Keywords: suspension bridge, stochastic response, geometrically nonlinearity, partial correlation function,.

In this study, the stochastic response of suspension bridges subjected to partially correlated seismic ground motions is carried out considering geometrically nonlinearity of suspension bridges. The partial correlation function is consisting of a term that characterizes the loss of coherence. For the loss of coherence, four different spatial correlation functions, commonly used in earthquake engineering, are used. These are developed by Harichandran and Vanmarcke [1], by Abrahamson [2], by Hindy and Novak [3] and by Uscinski [4]. As an example the Bosporus Suspension Bridge is chosen. As a ground motion filtered white noise ground motion model modified by Clough and Penzien [5] is used.

Under the effect of dynamic loading, one of the uncertainties in the structural analysis is the one arising from the dynamic loading to which the structure is subjected. Because dynamic effects like earthquake motions are random, there is a need to a process, which takes into account the uncertainty of the dynamic loading in the analysis. So, stochastic analysis should be made use of. The analysis due to random loading is defined as the stochastic analysis.

Suspension bridges consist of elements like tower, cable, hanger and deck; the behaviour of each one is different. Because, under the effect of external forces, especially cables and hangers are subjected to large tension forces, these forces have great effect on the element stiffness matrix. This characteristic, named as geometrically nonlinearity of the structural elements, should be taken into account in the analysis of suspension bridges [6]. As an example, the Bosporus Suspension Bridge [7] built in Turkey and connects Europe to Asia in Istanbul is chosen. The bridge has inclined hangers, steel towers and a steel deck of 1074 m main span, with side spans of 231 m and 255 m on the European and Asian sides respectively, without any side spans supported by cables. The roadway at mid-span is approximately 64 m above sea level and the towers are 165 m high. The two-dimensional finite element model of Bosporus Suspension Bridge is considered with 202 nodal points, 195 beam elements and 118 truss elements for the analyses.

Filtered white noise ground motion model modified by Clough and Penzien [5] is used as a ground motion model in which the spectral density function intensity parameter is determined according to the S16E component of the 1971 San Fernando earthquake of the Pacoima dam record.

The analyses performed are carried out with a newly developed computer code SVEM [8] based on STOCAL [9]. The analyses obtained when using 2.5% of damping ratio and the first 15 modes.

In this study, the stochastic analyses of suspension bridges subjected to partially correlated seismic ground motions is carried out considering geometrically nonlinearity of the bridges. Mean of maximum values calculated and compared with those of the uniform ground motion. It is shown that the results obtained from correlated ground motion are generally higher than those of uniform ground motion. As the total response is dominated by dynamic component for uniform ground motion, pseudo-static component has also significant contributions for correlated ground motion. Therefore, correlated ground motion should be considered in the analyses of suspension bridges. It is also observed that the correlation function model proposed by Harichandran and Vanmarcke [1] gives the largest response values.

1

Harichandran, R.S., Vanmarcke, E.H., "Stochastic Variation of Earthquake Ground Motion in Space and Time", Journal of Engineering Mechanics, 112(2), 154-174, 1986. doi:10.1061/(ASCE)0733-9399(1986)112:2(154)

2

Abrahamson, N.A., "Spatial Variation of Multiple Support Inputs", Proc. of the First U. S. Seminar, Seismic Evaluation and Retrofit of Steel Bridges, October 1993, 1-34, San Francisco.

3

Hindy, A., Novak, M., "Pipeline Response to Random Ground Motion", Journal of Engineering Mechanics Division, 106(2), 339-360, 1980.

4

Uscinski, B.J., The Elements of Wave Propagation in Random Media, McGraw-Hill, New York.

5

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

6

Adanur, S., Dumanoglu, A.A., Soyluk, K., "Comparison of Asynchronous, Antisynchronous and Stochastic Dynamic Analyses of Suspension Bridges", Fourth International Congress on Advances in Civil Engineering, 1-3 November 2000, Vol.1, 177-184, Gazimagusa, Northern Cyprus.

7

Brown, W.C., Parsons, M.F., "Bosporus Bridge, Part I, History of Design", Proc. Instn Civ.Engrs, 58, 505-532, 1975. doi:10.1680/iicep.1975.3556

8

Dumanoglu, A.A., Soyluk, K., "SVEM, A Stochastic Structural Analysis Program for Spatially Varying Earthquake Motions", Turkish Earthquake Foundation, Istanbul, 2002.

9

Button, M.R., Der Kiureghian, A., Wilson, E.L., "STOCAL-User Information Manual", Report No UCB/SEMM-81/2, Department of Civil Engineering, University of California, Berkeley, CA, 1981.

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