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Och Miljöteknik Air Influence on the Temperature inside a Concrete Bridge Box Section Cristina Cachada Avdelningen för Konstruktionsteknik Lunds Tekniska Högskola Lund Universitet, 2010 Rapport TVBK - 5188 Avdelningen för Konstruktionsteknik Lunds Tekniska Högskola Box 118 221 00 LUND Department of Structural Engineering Lund Institute of Technology Box 118 S-221 00 LUND Sweden Air Influence on the Temperature inside a Concrete Bridge Box Section Lufttemperaturpåverkan på temperaturen inuti ett lådtvärsnitt hos en betongbro Cristina Cachada 2010 Rapport TVBK-5188 ISSN 0349-4969 ISRN: LUTVDG/TVBK-10/5188+138p Examensarbete Handledare: Oskar Larsson Juni 2010 Preface At the last stage of, my master in civil engineering, I was faced with the opportunity of working together with the civil engineering department of the University of Lund’s. Therefore, this project was developed in two phases: The first phase, took place in Lund’s University, Sweden, and involved the entire introduction to the bridge temperatures thematic, the development of the computational model and the respective numerical results collection. The second phase of this work was developed in IST Lisbon, Portugal, and included the analysis of the numerical results and the development of the conclusions. Acknowledgments First of all, I would to thank Oskar Larson for introducing me to this thematic and to the informatics program, and mostly for all his time and patient guidance. I would also like to thank Professor Fernando Branco for giving me important ideas to improve my analysis as well as an important help on the thesis revision. Finally, I would like to express my gratitude for the help given by Filipa in the language revision of the thesis and for the support given by my parents, Margarida and Rodrigo during all the period of this work development. i Abstract The temperature on a bridge is a complex phenomena caused by several sources and it is quite difficult to forecast. Its effects cannot be ignored and during the last decades various studies have been made in this field. In order to reduce the complexity of these investigations, some simplifications, which do not entail large risks, are admitted making the problem easier to analyse. The main objective of this thesis is to analyse the thermal influence of the air temperature inside a concrete bridge box cross-section. Usually this ‘detail’ is ignored or simplified by the investigators. With the work developed and presented in this thesis it is possible to understand the dimension of the error introduced in the studies every time this simplification is introduced. To fulfil this purpose, two finite element models were developed in order to compare with experimental values. The experimental values were collected using the instrumentation installed on the new Svinesund Bridge in Sweden. In both the models (A and B) several thermal sources were introduced affecting the cross section from the outside such as air temperature, solar radiation and the night radiance. The difference between the two models is that in the first model (A) the air inside the box cross-section is taken into account and in the second model (B) that air is ignored. The quality of the fit of the values obtained using the models A and B with the experimental values from Svinesund allow to take the conclusions of this work. The difference between the models does not indicate that changes in this detail must be included in the future thermal studies. Keywords: • Air temperature • Bridge • Concrete • Finite Element • Svinesund ii Resumo Numa ponte, a temperatura é uma acção complexa originada por diferentes fontes e difícil de prever. Os seus efeitos não devem ser ignorados e por isso nas últimas décadas muitos estudos foram desenvolvidos neste campo. De modo a reduzir a complexidade associada a estas investigações, algumas simplificações, que não acarretam consequências graves, são usualmente introduzidas possibilitando uma análise mais simples. O objectivo principal desta tese é analisar a influência térmica da temperatura do ar dentro de uma secção em caixão de uma ponte de betão. Normalmente este ‘pormenor’ é ignorado ou simplificado em investigação. O trabalho desenvolvido e apresentado nesta tese permitirá ter noção da dimensão do erro introduzido nos estudos sempre que esta simplificação é feita. Para atingir este objectivo, foram desenvolvidos dois modelos em elementos finitos para comparar os resultados com valores experimentais, recolhidos recorrendo a instrumentação instalada na nova ponte de Snivesund na Suécia. Nos dois modelos (A e B) foram introduzidas diferentes acções que afectam termicamente a secção de betão tais como: a temperatura do ar, a radiação solar e a radiação nocturna. A diferença entre os dois modelos reside no facto de no modelo A se considerar o ar dentro da secção em caixão e de no modelo B este ser ignorado. A qualidade do ajuste dos valores obtidos usando o modelo A ou o modelo B aos valores experimentais permite tirar as conclusões deste trabalho. A diferença dos modelos não revela a necessidade de incluir este pormenor nos futuros estudos térmicos em pontes de secção em caixão. Palavras-chave: • Temperatura do ar • Ponte • Betão • Elementos Finitos • Svinesund iii Index 1 Introduction ....................................................................................................................................... 1 1.1 Importance of considering the thermal effects on bridge design ................................................ 1 1.2 The legislation .......................................................................................................................... 2 1.3 The study developed in this thesis ............................................................................................ 2 1.4 The structure ............................................................................................................................ 3 2 Heat transmission ............................................................................................................................. 4 2.1 Conduction ............................................................................................................................... 4 2.1.1 General ................................................................................................................................ 4 2.1.2 Application to bridge ............................................................................................................. 5 2.2 Convection ............................................................................................................................... 6 2.2.1 General ................................................................................................................................ 6 2.2.2 Application to the bridge ........................................................................................................ 7 2.3 Radiative Heat transfer ............................................................................................................. 8 2.3.1 General ................................................................................................................................ 8 2.3.2 Application to the bridge ...................................................................................................... 10 2.4 Solar radiation ........................................................................................................................ 10 2.5 Stresses produced by temperature ......................................................................................... 14 2.5.1 General .............................................................................................................................. 14 2.5.2 Uniform component, ..................................................................................................... 14 °Ã 2.5.3 Temperature difference, ................................................................................................. 15 ∆° 2.5.4 Non-linear distribution, ........................................................................................................ 15 2.6 Eurocode ................................................................................................................................ 16 2.6.1 Eurocode 1 Part 1.5 [17] ..................................................................................................... 16 2.6.2 Eurocode 1 Part 2.5 [1] ....................................................................................................... 17 2.7 Previous studies ..................................................................................................................... 19 2.7.1 Silveira [7] ........................................................................................................................... 19 2.7.2 Branco and Mendes [8] ....................................................................................................... 19 2.7.3 Elbadry and Ghali [16] ........................................................................................................ 19 2.7.4 Fu, Ng and Cheung [18] ...................................................................................................... 20 3 Svinesund Bridge [19] ..................................................................................................................... 22 3.1 Localization ................................................................................ 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