PSI - Issue 44

Alessandro Mei et al. / Procedia Structural Integrity 44 (2023) 2318–2325 Mei, et al./ Structural Integrity Procedia 00 (2022) 000–000

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2.1. Simplified constitutive models Two different constitutive models are considered. These two models have a different cyclic behavior but provide an identical monotonic static response, so they are indistinguishable for the nonlinear static seismic analysis. • Elastic-plastic model. It is the standard dissipative behavior assumed for ordinary steel and reinforced concrete structures. The N2 method, Fajfar, 2000, adopted by several building codes, is based on that model. The constitutive model equations are:

(1) where F is the force, K is the stiffness, d is the displacement, d p is the plastic displacement (internal variable), f is the yield function, F y is the yielding force, and γ is the plastic flow multiplier. • Pinching model. It is supposed to be the best-suited model for steel racks with dry joints. The energy dissipation is smaller than the elastic-plastic one due to the plastic behavior of connector hooks. The constitutive equations are:

(2)

which holds for d > 0 and where angular brackets denote the positive part operator, with < x > = max(0, x ). Analogous equations hold for d < 0. Figure 1 displays the response of the two models to a cyclic incremental load.

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b.

Figure 1. Cyclic response of the two simplified constitutive models: (a) elastic-plastic and (b) pinching.