Keywords: fragility curves, bridge, non-linear analysis, probability, push over analysis.

This paper describes a method to obtain fragility curves for bridges in a seismic environment through nonlinear simplified methods. The bridge capacity is described using the Modal Adaptive Push Over methods and the seismic demand by the response spectra. The incertitudes associated to both systems are quantified using a family of time histories well distributed in respect to seismic intensity and a random family of bridges. The results are compared with the ones obtained using a step by step integration in time and with a simplified pushover approach.

The study describes a method intended to obtain fragility curves using simplified analysis methods following a path started by Shinozuka and coworkers [1,2]. For the dynamics structural analysis a step by step non linear integration methods will be used and the statistical results obtained through a Monte Carlo computation will be used to check the ones due to a static non-linear approach.

This last one is in line with the methodology presented by the Applied Technology Council ATC 40 [3] under the Capacity Spectrum Method (CSM) name, that is the one followed by Shinozuka et al [1]. Other approach uses the so- called Dynamic Plastic Hinge Method (more specifically the curve Modal Load Deflection Line: MLDL) described by Montans et al [4] that can be considered as a Push Over Modal Adaptive (PMA) method.

The study is a step in the direction of reliability based criteria for design and retrofitting of bridges. It is focused on the development and comparison of different methods in the framework of simplified analysis that can be applied to the seismic engineering practice without loosing precision.

The fragility curves developed by nonlinear static simplified procedures give a good agreement for limit damage. For major damage the agreement is adequate, it is adequate because at this level the nonlinear characteristics show an essential role in the structural behavior.

1

Shinozuka, M., Feng, M.Q., Kim, H-K., and Kim , S-H. "Nonlinear Static Procedure for Fragility Curve Development". Journal of Engineering Mechanics, Vol. 126, No 12, December 2000. doi:10.1061/(ASCE)0733-9399(2000)126:12(1287)

2

Shinozuka, M., Feng, M.Q., Lee, J., and Naganuma , T. "Statistical Analysis os Fragility Curves". Journal of Engineering Mechanics, Vol. 126, No 12, December 2000. doi:10.1061/(ASCE)0733-9399(2000)126:12(1224)

3

Applied Technology Council (ATC).(1996). "Seismic Evaluation and Retrofit of Concrete Buildings". Rep. No. SSC 96-01 : ATC-40, 1, Redwood City, California.

4

F. Montáns and E. Alarcón. "Simplified Methods in the Computation of the Seismic Non-Linear Behaviour of Bridge". Ingeniería Civil No. 100, 1995.

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