O presente trabalho faz uma comparação entre resultados obtidos por um método prático e simplificado e o Método dos Elementos Finitos na determinação de esforços solicitantes em pontes celulares curvas em planta, submetidas à protensão. Na primeira parte, teórica, apresenta-se os conceitos fundamentais das vigas celulares curvas, mostrando-se principalmente as diferenças de seu comportamento em relação ao das vigas retas. Em seguida discute-se a protensão de peças de concreto com ênfase no seu efeito em vigas curvas. Finalmente, são apresentados os métodos a serem utilizados no cálculo, percorrendo as diversas situações de carregamento, mas sempre enfatizando o carregamento de protensão. Na segunda parte, prática, é elaborado um estudo comparativo, tomando-se como exemplo duas pontes rodoviárias em viga unicelular, sendo uma biapoiada e outra contínua, submetidas a protensão. Após a construção de modelos, tais vigas são processadas através de um programa comercial de elementos finitos. Alguns resultados são então comparados com aqueles obtidos através do método simplificado, elaborando-se assim observações práticas e que possam ser utilizadas nos projetos corriqueiros de engenharia. / This work compares the results from a practical and simplified method and the Finite Element Method to determinate section efforts in prestressed box-girder curved bridges. The first part, theoretical, introduces the basic principles of the cellular curved beams, showing the differences of its behavior comparing with straight beams. Next, prestressing of concrete members is discussed, emphasizing its effects in curved beams. Finally, calculation methods are presented, covering many loading situations, but always emphasizing the prestressing load. In the second part, practical, a comparative study is elaborated, taking two road unicellular bridges, one simply supported and another continuum, submitted to prestressing load. After models construction, such beams are calculated using a commercial software of Finite Element Method. Then, some results are compared with those calculated by simplified method, thus elaborating practical comments that can be used in the current designs of engineering.

O uso de aduelas pré-moldadas de concreto se transformou na técnica preponderante na construção de pontes com vãos médios a longos. No entanto, fatores econômicos têm continuamente exigido refinamentos nessas práticas de construção para o aumento da produtividade e redução do tempo de construção. As principais inovações desenvolvidas são: o uso de múltiplas chaves ou dentes de cisalhamento, que são saliências característica nas juntas entre os segmentos; uso de protensão externa e uso de juntas secas, sem epóxi. Por outro lado, um número insuficiente de investigações e análises sobre o comportamento desse tipo de estrutura tem sido realizado. Este trabalho tem como objetivo apresentar um estudo sobre o comportamento de estruturas segmentadas de concreto com protensão externa. O modelo computacional desenvolvido para a análise tridimensional do comportamento não-linear físico e geométrico dessas estruturas é baseado em uma formulação em elementos finitos. O concreto é representado no modelo através de elementos finitos hexaédricos e os cabos de protensão através de elementos lineares. As juntas, entre os segmentos justapostos, são modeladas através de elementos planos quadrangulares. O modelo de elementos finitos é capaz de representar o comportamento estrutural ao longo do processo de carregamento e consequentemente, obter as respostas da estrutura em termos de esforços, tensões e deslocamentos, por meio de uma análise incremental não linear. Foram testadas vigas monolíticas e segmentadas, em concreto armado e protendido, analisando o comportamento desse tipo de estrutura e comparando com valores experimentais encontrados na bibliografia. As vigas protendidas externamente, tanto monolíticas quanto segmentadas, apresentaram uma rigidez maior após o limite de proporcionalidade de tensões. Portanto, pode-se afirmar que o programa computacional desenvolvido é capaz de analisar peças com protensão externa, segmentadas ou monolíticas. / The use of precast concrete segments has become the predominant technique in bridge construction for medium to long span bridges. However, economic factors have continually claimed refinements in these construction practices to increase of productivity and reduction of construction time. The main innovations that have been developed are: the use of multiple shear keys, which are characteristic ledges in the joints between segments; the use of external prestressing and the use of dry joints, without epoxy glue. Otherwise, few studies exist about the behavior of this type of structure. This paper aims to present a study about the behavior of segmental concrete structures with external prestressing. The computational model developed for three-dimensional non-linear physical and geometric analysis of these structures is based on a finite element formulation. In this model concrete is represented by hexahedral finite elements and prestressing cables through linear elements. The joints, between the juxtaposed segments, are modeled through quadrangular plan elements . The finite element model is capable to represent the structural behavior during loading process and provides structure responses in terms of force, stress and displacement, using non-linear incremental analysis. The beams prestressed externally, both monolithic and segmented, have shown higher stiffness after reaching the proportional limit. This is due to the proposed model which does not consider the slip free of prestressing cables in the deviators. Comparisons with experimental data from the literature have shown good results for displacement values and stresses. Therefore, the computational program developed is able to analyze sections with external prestressing, segmental or monolithic, enabling further study of this type of structure.

