PSI - Issue 44

Fabio Mazza et al. / Procedia Structural Integrity 44 (2023) 147–154

150

Fabio Mazza et al. / Structural Integrity Procedia 00 (2022) 000–000

4

3. Structural, nonstructural and functional equipment modelling 3.1. Curved surface sliding bearings

Mechanical response of a CSSB is modelled as reported in Mazza and Labernarda (2022). No equivalent viscous damping ratio in the vertical direction is considered, whereas the variability of the axial load due to the vertical ground acceleration is accounted for. With the aim of taking into account the strong influence of axial load ( N ) and sliding velocity ( v ) on the friction coefficient ( µ ), the manufacturer (Nipponsteel Techical Report (2018)) proposed an expression where the friction coefficient is given by the product of µ 0 (friction coefficient for an axial pressure p =60 MPa and a sliding velocity v =0.4 m/s), α and γ representing the velocity and pressure dependency functions respectively. These functions are obtained by interpolating experimental data obtained from different full-scale tests on CSSBs characterised by different geometric dimensions and testing conditions. With the aim of studying the influence of parameters like N and v , also including temperature at the sliding interface and the breakaway and stick-slip phases, three models, increasing in complexity, are considered: a simplified model (SM), with constant values of N and µ ; a first advanced model (AM 1 ), accounting for variable N in combination with friction coefficient variability as function of v and p ; a second more accurate advanced model (AM 2 ), also accounting for the variability of friction coefficient at breakaway and stick-slip phases and for the temperature increase at the sliding interface. Parameters for the AM 1 and AM 2 models are reported in Table 2, with reference to the values µ HV =0.013, µ LV = µ HV /1.3 and µ St =2 µ HV at an axial pressure of 60 MPa, according to the manufacturer (NIPPON STEEL (2019)), where µ HV and µ LV are the kinetic friction coefficients at high and low velocity, respectively, and µ St is the static friction coefficient. Shape controlling parameters (i.e. α dyn , α St , A HV , A LV , A St , n HV , n LV and n St ) are estimated by means of a nonlinear least squares surface fitting algorithm (MATLAB (2018)), between the reference function, proposed by the manufacturer (Nipponsteel Techical Report (2018)), and the governing equations of AM 1 and AM 2 ; c ref and β are assumed as in Mazza and Labernarda (2022). The in-plane (IP) and out-of-plane (OOP) nonlinear dynamic response of partitions is represented through a five element macro-model. This modelling strategy, previously implemented for masonry infills (Mazza (2019); Mazza and Donnici (2021)), is generalised to represent seismic response of any interior or exterior closing element. Light steel-framed partition walls are employed to define internal spaces for different medical purposes. Slip-track partitions are selected among available technological solutions (Blind Prediction Contest (2020)). Experimental observed damage is referred to an interior partition: a 5 m long double gypsum layer (12.5 mm +12.5 mm) wall with a door (0.9 m wide), placed at first floor. Wall steel P-65 studs are spaced 455 mm while gypsum elements have standardised dimensions (900 mm x 2400 mm x 12.5 mm). Gypsum panels have compressive strength 3.0 MPa, tensile strength 0.8 MPa and elastic modulus 2000 MPa. All geometrical and mechanical data of steel components (i.e. studs and tracks) have been provided by the manufacturer. The seismic behaviour of such partitions can be reproduced by assigning reliable IP and OOP force-displacement backbones to the infill macro-model (Figure 3). A tri-linear backbone curve defined by elastic, post-elastic and softening branches is evaluated (Figure 3a), based on IP parameters by Davies et al. (2011). The OOP global elastic behaviour can be simplified as a system of studs working in parallel. Only internal studs contribute to the OOP backbone parameters, as external ones form the perimetral supporting frame together with tracks. The OOP backbone is described by an elastic multi-phase behaviour (Figure 3b), characterised by different effective cross section stiffnesses triggered by progressive gypsum cracking. The inelastic OOP response is represented by the softening branch till collapse. The IP and OOP hysteretic behaviour is simulated through a pivot model. Table 2. Parameters of the AM 1 and AM 2 for CSSBs of the base-isolated structure. α dyn [s/cm] α St [s/cm] A HV A LV A St n HV n LV n St c ref [kN·cm 2 /s] β 0.068 0.68 0.8888 0.6837 1.7776 0.4031 0.3198 0.4031 4.078·E08 0.60 3.2. Partitions, piping system and elevated tanks