Fizemos uma apresentação detalhada, com um enfoque geométrico, da Teoria de Homotopia Simples e como aplicação, uma análise detalhada da classificação por homotopia e homotopia simples dos Espaços Lenticulares / We made a detailed presentation, with a geometric approach, of Simple Homotopy Theory and as a major application we present a detailed analysis of homotopy and simple homotopy classification of Lens Spaces

Neste trabalho, estudamos a ação dos grupos split metacíclicos \'D IND. (2h+1) POT. 2 nas esferas. Encontramos uma região fundamental dos espaços quocientes, chamados de Formas Espaciais Esféricas Metacíclicas, que foi utilizada para construirmos um conveniente complexo de cadeias destas formas com o qual calculamos o anel de cohomologia e a torção de Reidemeister. Obtivemos também uma relação entre as diferentes torções encontradas / In this work, we study the action of the split metacyclic groups \'D IND. (2h+1) POT. 2 on the spheres. We find a fundamental domain of the quotient spaces, called Metacyclic Spherical Space Forms. Through this region we have built a convenient chain complex of these spaces and we used it to calculate their cohomology ring and Reidemeister torsion. We obtained also a relation between the different torsions found

Orientadores: Antonio Jose Ramirez Londono, Sérgio Tonini Button / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T08:59:11Z (GMT). No. of bitstreams: 1 Fonseca_EduardoBertonida_M.pdf: 6113689 bytes, checksum: 7822b778729271cdd221fc4ab3b1a0cc (MD5) Previous issue date: 2013 / Resumo: Simulação física da soldagem por atrito com pino não consumível (SAPNC) foi realizada com o objetivo de se determinar as condições termomecânicas impostas ao material durante o processo, as quais são essenciais para o melhor entendimento da soldagem e para o desenvolvimento da simulação numérica da SAPNC. Por isso, ensaios de torção a quente foram realizados no aço inoxidável duplex (AID) UNS S32205 utilizando um simulador termomecânico Gleeble 3800®. Foi desenvolvido um sistema de resfriamento com nitrogênio líquido para se reproduzir, nos ensaios de torção, a história térmica medida durante a SAPNC do AID. Assim, foram reproduzidas as microestruturas da zona termomecanicamente afetada (ZTMA), tanto do lado de avanço quanto do lado de retrocesso, e da zona misturada (ZM) central. As microestruturas foram comparadas em termos de morfologia, de fração volumétrica, de tamanho de grão médio e de fração recristalizada de cada fase, por meio de microscopia óptica e difração de elétrons retroespalhados (EBSD). Além disso, foram analisados os mecanismos de amaciamento de cada fase durante a deformação a quente. Simulações numéricas do ensaio de torção foram realizadas para determinar a deformação verdadeira e a taxa de deformação em cada região simulada. A ZTMA foi simulada fisicamente a 1030 °C, 500 a 750 rpm e 0,50 a 0,75 revolução, o que corresponde a deformações verdadeiras entre 0,50 e 0,65 e taxa de deformação de 11 s-1. Embora tenha sido observada boa semelhança morfológica, o tamanho de grão médio das regiões simuladas se mostrou inferior àquele da ZTMA real. Observou-se recristalização dinâmica contínua da ferrita e recristalização dinâmica parcial da austenita, resultando em estrutura majoritariamente deformada. Já a ZM foi simulada fisicamente a 1130 °C, 500 a 750 rpm e 1,2 revolução, o que corresponde à deformação verdadeira de 1,30 e taxa de deformação de 15 s-1. O refinamento de grão da ZM foi reproduzido pelos ensaios de torção, porém com pequenas diferenças morfológicas devido à falta de mistura mecânica na simulação física. Foi apontada a ocorrência de recuperação e recristalização dinâmicas na austenita e recristalização dinâmica contínua na ferrita / Abstract: Physical simulation of friction stir welding (FSW) was employed to determine the thermomechanical conditions imposed to the material during the process, which are essential for the better understanding of the process and for the development of FSW numerical simulation. Therefore, hot torsion tests were carried out on UNS S32205 duplex stainless steel (DSS) using the thermomechanical simulator Gleeble 3800®. A liquid nitrogen quench system was developed in order to reproduce during the torsion tests the thermal history previously measured during FSW of the DSS. As a result, the microstructures from the thermomechanically affected zone (TMAZ), both advancing and retreating sides, and from the center of the stir zone (SZ) were reproduced. Microstructures were compared in terms of morphology, volume fraction, average grain size, and recrystallized fraction of each phase, by means of optical microscopy and electron backscattered diffraction (EBSD). Moreover, the softening mechanisms of each phase during hot deformation were investigated. Numerical simulation of the torsion tests were carried out in order to determine the true strain and the strain rate associated with each simulated microstructure. The TMAZ was physically simulated at 1030 °C, 500 to 750 rpm, and 0.50 to 0.75 revolution, which corresponds to true strains between 0.50 and 0.65, and strain rate of 11 s-1. Although good morphological resemblance was observed, the average grain size of the simulated regions remained smaller than the real TMAZ. The softening mechanisms observed were continuous dynamic recrystallization of the ferrite and partial dynamic recrystallization of the austenite, which resulted in a highly deformed structure. The SZ was simulated at 1130 °C, 500 to 750 rpm, and 1.2 revolution, which corresponds to true strain of 1.30 and deformation rate of 15 s-1. The grain refinement reported in the SZ was reproduced by the torsion tests, but morphological differences were observed due to the absence of stirring in the physical simulation. Dynamic recovery and dynamic recrystallization of the austenite were observed, as well as the continuous dynamic recrystallization of the ferrite / Mestrado / Materiais e Processos de Fabricação / Mestre em Engenharia Mecânica