No contexto da modernização da construção civil, a aplicação de elementos estruturais de concreto pré-moldado nas construções oferece comprovados benefícios à estratégia de execução das obras, dentre os quais se destacam o atendimento a vãos relativamente grandes, rapidez de montagem, leveza e excelente qualidade dos elementos que compõem a estrutura. Tratando-se especialmente do comportamento dinâmico das estruturas de concreto, os elementos pré-moldados, por apresentarem diversas situações transitórias de solicitação, devem ser avaliados quanto aos efeitos dinâmicos decorrentes da sua produção, transporte, montagem, execução das ligações, finalização da obra e uso. Considerando, nesse contexto, que a protensão é um recurso frequentemente utilizado nos elementos, evidencia-se a necessidade de estudos sobre a sua influência nos parâmetros dinâmicos. Em particular, elementos pré-fabricados protendidos, tais como painéis tipo duplo-T e lajes alveolares, têm sido muito utilizados em pisos de edifícios, todavia e não raras vezes sem uma prévia análise dinâmica quanto à vibração e ao atendimento aos limites de vibração em serviço. O presente trabalho apresenta uma síntese dos procedimentos de cálculo e verificação indicados por normas técnicas do Brasil e do Exterior para a avaliação do conforto humano quanto a vibrações excessivas, assim como os métodos analíticos empregados na determinação da frequência natural de um elemento estrutural, seja ele protendido ou não. Efetuou-se um estudo comparativo dos resultados analíticos com os de uma simulação numérica de painéis duplo-T e lajes alveolares, feita com programa computacional ANSYS, baseado no Método dos Elementos Finitos, sendo eles discutidos quanto ao Estado Limite de Vibrações Excessivas (ELS-VE). Este trabalho apresenta também um estudo experimental sobre um modelo físico de viga de concreto protendido com cabos externos, com o objetivo de demonstrar a aplicação de técnicas de caracterização dos parâmetros dinâmicos e discutir eventuais soluções para o controle ou atenuação de vibrações excessivas. Essa viga foi também analisada numericamente com o programa computacional ANSYS e feita a comparação dos resultados experimentais e numéricos. Conclui-se que, do ponto de vista do ELS-VE, os painéis duplo-T e lajes alveolares particularmente analisados são passíveis de restrições a partir de certos vãos e que, sob determinadas condições ora discutidas, o emprego de tirantes externos, protendidos ou não, podem ser aplicados no controle de vibrações, seja por aumento da rigidez do sistema viga-tirante, seja pelo controle da fissuração do concreto. / In the context of construction modernization, the application of precast concrete elements offers a good and reliable alternative in the construction strategy, among them large spans, fast assembly, lightweightness and excellent structural members quality. Dealing about dynamic behavior of concrete structures, precast elements are subjected to several loading conditions, from their manufacturing, transport, assembly, connection and finally to service. Prestressing technique is often applied in precast elements, so the influence of prestressing forces on dynamic parameters must be considered. Precast prestressed concrete elements, such as double-T panels and hollow core slabs are commonly used in building floors, but not always a previous dynamic evaluation is accomplished, so vibration problems are likely to occur. This work presents a synthesis of design procedures as recommended by the brazilian and foreign codes regarding to human comfort under vibration conditions. Analytical methods allow the determination of natural frequency of structural elements, being them prestressed or not. Also typical double-T panels and hollow core slabs were analyzed by Finite Element Method (ANSYS software) and analytical and numerical results were compared. A discussion of the results about the Service Vibration Limit State is made. This work also presents an experimental study on a reinforced concrete beam provided with external prestressing tendons. The goal of this study was to demonstrate dynamic tests to characterize dynamic parameters and to discuss vibration control. The tested beam was also simulated on ANSYS to compare theoretical and experimental results. Some conclusions has been drawn, such as typical double-T panels and hollow core slabs may suffer restrictions above certain span dimensions. Also the application of external tendons, with or without prestressing forces may be applied to reduce vibration levels, either by increasing stiffness of the structure or controlling cracking of the concrete beam.

