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.

This paper presents a generalized reduced-order nonlinear model subjected to multi-support seismic excitation. The hysteretic, nonlinear, relationship of piers is phenomenologically captured by a calibrated Bouc-Wen model. This generalized reduced-order model is benchmarked against legacy physical experimental tests performed at the University of Bristol.A deterministic approach using real spatiotemporal ground motions recorded at the SMART-1 array, Taiwan, is employed as an alternative to a stochastic methodology used in current provision codes. This is so that the influence of nonlinearity and ground motion aleatory and epistemic effects are fully captured. Incremental Dynamic Analysis (IDA) is then performed to identify the performance levels at which this system transitions from elastic to inelastic behaviour. A parametric study is then performed to explore the effect of the spatial variability of the ground motion while bridge alignment, valley profile and ground motion intensity are modified. Results indicate that bridges over shallow valleys with a central rise are prone to significant analysis errors if multi-support excitation is not employed.

This study uses a generalized and parametrized reduced-order model in the frequency-domain to evaluate the effects of asynchronous excitation on the lateral response of bridge structures. Bridge geometry parametric regions, corresponding conceptually to valley profile shapes, are explored. Both modal and bounding analyses, that are dependent on bridge geometry alone, are employed to highlight regions where the first mode is anti-symmetrical and the likely error between identical support excitation (ISE) and multi-support excitation (MSE) analyses is large. Numerical time history analyses, using a heuristic bridge case and spatiotemporal ground motion from the SMART-1 array, are employed. These analyses confirm that in parametric configurations where the first mode is anti-symmetrical the error between MSE and ISE is often larger. This confirms the utility of geometry only modal and bounding analyses in identifying critical regions. These critical parametric cases of a first mode that is anti-symmetrical correspond to shallow valleys with a central rise. In these cases it is recommended that both ISE and MSE analyses should be employed to be conservative.

This correction is published in order to inform that typesetter overlooked author corrections regarding older figures & captions in the original publication. Old version published which does not match the context of the paper. Second, bold/non-bold for equations (15) onwards, were not inserted correctly. Third, caption of Fig.10, should be subscript of sigma not in the line. Original article has been updated. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.