The dynamic response (i.e., acceleration and displacement) of a bridge under vehicular load is an important component of design and evaluation. Field measurement of girder displacement, however, is generally nontrivial. Traditional sensors often require a stationary reference such as temporary scaffolds or a suspended cable. In either form, there are added costs, restrictions, and labor. As a result, there are both economic and practical incentives for developing methods that can use an accelerometer to measure both acceleration and displacement. One difficulty of this, however, is the presence of small low-frequency errors in the measured signal, which become sufficiently large through successive integrations and lead to a significantly distorted displacement profile. The objective of this article is to examine an analytical model based on the state-space approach for minimizing such errors and to compare results with two time domain correction methods. Field measurements from a threespan continuous bridge are used to assess the accuracy of each routine.
ResumoModeling the traffic loads on bridges has been the subject of numerous studies. Defining a live load model to be used for bridge design is not an easy task. It demands among many other things a reliable dataset, a well-defined procedure for filtering data and also the determination of statistics for single and multiple presence occurrences. This study examines and characterizes the live load statistics for Brazilian concrete bridges. Single and multiple truck presence are evaluated for different bridge spans and truck daily volume. The sample is comprised of the thirteen months of data from a High Speed Weigh-In-Motion station (HS-WIM) in a resolution of one hundredth of a second currently operating on the Fernão Dias highway, also known as BR-381. The system provides eleven thousand records on a daily basis. After the filtering process three thousand trucks remain. The station takes measures in an same-direction two-lane highway, which allows the evaluation and characterization of both single and multiple presence statistics. Three case of multiple presence are considered: following, side-by-side and staggered cases. The consideration of truck multiple presence on concrete bridges is mandatory to understand and characterize live load models. The results show that with the exception of the side-by-side case, the frequency of multiple truck presence is significantly affected by span length. It also shows that the daily truck volume considerably affects the multiple presence statistics for all load patterns. The results show that the general tendency of the occurrence of all multiple presence events is to increase as the truck volume increases.
Girder displacement is an important component of bridge design and evaluation because it is directly related to bridge stiffness and flexibility. The complex interaction between vehicle and bridge dynamics will result in vibration and deflection greater than that under equivalent static loading. However, field measurement of girder displacement generally is non-trivial. Different sensors and instrumentation systems can be used to measure bridge displacement. Some of these provide direct measurements, whereas others indirectly provide displacement through measurements of the angle of rotation, velocity, or acceleration of the girder. Indirect methods, however, require additional signal processing analyses to remove the effect of small errors in recordings caused by sensor drift, unknown initial bridge conditions, and signal noise. These errors become sufficiently large through successive integrations and greatly distort the integrated velocity and displacement signals. Two correction methods are examined, namely, the velocity estimation method and the linear baseline correction method (BCM), for minimizing such errors in obtaining displacements indirectly from acceleration records. Independently measured girder acceleration and displacement records from a three-span continuous bridge under controlled live load testing are used to evaluate the accuracy of each method. It is found that the linear BCM results in a corrected displacement profile that more reasonably approximates the measured trace under various loading patterns. The choice of integration boundaries is also shown to affect the accuracy of both methods. An objective approach based on the energy content of the signal is proposed.
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