Keywords: bridge, modelling, earthquake, passive, semi-active, control, simulations, user element.

The ASCE benchmark on cable-stayed bridges [1,2] has gathered, in recent years, the interest of many specialists in the field of the structural control and the dynamic response of long span bridges. Starting from the structural model of the original benchmark statement, a refined version is developed in a commercial finite element environment so as to include new modeling aspects, in the simulation of the stay cables dynamics and in the implementation of the seismic external excitation.

The bridge control strategy starts from passive issues using the elements available in the ANSYS [3] commercial finite element code evaluating their efficiency in the seismic effects mitigation. Subsequently, the implementation of the Bouc-Wen hysteretic model in ANSYS, by a user element, for a better simulation of the passive and semi-active control devices, is undertaken.

The work deepens the results of previous investigations carried out in the original framework of the benchmark. A refined model of the bridge is studied using the ANSYS commercial finite element code which has proven capable for the implementation of structural control systems. Since the original benchmark was carried out in MATLAB, the files with the nodes and elements information were converted to the new analysis framework.

This paper introduces advances in the problem simulations: the vertical component of the earthquake is considered, the delayed seismic input is not the same on all the supports but a coherence function is introduced so as to have different signals satisfying a fixed correlation function. The soil type regulates the correlation degree.

The model comprises soil-structure interaction through the use of impedance functions, the foundation are simulated by lamped masses with equivalent spring and dampers.

Focusing the attention on the simulation of the structural dynamics, the cable model is refined moving from the single rod type representation, used in the benchmark, to a description with six rope elements for each cable.

The acceleration time histories are obtained by a procedure which relies on the spectral representation method by Shinozuka [4]. At all stations, the generated accelerations satisfy the well known Kanai-Tajimi Power Spectral Density, as modified by Clough and Penzien [5]. The statistical differences between the motions at different stations satisfy the coherency function proposed by Luco and Wong [6]. Furthermore, the parameters of the Clough and Penzien Power Spectral Density are selected so as to give an average acceleration response spectrum which matches that of Eurocode 8 [7].

1

M. Domaneschi, L. Martinelli, "Modelling the ASCE Cable-Stayed Bridge Benchmark with Passive Devices", in "Proc. Of 4th European Conference on Structural Control", St Petersburg, Russia, September 8-12, 2008.

2

M. Domaneschi, "Feasible Control of the ASCE Benchmark Cable-stayed Bridge", in "Structural Control and Health Monitoring", Wiley & Sons, accepted, May 8, 2009.

3

ANSYS release 10.0, Ansys Inc, USA.

4

M. Shinozuka, "Monte Carlo Solution of Structural Dynamics", Computer & Struct., 10, 855-874, 1972. doi:10.1016/0045-7949(72)90043-0

5

R.W.Clough, J. Penzien, "Dynamics of structures", McGraw-Hill, New York, USA, 1975.

6

J.E. Luco, H.L. Wong, "Response of a Rigid Foundation to a Spatially Random Ground Motion", Earthquake Eng. Struct. Dyn., 14, 891-908, 1986. doi:10.1002/eqe.4290140606

7

Eurocode 8, UNI ENV 1998, "Design of structures for earthquake resistance".

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