Keywords: multi-support excitation, SMART-1, bridge dynamics, torsion.

This paper considers the problem of multi-support excitation (MSE) of single span bridges. It particular it discusses the errors in structural responses that can be produced if identical-support excitation (ISE) is assumed instead of MSE. Rather than employing an empirical model of ground incoherence, the aim is to revisit actual ground acceleration data recorded at the SMART-1 array in Taiwan [1,2].

The SMART-1 acceleration records are corrected using a wavelet de-noising algorithm, bidirectional filtering and second order instrument deconvolution [3]. These processes are at present not performed on the raw data. In this paper, the novel application of wavelet de-noising is to mitigate the quantisation noise present.

The bridge model is derived in general for n flexural models and m torsional modes. The equations of motion are derived employing a vectorial Euler-Lagrangian approach. As a heuristic case, this paper characterises a general simple span bridge by two lateral flexural modes and one torsional mode, i.e. a coupled 3 degree of freedom linear system. However, the uncertainties reside more significantly in the forcing of such a system rather than the system complexity itself. A theoretical estimate of the range of various system parameters is introduced to narrow the investigation of the solution space to the plausible.

Numerical studies presented in this paper demonstrate that even short span bridges, of about 50m span, are subject to significant differential ground motion. This limit is a consequence of the low power content of the ground motions, in this study, above about 8Hz.

In the case of multi-support excitation (MSE), it is observed that directional alignment of the bridge has a significant influence on the response behaviour. For span lengths, >=90m, there is some evidence that approximate alignment of the bridge in a normal to epicentral direction can produce maximal structural responses. However for shorter spans this is not the case, i.e. maximal structural responses are not correlated with a bridge aligned in normal to epicentral direction.

Modelling the ground motion, by ignoring the actual complex differential ground motion (ISE), is not always a conservative assumption. Corrected, real, ground motion data from the SMART-1 array was employed to validate this. It has been shown, for certain span-alignment combinations, that ISE can be highly conservative, over-estimating structural responses by 250% in the worst case. This was for spans of approximately 50m aligned in the epicentral direction. However, for other span-alignments ISE is shown to be non-conservative, under-estimating the structural responses, in the worst case, by approximately 30%. Further numerical studies on other data sets are required to confirm the generality of these conclusions.

1

Institute of Earth Science, "SMART-1 Array data repository", Tawain. http://www.earth.sinica.edu.tw/~smdmc, 1980-1991.

2

Abrahamson N.A., Bolt B.A., Darragh R.B. Penzien J., Tsai Y.B., "The Smart-1 accelerograph array (1990-1987): A review", Earthquake Spectra, 3(2), 1987. doi:10.1193/1.1585428

3

A.A. Chanerley and N.A. Alexander, "An Approach to Seismic Correction which includes Wavelet De-noising", in Proceedings of the Third International Conference on Engineering Computational Technology, B.H.V. Topping and Z. Bittnar, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 44, 2002. doi:10.4203/ccp.75.44

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