A numerical investigation of the dynamic behaviour of continuous, multi-span railway bridges
Master Thesis
2018
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University of Cape Town
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Abstract
The dynamic behaviour of railway bridges has been investigated for over a century [Ichikawa et al., 2000]. With the introduction of high speed trains in recent history, a host of complex problems regarding resonance have been observed and studied. These studies, which include Bjorklund [2004]; Gabald´on et al. [2009]; Goicolea et al. [2002]; Rigueiro et al. [2010]; Kumaran et al. [2003]; Kwark et al. [2004] and Xia and Zhang [2005], have focused on resonance in relatively short-spanned simply supported railway bridges. New design methods were incorporated in design codes such as Eurocode (EN 1991-2) [2003] to address these problems in practice. In the past, railway bridges were designed for static effects, while dynamic effects were accounted for by the application of an amplification factor. It has become increasingly necessary to perform a full dynamic analysis, especially with regard to high speed trains. In the case of continuous, multi-span railway bridges carrying heavy haul trains, such an analysis is not explicitly specified. Design codes, even as recent as the modern Eurocode (EN 1991-2) [2003], do not address scenarios where axle loads are higher than 30 tonnes/axle, or trains become very long. Previous work on the dynamic behaviour of continuous bridges is limited. The dynamic properties of continuous beams was studied as early as Lin [1962], and more recently by Saeedi and Bhat [2011]. The response of continuous beams or bridges subjected to moving forces or masses was studied by Cheung et al. [1999], Johansson et al. [2013] and Ichikawa et al. [2000]. These investigations were limited to analytical methods to determine the dynamic properties (natural frequencies and mode shapes) and response of beams or bridges. In this research, the response of multi-span, continuous bridges trafficked by heavy haul trains travelling at low to moderate speeds was investigated. The study comprises an investigation of bridges with spans ranging from one to ten, and span lengths of 40 m, 45 m and 50 m modelled using the Finite Element Method in SOFiSTiK. Loading is based on heavy haul trains, which were modelled using the moving forces load model. Natural frequencies and mode shapes were obtained, and displacements and accelerations were calculated for train speeds varying from 20 km/h to 100 km/h. A case-study of the Olifants River Viaduct (ORV), the longest continuous railway bridge in South Africa, is also carried out. From the study it is evident that as the number of bridge spans increase, the envelope of natural frequencies in the concentrated zone increase but the frequencies become very closely spaced, indicating that the modes might be difficult to determine experimentally. Displacement and accelerations were generally higher in the first and last span of the multi-span models. A difference in maximum displacements was only noticeable when comparing models with the number of spans ranging from 1 – 4, thereafter maximum displacements were not affected by the number of spans in the model. Accelerations increased as the speed increased. At low speeds, the number of spans did not significantly influence the peak deck acceleration, however, at higher speeds models with the greater number of spans generally had lower maximum accelerations.
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Ludwig, C. 2018. A numerical investigation of the dynamic behaviour of continuous, multi-span railway bridges. University of Cape Town.