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A fragility analysis of a fan type cable stayed bridge using a probabilistic risk analysis (PRA) procedure is presented to determine its probability of failure under random ground motion. Seismic input to the bridge support is considered to be a band-limited white noise at the bedrock. For the response analysis, the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of the cable—tower—deck system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges.The responses of the bridge deck are obtained by the response spectrum method of analysis for multiple-degrees-of-freedom system. The fragility analysis includes uncertainties of responses due to the variation in ground motion, material properties, modeling and method of analysis. Uncertainties of the capacity of the structure are considered, such as ductility factor variation and damage concentration effects. Failure of the bridge is assumed to take place when the bridge deck moment at any section within a supported span reaches the yield value. The probability of failure of the bridge deck is determined by the first order second moment (FOSM) reliability method. A three-span double-plane symmetrical cable stayed bridge is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations which include ratio of the components of ground motion, spatial correlation of ground motion, angle of incidence of earthquake, ductility ratio and coefficients of variation of the uncertainty factors. The results of the study show that these factors have considerable effect on the probability of failure of the bridge.

A frequency domain response analysis is presented for building frames passively controlled by viscoelastic dampers, under harmonic ground excitation. Three different models are used to represent the linear dynamic force-deformation characteristics of viscoelastic dampers namely, Kelvin model, Linear hysteretic model and Maxwell model. The frequency domain solution is obtained by (i) an iterative pseudo-force method, which uses undamped mode shapes and frequencies of the system, (ii) an approximate modal strain energy method, which uses an equivalent modal damping of the system in each mode of vibration, and (iii) an exact method which uses complex frequency response function of the system. The responses obtained by three different methods are compared for different combinations of viscoelastic dampers giving rise to both classically and non-classically damped cases. In addition, the effect of the modelling of viscoelastic dampers on the response is investigated for a certain frequency range of interest. The results of the study are useful in appropriate modelling of viscoelastic dampers and in understanding the implication of using modal analysis procedure for building frames which are passively controlled by viscoelastic dampers against base excitation.

Response of structures to non-stationary ground motion can be obtained either by the evolutionary spectral analysis or by the Markov approach. In certain conditions, a quasi-stationary analysis can also be performed. The first two methods of analysis are difficult to apply for complex situations such as problems involving soil-structure interaction, non-classical damping and primary-secondary structure interaction. The quasi-stationary analysis, on the other hand, provides an easier solution procedure for such cases. Here-in, the effectiveness of the quasi-stationary analysis is examined with the help of the analysis of a single degree-of-freedom (SDOF) system under a set of parametric variations. For this purpose, responses of the SDOF system to uniformly modulated non-stationary random ground excitation are obtained by the three methods and they are compared. In addition, the relative computational efforts for different methods are also investigated.

Dissipation of hysteretic energy in the isolator of the base isolated structure under seismic excitation is investigated. The hysteretic force-deformation characteristics of the base isolator is specified by a nonlinear differential equation. The parameters of the equation can be adjusted to obtain various types of hysteretic models of the isolator including the elastoplastic type. The variation of hysteretic energy dissipated in the isolators is obtained for both harmonic and El-Centro 1940 earthquake ground motion for a set of important parameters. They include time period of superstructure, ratio of superstructure mass to base mass, level of yield strength of the isolator, post- to preyielding stiffness ratio, and the ratio of harmonic excitation frequency to base isolation frequency. It is shown that the dissipation of hysteretic energy in the isolator is significantly influenced by the above parameters.