30 Seismic Random Vibration of Long-Span Structures Jiahao Lin

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Dalian University of Technology

Yahui Zhang

Dalian University of Technology

30.1 Introduction ........................................................................ 30-2

Basic Concepts of Random Vibration † Three Methods for

Structural Seismic Analysis

30.2 Seismic Random-Excitation Fields .................................... 30-11

Power Spectral Density of Spatially Varying Ground

Acceleration † Several Coherence Models † Generation

of Ground Acceleration Power Spectral Density Curves

from Acceleration Response Spectrum Curves † Seismic

Equations of Motion of Long-Span Structures † Seismic

Waves and Their Geometrical Expressions

30.3 Pseudoexcitation Method for Structural Random

Vibration Analysis ............................................................... 30-16

Structures Subjected to Stationary Random Excitations †

Structures Subjected to Nonstationary Random

Vibration † Precise Integration Method

30.4 Long-Span Structures Subjected to Stationary

Random Ground Excitations ............................................. 30-27

The Solution of Equations of Motion Using the

Pseudoexcitation Method † Numerical Comparisons

with Other Methods

30.5 Long-Span Structures Subjected to Nonstationary

Random Ground Excitations ............................................. 30-34

Modulation Functions † The Formulas for Nonstationary

Multiexcitation Analysis † Expected Extreme Values

of Nonstationary Random Processes † Numerical

Comparisons with the Corresponding Stationary

Analysis

30.6 Conclusions ......................................................................... 30-39

Summary

Particular considerations must be made during the design of long-span bridges with regard to safety during

earthquakes. These include: the wave-passage effect caused by the different times at which seismic waves arrive at

different supports; the incoherence effect due to loss of coherency of the motion caused by either reflections and

refractions of the waves in the inhomogeneous ground medium or the difference in the manner of superposition of

waves from an extended source arriving at various supports; and the local effect because of the differences in soil

conditions at different supports and the manner in which these influence the amplitude and frequency content of the

bedrock motion. This chapter deals with the random vibration approach to analyzing these structures, which is

based on a statistical characterization of the set of motions at the supports. This approach is particularly suitable for

dealing with the above spatially varying input motions. The computational problems may be largely overcome by

the pseudo excitation method. This approach is presented here. Numerical comparisons are given to show the

30-1

© 2005 by Taylor & Francis Group, LLC

accuracy of the method and its capability of dealing with the spatial effects and nonstationary effects. Further topics

related to this chapter are discussed in Chapter 5.

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