20 Calibration of a Large Nonlinear Finite Element Model of a Highway Bridge with Many Uncertain Parameters 179 Fig. 20.1 Batch-recursive estimation procedure for large FE models with high-dimensional parameter space steel and concrete of the structural components have nominal yield strength of 420 MPa and maximum compressive strength of 25 MPa, respectively. More information about the bridge is available in [10]. The open-source software platformOpenSees [11] was used to model the bridge. The superstructure, which includes the girders and the deck, was modeled with an equivalent cross-section. The rigid offsets of the structure were modeled with rigid linear beam-column elements (Fig. 20.3). The piers were modeled using nonlinear distributed plasticity beam-column elements and the concrete and steel fibers considered the constitutive laws concrete04 and steel02 as available inOpenSees. The reinforcing steel model is defined by four primary parameters: elastic Young’s modulus (E0), initial yield stress (fys), strain hardening ratio (bs), and a parameter describing the curvature of the transition curve between the asymptotes of the elastic and plastic branches during the first loading (R0). The concrete model is defined by four parameters, modulus of elasticity (Ec), maximum compressive strength (fc ), strain at the maximum compressive strength (εc), and strain at the crushing strength (εcu). The seismic isolators were modeled employing the Elastomeric Bearing element available in OpenSees, which is defined by five parameters, the initial elastic stiffness (Ke), yield strength (fy), post-yield stiffness ratio of linear hardening component (b), post-yield stiffness ratio of nonlinear hardening component (α2), and an exponent of non-linear hardening component (μ). The mass properties of the bridge were computed based on the volume of the components and their material densities and were lumped at the nodes of the FE model. Rayleigh damping model with critical damping ratio of 2% for the first longitudinal and transverse modes was assumed. No contribution of the isolators was considered in the Rayleigh damping model. Uniform base excitation was considered at both bridge ends and at the bottom of the piers. The 90◦, 0◦, and UD (vertical) ground motion components recorded at the Los Gatos station during the 1989 Loma Prieta earthquake (Fig. 20.4) were considered in the longitudinal, transverse, and vertical directions of the bridge. More details about the FE model can be found in [12].
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