Computation:of Historical Arch Bridges
The described loadings on bridges in the preceding chapter cause a certain reaction of the arch bridge if applied to the bridge. This reaction is either admissible or inadmissible. Inadmissible reactions of bridges include damages or failure of the bridge
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“An arch bridge can bear everything, except a static computation.” Unknown author (Weber 1999)
3.1 Introduction The described loadings on bridges in the preceding chapter cause a certain reaction of the arch bridge if applied to the bridge. This reaction is either admissible or inadmissible. Inadmissible reactions of bridges include damages or failure of the bridge. To prevent such effects, the reaction of bridges exposed to loads is usually studied in advance. Such studies or structural analysis requires the development of an appropriate numerical model. These models usually reflect the knowledge of humans about the structure. This fact becomes especially visible for structure types with a long history, such as arch bridges. Here, completely arbitrary models are models from Von Leibbrand (1897), Haase (1899), Gilbrin (1913), Fain (1953), Wolf (1989), Lachmann (1990), and Falter (1998). Of course, this chapter gives a much more detailed and structured list about certain types of models. However, a simplified rule for choosing an appropriate model cannot be given. Even very simple empirical rules have shown to be a solid basis for bridges with ages of centuries and millenniums. The choice of the model or model type depends on the respective question and the provided resources. During the COST-345 (2004) report for the EU commission, different description classes for structures and their applications were discussed. Table 3-1 lists different levels of assessment. This chapter starts with a discussion of simple empirical rules and advances to the latest numerical models in terms of finite element and discrete element models. Many further recommendations about the different levels of bridge assessment can be found in literature (Schueremans et al. 2003, Diamantidis 2001, Rücker et al. 2006, Enevoldsen 2008, Brühwiler
D. Proske, P. van Gelder, Safety of Historical Stone Arch Bridges, DOI 10.1007/978-3-540-77618-5_3, © Springer-Verlag Berlin Heidelberg 2009
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3 Computation of Historical Arch Bridges
2008, O’Connor et al. 2008, Jensen et al. 2008, Ruiz et al. 2008, and SIA 269 2008).
3
4
5
FEM analysis of specific details of the structure being assessed not considered in the previous levels
Reliability analysis based on probabilistic models
Two- or three-dimensional, linearelastic or nonlinear, elastic or plastic, allowing for cracking
Empirical or two-dimensional-model, linear-elastic arch frame
Arch bridges
Bridges
Structure Subtype Description level type 1 2
Two- or three-dimensional, linear or nonlinear, elastic or plastic, grillage or FEM (upstand model if necessary), allowing for soilstructure interaction, cracking, site- specific loading and material properties
Table 3-1. Analysis methods recommended for each level of assessment (COST345 2004)
3.2 Empirical Rules 3.2.1 Historical Rules In 1717, Gauter listed the following five tasks during the design process of natural stone arch bridges (taken from Heyman 1998): • • • • •
Choice of the shape of the arch Choice of the arch thickness at the key
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