Dynamic Analysis of Suspension Bridges and Full Scale Testing

This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account. The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation governing the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected to three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. By this means a realistic appraisal is achieved for torsional response as well as for the other types of vibration. The modal response spectrum technique is applied to evaluate the seismic loading for the combination of these vibrations. Various numerical examples are introduced in order to demonstrate the method of analysis. The procedure described enables the designer to evaluate the nonlinear dynamic response of suspension bridges in a systematic manner.

Finite element model validation of bridge based on structural health monitoring——Part Ⅱ:Uncertainty propagation and model validation

Because of uncertainties involved in modeling, construction, and measurement systems, the assessment of the FE model validation must be conducted based on stochastic mea- surements to provide designers with confidence for further applications. In this study, based on the updated model using response surface methodology, a practical model vali- dation methodology via uncertainty propagation is presented. Several criteria of testing/ analysis correlation are introduced, and the sources of model and testing uncertainties are also discussed. After that, Monte Carlo stochastic finite element （FE） method is employed to perform the uncertainty quantification and propagation. The proposed methodology is illustrated with the examination of the validity of a large-span prestressed concrete continuous rigid frame bridge monitored under operational conditions. It can be concluded that the calculated frequencies and vibration modes of the updated FE model of Xiabaishi Bridge are consistent with the measured ones. The relative errors of each frequency are all less than 3.7%. Meanwhile, the overlap ratio indexes of each frequency are all more than 75%; The MAC values of each calculated vibration frequency are all more than 90%. The model of Xiabaishi Bridge is valid in the whole operation space including experimental design space, and its confidence level is upper than 95%. The validated FE model of Xia- baishi Bridge can reflect the current condition of Xiabaishi Bridge, and also can be used as basis of bridge health monitoring, damage identification and safety assessment.