Modelling of Traffic Loads on Bridges Based on Measurements of Real Traffic Loads in Sweden
Abstract: This thesis treats traffic load effects in road bridges and in particular bending moment and shear force in different types of bridges. All traffic load effects are described in terms of statistical distribution functions for annual extreme values. The statistical distributions are based on measurements of real traffic, made in Sweden during 2002-2003. The measurements are managed by the Swedish Road Administration and accounted for in Vägverket (2004b). The data base contains information about 280000 vehicles out of which approximately 31000 are classified as heavy vehicles. Only vehicles that are defined as heavy are decisive for the design of bridges. The data base contains information about the time when the vehicles passed the measuring station, the number of axles on the vehicle, the mutual distance between axles and weight of every single axle. With such information it is possible to determine section forces in different types of bridges very accurately. Information about when vehicles pass the measuring station is used to verify assumptions regarding for example the mutual distance between two consecutive heavy vehicles. This is of interest when section forces in longer bridges are studied. For variable loads the characteristic value is used to define the load. Codes used to design bridges, usually define the characteristic value as the 98th percentile of the annual maximum distribution, i.e. a 50 year return period. The data material used here is collected during 51 days at 8 different locations in Sweden. Using the measured vehicles as input the statistical distribution functions for traffic load effects in different types of bridges are determined. The information of interest here is to describe the maximum load effects during the reference period, so called extreme value distributions. Collecting the necessary amount of data to determine extreme value distributions directly would be too costly and time consuming. Instead some kind of extrapolation method must be applied. In this thesis the POT-method, (Peaks Over Thresholds) and simulations are used to determine the extreme value distributions for traffic load effects. The POT-method implies that only the section forces which exceed a certain level (threshold), are fitted to a standard distribution. From that distribution the extreme value distributions for the section forces are determined. The advantage of using this method is that it is possible to determine the extreme value distributions and the characteristic values at different traffic intensities in an easy way. This report contains tools to determine the extreme value distributions for section forces in bridges with different traffic intensity. In probability based analysis of structures statistical information about all the basic variables in the limit state function must be available, i.e. the statistical distribution functions must be known. The most dominating variable load on bridges is the load generated by traffic; see e.g. Das (1997) and Bailey (1996). These loads affect the result of the bridge analysis to a great extent and accurate information about these loads is therefore very important. When a new bridge is designed the consequence of using too high loads is in most cases negligible, i.e. the extra cost for a larger cross section is manageable. In contrast, if the safety level in an existing bridge is considered too low, the load level is of major importance. Strengthening or in the worst case replacement of the bridge is very expensive. Evaluation of existing bridges are often based on a deterministic analysis where the loads are taken from some bridge code, e.g. Vägverket (2004a), i.e. the actual traffic load for the specific bridge is not taken into account. The traffic loads in deterministic codes are generally very conservative because they are intended to cover all types of bridges. Instead of using deterministic methods to determine the safety level of an existing bridge, more sophisticated methods that can account for specific information about a bridge should be applied. Probability based methods are very applicable in these cases. An advantage with probability based methods is that specific information about the bridge can be included in the analysis. An example of such information is measurements of the material properties in the bridge. Another possibility more seldom used is to determine the traffic load effects based on the traffic intensity at the actual bridge site. The traffic intensity is measured by the Swedish road administration on many locations on the Swedish road net. With the methods described in this report it is possible to determine the extreme value distributions for the section forces with the traffic intensity as input. Two case studies are used to illustrate the method. Of course, a probability based method is not the whole solutions to bridges with insufficient safety. The method shall be seen as one out of several possible ways to evaluate the condition of a bridge. Every bridge that can be saved for a new period of time by use of more sophisticated methods implies substantial saving of money.
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