Accelerations- och bromskrafter för järnvägsbroar: Analys av reduktionsfaktor
Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
In January 2010 European design standards for structures entered Sweden, replacing the previous standards of railway bridges, Bro 2004 and BV Bro, version 9. This brings changes of the rules concerning calculations of the forces which act on the superstructure of the bridge, and consequently the forces on the fixed bearings, due to traction and braking. In EN 1991-2, which determines the traffic loads on railway bridges according to the European constructions standards, there are different methods to take the interaction between the track and the superstructure of the bridge into account. For example interaction occurs because of accelerating and braking forces in the rails. This master thesis has been initiated in order to clarify the limits of the methods, how to use them and the advantages and disadvantages of each method. The methods consist of one general method and two simplified methods applicable under different conditions. In addition to the methods given in EN 1991-2 this report also includes well-known methods produced by Banverket (the Swedish railway administration), International Union of Railways (UIC) and Ladislav Frýba. Moreover a simplified, theoretical method is derived according to the current standard. The interaction between the track and the superstructure of the bridge due horizontal forces depends of a couple of parameters. Some examples are the configuration and properties of the track and the structure of the bridge. This means that the track over and next to the bridge and the superstructure, fixed bearings, substructure and the foundation of the bridge should be included in the analysis. It is important to consider the connection between the track and the superstructure of the bridge and its resistance to shear forces in longitudinal direction. The force-displacement behavior of the coupling has proved to be nonlinear, which is simplified as a bilinear behavior with elastic and plastic part. Because of this a nonlinear analysis is required when the forces in the couplings exceeds the yielding force. The analytical model in this report is however only valid for elastic behavior. In the analysis of the effects due to traction and braking the stiffness in longitudinal direction is the essential parameter concerning to the superstructure, fixed bearings, substructure and foundation of the bridge. This report consists of several case studies in order to determine the reduction factor ξ for the determination of the longitudinal forces in the superstructure of the bridge and the fixed bearings due to acceleration and braking forces. The case studies include five existing bridges and a sensitivity analysis. The bridges, whose lengths are in parentheses, are two portal frames (15/23m), two girder bridges (52/150m) and one truss bridge (82m), where the girder bridges are continuous while portal frames and the truss bridge consist of only a single span. Furthermore the analysis of the portal frames take a spread foundation into account, but analysis of the other bridges take both spread and pile foundation into account. In the sensitivity analysis the theoretical model of calculation is used to clearly identify the main parameters with regard to the reduction factor ξ. The methodology which is expected to describe the real behavior in the most proper way is the general method according to EN 1991-2, where the FE-program FEMAP is used for the nonlinear analysis. Modeling in FEMAP includes the parts of the bridges and associated factors which are important for the results. Furthermore FEMAP is used to calculate necessary parameters for the other calculation methods. According to the analysis in FEMAP with spread and pile foundation the reduction factor ξ are 0.51 (15m) and 0.52 (23m) for the portal frames, 0.65/0.72 (52m) and 0.74/0.73 (150m) for the girder bridges and 0.79/0.77 (82) for the truss bridge, where the value in the parentheses. The results from FEMAP have a very good conformance compared with the results from the analytical methodology of calculation within its validity range. The biggest difference between the methods is 5 percentage points. The methods according to Banverket and UIC also appear to match the results from FEMAP moderately, but not to the same extent as the analytical method. The simplified approach according to Frýba differs markedly from the other methods. The simplified methods according to EN 1991-2 results in a reduction factor ξ close to 1.0 for the portal frames, which means no reduction of the acceleration and braking forces. Thus the results differ markedly from the general method, where FEMAP is used. For the girder bridge with a length of 52 m the results appear to match in the case with pile foundation, but not to the same extent in the case with spread foundation. Because the calculations methods according to EN 1991-2 result in various degree of reduction due to acceleration and braking forces they are beneficial to use in different situations. The analytical method is recommended over the other simplified methods as a result of the accordance to the output from FEMAP. Moreover the analytical method includes all of the parameters, which have a significant impact on the reduction factor according to the sensitivity analysis. The actual parameters are the stiffness of the fixed bearings, the length of the bridge and to some extent the superstructure of the bridge and the shear resistance in longitudinal direction. The conclusion from the case studies is that a simplified method should be used to take the interaction between track and superstructure of the bridge due to acceleration and braking forces into account. The reason for this is to reduce the required to calculate the loads on the structure. It is possible to use the analytical model up to a theoretical length of 60 to 100 m depending on the bridge design, and over this length it is appropriate to use the general method with any FE-program. A possible way to simplify the calculations further is to create a model where the only length of the bridge gives the reduction factor ξ. To create such model the most common type of bridge may be studied for different lengths with respects to the longitudinal stiffness of the fixed bearings, which subsequently gives the reduction factor. The literature study in the report also indicate that the values which describe the resistance of the track in longitudinal direction according Eurocode can be strongly conservative in relation to measurements of the prevailing conditions in Sweden. In order to clarify if these indications are correct an investigation is proposed for the shear resistance of the track in longitudinal direction.
Place, publisher, year, edition, pages
2010. , 308 p.
Teknik, Eurokod, kombinerad respons, longitudinell kraft, reduktionsfaktor, accelerations- och bromskraft, interaktion spår – bro, longitudinell styvhet, spår
IdentifiersURN: urn:nbn:se:ltu:diva-55016Local ID: bedb1d0f-96aa-4930-9f4a-df84a48b456fOAI: oai:DiVA.org:ltu-55016DiVA: diva2:1028397
Subject / course
Student thesis, at least 30 credits
Civil Engineering, master's level
Validerat; 20110119 (anonymous)2016-10-042016-10-04Bibliographically approved