The diploma thesis deals with the design of selected parts of reinforced concrete elements of the exhibition room. Simultaneously, the optimization of selected elements according to valid standards and Eurocodes was carried out and the impact of these changes on the economy of construction was developed.

Master's thesis deals with the reinforcement and expansion of girder bridge (continuous bridge with three spans) across the river Jihlava in Ivančice and reinforcement on the load class A. This is done by using an additional external prestressing cables and composite monolithic slab. Amplification is verified by calculation of load capacity.

The diploma thesis deals with design of plan – curved footbridge over Berounka river near the town of Čivice. Three different options were developed. First option includes a single – beam prestressed integral construction with haunches. The second option includes suspension footbridge construction, where the bridge deck is suspended at one side. In the third option the main span is built from concrete segments. Those are suspended on a pair of steel arches. The access ramps are cast – in – place, and they are supported by round steel piers. This variant was finally chosen as the best one and it was further processed. The construction was analyzed with Scia Engineer 2015 software, considering the construction process. The footbridge was loaded with dead loads and live loads including traffic and thermal actions. The internal forces were calculated and the construction was assess to the serviceability and ultimate limit states. In terms of serviceability, stress in concrete sections and deformations were checked. In terms of the ultimate limit state, the ultimate load capacities were calculated. The steel arches and piers were checked for possibility of loss of stability by buckling. The loss of stability was also checked by the software. Finally the dynamic behaviour of the construction was assessed, especially the harmonic excitation response. Then the construction plan and the drawings were made. The drawings include overview drawings and detailed drawings.

