The Use of Experimentally Ascertained Modal Data for a Calculation of a Bridge Structure Response on a Dynamic Load and for a Service Life Estimate
M. Polák
CTU, Faculty of Civil Engineering, Dept. of Structural Mechanics,
Thákurova 7,166 29 Praha 6
It is important to determine properties of many bridge structures in the certain time of their durability for an objective estimation of the residual service life or the loading capacity with an adequate accuracy and eventual for a decision about a strategy and a method of their service. This is the reason to create deterioration models of bridge structures for description of their static and dynamic behaviour and their properties after the certain time of their operation. The parameters of these models can be specified by experimental methods.
The experimentally - estimated frequencies, modes of natural vibration, corresponding damping values realize the real immediate state of the observed structure and its spatial behaviour. This is the reason for using the experimental modal parameters such as for identification, optimalization or a verification of a bridge design model. This model is shaped under certain physical and mathematical hypotheses. Therefore a succession of design models is possible to create for a given bridge structure in given time. The aptness of these models is important to verify by the experimental investigation of the studied bridge.
In addition, the apposite spatial model of the monitored bridge could be created directly from the finite number of experimentally - obtained modal parameters of this bridge (so-called the modal model). This spatial model enables to realise the calculation of the bridge spatial response under the spatial dynamic and static load as a time dependent function.
The results of the experimental modal analysis of the several road and railway bridges in Czech republic are saved in the data bank of Department of Structural Mechanics, Faculty of Civil Engineering, CTU Prague. The transducer of the bridge response in the reference point was used for the normalisation of the measured modes of natural vibration at several measurements in situ (the foot bridge by underground station Háje in Prague, the concrete road bridge across Labe river at Mělník town, the steel railway bridge across Ohře river at Stráž nad Ohří town), at other measurements the bridge response was related to the excitation force (the concrete road bridge across Radbuza river at Pilzen town, the concrete highway bridge across Sedlice’s creek, the steel cable-stayed road bridge across Labe river at Ústí nad Labem town). The creation of the bridge modal model from results of the separated methodologies requires the different procedures. Detailed description of the process of the modal model generation and of the response calculation on dynamic moving load is mentioned in [1] and [4].
Today the stress is the main criterion of the load carrying capacity check of a structure and its variability in time is the main criterion of the fatigue life check. It is possible to evaluate the response of the modal model under the live load on a stress quantity scale. The stress in a given checked detail of a structure can be determined on the basis of results of the bridge experimental testing in situ or of the calculation. In the first way the strain gauge is located in a given place of a structure, where the stress check is executed. After a processing the stress measured with this strain gauge is direct inserted in the modal model. In the second way the calculated response is exploited as the boundary conditions for computation of stress in an observed segment of a structure, which is modelled by means of the finite element method (so-called the substructuring ). The calculated time histories of the stress in given details of a structure can be processed by one of classification methods, for example the rain flow method can be used [4]. Afterwards it is possible to make the estimation of influence of the observed dynamic load on a reduction of the fatigue life of the monitored structure on a base of the obtained results and the Palmgren - Miner hypothesis.
The moving load of the bridge is modelled as a traffic flow - a group of real vehicles. The vehicles are modelled as a non-linear space system of mass elements mutually interconnected by immaterial force links by means of the component element method. The convenience of this form of the modelling of vehicles was demonstrated before. Since the position of the vehicles on the bridge is the function of time, also the position of points of contact varies in time . The displacement of the structure and the unevennesses of the carriageway surface in points of contact also vary in time. In this way a kinematics excitation of the vehicles takes place which, in return, influences the bridge structure by its forces.
The response of the modal model under the both dynamic and static influence of the moving load is calculated by the method of the expansion with respect to the modes of natural vibration. The system of differential equations of motion both the bridge and the vehicles is integrated by direct (step by step) method. The central difference method is used.
The verification of the applicability of the modal model for a calculation of a dynamic and static response of the bridge was carried out on the basis of the comparison of experimentally - obtained data with calculated response of the bridge under passages of trucks [1] [2] [3]. The very good congruity was achieved between the experiment and calculation results.
The direct use of the modal model of the bridge for the calculation of its dynamic response is an interesting method for the study of its service life and of the vehicle/bridge interaction problem.
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