Keywords: cable-stayed bridge, finite propagation effect, random vibration, spectral analysis, response spectrum method, deterministic analysis.

This study compares random vibration and deterministic responses of a cable- stayed bridge for different values of ground motion wave velocities. Random vibration methods are based on the spectral analysis approach and the response spectrum method. Although the deterministic analysis of cable-stayed bridges is performed previously for travelling wave effect, the random vibration analysis of these bridges has not been performed for finite propagation effect of earthquake ground motions. As a coherency function describing the variability of the ground acceleration processes for support points the model used by Harichandran and Wang [1] is employed by including just the wave passage effect. For the spectral analysis approach, the power spectral density function of the ground acceleration characterising the earthquake process is assumed to be of the form modified by Clough and Penzien [2]. For the response spectrum method the model proposed by Der Kiureghian and Neuenhofer [3] is used which provides the response of a linear system subjected to incoherent support excitations directly in terms of the conventional response spectra at the support degrees of freedom and a coherency function describing the spatial variability of the ground motion.

In this study, the Jindo Bridge built in South Korea is chosen as a numerical example. It is assumed that the bridge supports are constructed on homogeneous soil types and the ground motion is propagating across the bridge from Jindo Island site to mainland site with finite velocities, of 250, 500 and 1000 m/sec, as well as with infinite wave velocities. As an earthquake ground motion the east-west component of Erzincan earthquake in 1992 in Turkey is employed. The considered earthquake ground motion lasting up to 20.95 seconds is applied to the bridge in the longitudinal direction, either in power spectral density shape or in response spectrum form for random vibration analysis and in the form of time history record for deterministic analysis. In all cases the ground motion is applied to the bridge supports with a time delay to be able to include the finite wave propagation effect of earthquake ground motion.

Mean of the absolute maximum values of responses at the deck calculated by the spectral analysis approach and the response spectrum method for 500m/s wave velocity case are compared with each other and with those of the deterministic analysis results. It can be observed that as the results obtained for random vibration analysis are mean of the absolute maximum values and the deterministic method yields absolute maximum values, the results obtained by the deterministic method are larger than the results obtained from random vibration methods. Response spectrum method based on the response spectrum specification of the input motion cause larger response values than those of the spectral analysis approach. Although the response spectrum method induces mean of the absolute maximum values, the obtained results are not much smaller than the absolute maximum results obtained by the deterministic method. In spite of the fact that there is a significant discrepancy between random vibration and deterministic results, the structural responses show consistent trends.

It is also observed that depending on the shape of the spectral density functions, the pseudo-static and dynamic responses obtained for the soft soil conditions induce the largest values and the same responses obtained for firm soil conditions take the smallest values.

By comparing the deck bending moments for finite wave velocities of earthquake ground motions calculated by the response spectrum method, the spectral analysis approach and the deterministic method, the response values show important amplifications depending on the decreasing ground motion wave velocities. Additionally, the obtained increment ratio of the response values depending on the decreasing wave velocities are very close to each other for each analysis.

The relative contributions of pseudo-static, dynamic and covariance components to the total response values are also presented in the paper for random vibration methods. As the responses are mostly dominated by dynamic component, the pseudo-static component has also contributions especially at the rigid parts of the bridge. However, because of the longitudinally applied ground motion the longitudinal tower displacements are mostly dominated by pseudo-static component. The contribution of the covariance component is generally small.

1

Harichandran, R.S., Wang, W., "Response of One- and Two-Span Beams to Spatially Varying Seismic Excitation", Report to the National Science Foundation MSU-ENGR-88-002, Michigan State University, Michigan, 1988.

2

Clough, R.W., Penzien, J., "Dynamics of Structures", Second Edition, McGraw Hill, Inc., Singapore, 1993.

3

Der Kiureghian, A., Neuenhofer, A., "A Response Spectrum Method for Multiple-Support Seismic Excitations", Report No. UCB/EERC-91/08, Berkeley (CA), Earthquake Engineering Research Centre, College of Engineering, University of California, 1991.

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