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There are a great number of old structures around the world, some of which were designed for completely different purposes than in their current application. Swedish railway bridges were for example only designed for maximum axle loads of 200 kN in the beginning of the 20th century, while the highest axle loads of today are twice as high. The traffic intensities have also increased dramatically and the velocities are now higher than ever before. Reinforced concrete trough bridges were typically designed and built in the mid-20th century and it is still one of the most frequent railway bridge types in Sweden. The trough bridges were normally designed for traffic loads which were smaller than the loads today and in order to maintain an old structure as the loads increases, structural upgrading of the load bearing capacity might be necessary. Upgrading the load carrying capacity can be performed in two ways, namely administrative upgrading or strengthening. Administrative upgrading refers to refined design calculations, using real material data, geometry and loads, which provides a higher capacity than the original design and the bridge can thereby be upgrading with minor physical impact. Upgrading by strengthening on the other hand, refers to, often, larger physical alteration of the structure in order to enhance the original load carrying capacity.Upgrading methods for increased flexural resistance of concrete trough bridges has been developed and tested previously, but strengthening methods for increased shear resistance in the bridge deck are still absent. The objective of this thesis is therefore to find an existing- or develop a new strengthening method which can be applied in order to enhance the shear resistance of concrete trough bridge decks. The difficulties associated to strengthening of existing railway bridges include traffic during the strengthening work and concrete surfaces concealed by the ballast.The State-of-the-Art indicated that none of the existing strengthening techniques were sufficient for this application and internal unbonded post-tensioning in the transverse direction was nominated as the most promising method. The research was thereafter focused on testing the possibilities and strengthening effects of post-tensioning. Two laboratory investigations were performed during the research project and the method was finally tested in a field test on a 50 years old trough bridge in Haparanda, Sweden. The strengthening procedure of internal unbonded post-tensioning consists of four consecutive steps:1.Transverse drilling of the horizontal holes through the bottom slab.2.Installation of the prestressing system.3.Post-tensioning of the system.4.Sealing of the prestressing system.The laboratory and field tests were successful and the results proved that the internal steel reinforcement within the concrete was compressed when the trough bridge was post-tensioned. Due to the compression, a higher load could be carried by the bridge deck before the tensile reinforcement yields and the bridge fails. In other words, the flexural capacity of the bridge deck was increased. The field test actually showed that eight steel bars, post-tensioned with 430 kN per bar on the Haparanda Bridge, completely counteracted the tensile stresses caused by a train with 215 kN axle loads. The effect on the shear resistance was however not as easy to measure, but the laboratory test recorded a significant strain reduction in the tensile reinforcement which was bent up at the transition zone between the bridge deck and the main girders. The reduced strain might be interpreted as lower shear stresses and post-tensioning can thereby be considered to have a positive effect on the shear resistance of the bridge deck. Shear design according to the protocol of Eurocode 2 or BBK was however found to be restrictive in predicting the post-tensionings effect on the shear capacity and further research is proposed in chapter 8. / Det finns ett stort antal gamla konstruktioner runtom i världen och många byggdes för helt andra användningsområden än vad de numera används till. Som ett exempel kan nämnas att svenska järnvägsbroar i början av 1900-talet byggdes för att klara av att bära axellaster på maximalt 200 kN, medan några av våra nybyggda broar är konstruerade för dubbelt så stora axellaster. Även traffikmängden har mångdubblats och tåghastigheterna är nu högre än någonsin. Trågbroar i armerad betong är en typisk bro som byggdes i Sverige framförallt på 50-talet och den är fortfarande en av de vanligaste brotyperna i Sverige. Trågbroarna konstruerades normalt för att bära lägre laster än vad vi har idag och för att kunna ha kvar dessa broar när lasterna ökar kan det krävas någon form av uppgradering av bärförmågan. Det finns två sätt att förbättra bärförmågan på en gammal bro, nämligen administrativ uppgradering eller förstärkning. Administrativ uppgradering innebär att nya förbättrade beräkningsmetoder används tillsammans med verkliga materialhållfastheter, geometrier och laster för att mer noggrant räkna ut brons bärförmåga. Normalt visar det sig att bärförmågan är högre än vad de ursprungliga beräkningarna antydde. På så vis höjs kapaciteten med minimal fysisk åverkan på bron. Uppgradering genom förstärkning innebär däremot att konstruktionens bärförmåga höjs genom att förändra bron ur ett rent fysiskt perspektiv. Metoder för att öka böjkapaciteten på trågbroar i betong har utvecklats och testats tidigare, men förstärkningsmetoder för att höja tvärkraftskapaciteten saknas däremot fortfarande. Målet för denna avhandling ligger därför i att utveckla en förstärkningsmetod som kan användas för att förbättra tvärkraftskapaciteten för bottenplattan på trågbroar i betong. Det finns dock några svårigheter sammankopplade med förstärkning av befintliga järnvägsbroar, t.ex. tågtraffik under förstärkningsförfarandet och att viktiga betongytor är skyddade av ballast.Inga befintliga förstärkningsmetoder bedömdes däremot som lämpliga för det avsedda användningsområdet vid ”State-of-the-Art’’ studien. Invändig efterspänning av broplattan i tvärledd bedömdes som den bäst lämpade förstärkningsmetoden och efterföljande forskning fokuserades på att reda ut möjligheter för och förstärkningseffekter av efterspänning. Två olika laboratorieförsök genomfördes under forskningsprojektet och förstärkningsmetoden testades slutligen vid ett fältförsök på en 50 år gammal järnvägsbro i Haparanda.Själva tillvägagångssättet för förstärkningsmetoden består av fyra viktigaoch sammanhängande arbetssteg:1. Borrning av horisontella hål tvärs igenom trågbrons bottenplatta.2. Installation av själva försstärkningssystemet.3. Efterspänning av förstärkningssystemet.4. Förslutning av förstärkningssystemet.Både laboratorie och fältförsöken blev lyckade och resultaten visade att stålarmeringen inuti betongen trycktes ihop när trågbron efterspänndes. Tack vare denna kompression så kan broplattan bära högre laster innan dragarmeringen börjar flyta och bron slutligen går sönder. Med andra ord så höjdes brons böjkapacitet. Fältförsöket visade att de åtta spännstagen, efterspännda med 430 kN per stag, helt och hållet motverkade dragarmeringens påkänningar av ett tåg med axellasten 215 kN. Förstärkningsmetodens effekt på tvärkraftskapaciteten är däremot inte lika lätt att påvisa men laboratorieförsöken visade att töjningen reducerades betydligt i den uppbockade dragarmeringen, i zonen där plattan fäster i huvudbalkarna. De lägre töjningsnivåerna kan tolkas som lägre skjuvpåkänningar och efterspänningen kan därmed ha en positiv effekt på broplattans tvärkraftskapacitet. Laboratorieförsöken visade däremot att både Eurokod 2 och BBK är restriktiva när det gäller att uppskatta efterspänningens effekt på tvärkraftskapaciteten. En ny förstärkningsmetod för trågbroar i betong har därmed föreslagits i och med denna avhandling, men en del frågetecken kvarstår och i kapitel 8 ges därför förslag på fortsatta forskningsområden.

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