza et al. / Procedia Structural Integrity 84 (2026) 944–951

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(  =50 W/m²·K) and unheated (  =4 W/m²·K) surfaces and emissivity (  =0.7). Two-dimensional thermal mappings of cross-section of the interior beams are plotted, with reference to the instant of time corresponding to the maximum temperature reached at location A, for SV4 (t max =3600 s, Fig 6a) and SV4.4 (t max =4700 s, Fig. 6b) fire scenarios. The corresponding reduction factors of the flexural stiffness, evaluated with the 500 °C isotherm method (EC2, 2004), confirm that multiple crash of vehicles can lead to the bridge disruption due to excessive vertical deformation. By contrast, three-dimensional plots are considered for the non-isotropic isolators, using tetrahedral elements with sizes ranging from 5 mm to 20 mm and considering constant thermal properties: i.e. thermal conductivity (  =0.27 W/m/K); coefficient of convection on heated (  =25 W/m²·K) and unheated (  =4 W/m²·K) surfaces; emissivity (  =0.7). Thermal mappings of the fire-exposed HDRBs at location B are represented in Figs. 6c,d (t max =3000 s) for the same fire scenarios above considered, highlighting that their integrity is destroyed when the rubber temperature exceeds the critical isotherm (i.e. T=150 °C) representing the vulcanization value with steel plates (Mazza, 2017).

(a) A.SV4.

(b) A.SV4.4.

(c) B.SV4. (d) B.SV4.4. Fig. 6. Thermal mappings of a PC beam and a HDRB for simple (SV4) and complex (SV4.4) fire scenarios.

It is interesting to note that heat conduction through a HDRB takes place mainly through its end steel plates and intermediate steel shims and it is much lower through layers of rubber, so requiring an accurate modelling in order to best reproduce the boundary conditions and the heat conduction phenomena. Time-temperature curves in some points in the proximity of the end steel plates and at half isolator height are reported in Figs. 7 and 8, respectively, for the B.SV4 fire scenario. A significant difference exists between the temperature time-histories resulting from the 2D (Figs. 7a and 8a) and 3D (Figs. 7b and 8b) models; specifically, the 2D results underestimate the temperature, especially at the HDRB's mid-height (Fig. 8).

(a) 2D model. (b) 3D model. Fig. 7. Time-temperature curves at different points of a central HDRB in the proximity of the end steel plate.