Abstract
A generalized reduced-order model of a multi-span continuous bridge, on flexible discrete supports, that is subjected to multi-support seismic excitation is presented. This model highlights the key non-dimensional system parameters. Real spatiotemporal ground motion time-series (from the SMART-1 array, Taiwan) are used, as an alternative to employing artificial ground motion based on some spatial incoherence kernels. Benchmark experimental test data, using the multiple support excitation rig of a four-span bridge and SMART-1 array excitation, is used to validate/calibrate the proposed reduced-order model. An operational modal analysis is conducted to obtain least-square estimates of these key dynamic parameters using a Levenberg–Marquardt algorithm. The computationally efficient reduced-order model is then employed for a parametric study that explores the effect of spatial incoherence, bridge alignment and archetypal symmetrical and asymmetrical bridge geometries. A comparison of identical and multi-support excitation cases indicate the likely range of beneficial/adverse errors in neglecting the spatiotemporal nature of ground motions in design analyses.
Highlights
The incorporation of spatially variable seismic excitation in the design of life-line structures has received much attention over the last few decades (Zanardo et al 2002; Lin et al 2004; Lupoi et al 2005; Ye et al 2011; Camara et al 2014)
In the design of artifacts such as multi-span bridges, the structural engineer would like to know whether, and when, it is necessary to model the spatial variation in ground motion (Nazmy and Abdel-Ghaffar 1992; Zerva 2016)
Equations (16) and (17) represent the dynamics of a multi-span continuous bridge with n − 1 spans of span length L. These equations of motion represent a reduced order nondimensional model and this is expressed in terms of system parameters, (1) frequency parameter, (2) pier to deck lateral stiffness ratios i and (3) damping coefficients k, m that are determined by assuming modal ratios of critical damping. Validation of these equations of motion is achieved by comparing numerical results from time-history analyses and a benchmark experimental physical bridge model that was subjected to multi-support excitation
Summary
The incorporation of spatially variable seismic excitation in the design of life-line structures has received much attention over the last few decades (Zanardo et al 2002; Lin et al 2004; Lupoi et al 2005; Ye et al 2011; Camara et al 2014). Using ground motion models whose spatial variability are parametrically stochastic is attractive as they enable the use and extension of recorded singleton station records to the generalized spatiotemporal case. This allows a sensitivity analyses to be performed with respect to these stochastic model parameters. Zerva (1990, 1991) carried out comprehensive analyses of two-span and three-span continuous beams, of varying span lengths, under different arrangements of spatially varying ground motions She concluded that, for symmetrical structural configuration, ISE could only excite the symmetric modes, while MSE could excite all modes, i.e. symmetrical and anti-symmetrical modes. We make use of the validated/calibrated reduced-order bridge model to explore parametrically the likely errors (both over and under estimations) when using identical support excitation (ISE) rather than real multi-support excitation (MSE)
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