Les termes « retournement », « renversement », « inversion », « conversion » etc. appartiennent à un lexique récurant dans les textes de Bergson. La présence fréquente de ces mots sous sa plume, et des adjectifs et des verbes associés, annonce notre point de départ. De ce lexique nous prenons l’élan pour dévoiler une lecture de Bergson à travers un filtre qu’il faut, avant tout, bien calibré. C’est ainsi qu’une image surgit ; image qu’il faut prendre, au premier abord, dans un sens tout à fait vague, et que nous considérons comme «image médiatrice»; image, ensuite, qui se clarifie comme «centrale» ou «primitive» à partir de laquelle d’autres images rayonnent. À la recherche du style de la pensée, à travers des moments de l’écriture plus que des thèmes, nous parcourrons les œuvres majeures de Bergson pour mettre en lumière des moments de modification, soit proposés par l’auteur dans sa doctrine, soit envisageables dans la pratique de la pensée, dans son exercice, ou, autrement dit, dans l’application de la méthode. Une difficulté majeure s’impose pour demeurer irrésolue, mais plein d’une tension féconde : le paradoxe d’exprimer l’inexprimable se mêle avec celui d’explorer le bergsonisme à partir de sa langue d’expression. Ce parcours, semé d'impasses, nous conduira à l’identification de deux moments principaux: un moment de retournement subjectif-épistémologique et un moment ontologique-métaphysique. Le premier concerne le sujet et sa dimension existentielle (voir sa conduite) en tension avec la méthode philosophique en tant que inversion de la destination spontanément pratique de l’intelligence. Le deuxième touche directement la doctrine et, notamment, la théorie de la perception dans Matière et mémoire ainsi que la genèse de la matérialité et de l’intellectualité dans L’évolution créatrice. C’est dans l’œuvre de 1907 et dans ses possibles prolongements (que nous laissons entrevoir), qu’on trouve aussi la correspondance et la complication des deux moments. Avec eux nous atteignons l’image conclusive d’un accord reversable à travers lequel faire résonner la philosophie de Bergson. / Such terms as « retournement », « renversement », « inversion », « conversion » etc. belong to a recurrent lexicon in Bergson’s works. The frequent presence in his writings of these words, and related adjectives and verbs, announces our departing point. Its from this lexicon that we move to unveil our reading of Bergson through a filter which, first of all, must be well calibrated. Thus, an image arises, one that we must take, at first, with a certain vagueness, considering it « image médiatrice »; an image which then clarifies itself as «centrale» or «primitive», from which other images radiate. Looking for the style of thought, through moments of writings more then themes, we cover Bergson’s major works to uncover moments of change, whether proposed by the philosopher in his doctrine, or traceable in the practice of thought, its exercise, or, in other words, the application of the method. A major difficulty comes forth, unsolved, but full of fruitful tension: the paradox of expressing the inexpressible entwines itself with that of exploring bergsonism with its language of expression as a starting point. This path, dotted with impasses, will take us to the identification of two principal moments: a moment of subjective-epistemological reversal and an ontological-metaphysical one. The first one applies to the subject and its existential dimension (read behavior) in strained relationship with the philosophical method as inversion of the spontaneously practical destination of intelligence. The second one touches directly the doctrine and, in particular, the theory of perception in Matière et mémoire as well as the genesis of materiality and intellectuality in L’évolution créatrice. It’s in the 1907 work and its possible extensions (which we only glance at), that we also find the correspondence and complication of the two moments. With these we achieve the final image of an invertible chord through which Bergson’s philosophy resounds.

De part sa nature multi-physique, un pyromécanisme est un système complexe à modéliser et sa simulation nécessite la mise en oeuvre de plusieurs ressources de calcul spécifiques couplées. Le but de ce travail est de fournir un outil numérique capable de modéliser un pyromécanisme et de simuler son fonctionnement en intégrant les interfaces nécessaires au pilotage des différentes ressources de calcul. La faisabilité d'un tel outil est illustrée pour un pyromécanisme spécifique : l'enrouleur pyrotechnique de ceinture. La conception de l'outil numérique proposé est basée sur l'approche Orienté Objet (OO) pour modéliser la structure technologique du pyromécanisme et l'interfaçage avec les ressources de calcul externes. Le modèle OO technologique est construit par héritage des modèles Core Product Model (CPM) et Open Assembly Model (OAM) développés au NIST (National Institute of Standards and Technology). Grâce aux modèles CPM-OAM, un système mécanique peut être décrit comme une hiérarchie d'assemblages et de pièces, reliés par des liaisons cinématiques. La simulation complète du pyromécanisme enrouleur de ceinture requiert des ressources de calcul spécifiques : Un module simulant le fonctionnement du générateur de gaz de l'enrouleur a été développé, implémenté sous Scilab. Ce module calcule la pression exercée par le générateur de gaz sur la chaîne cinématique chargée de transmettre le mouvement jusqu'à la bobine enroulant la ceinture. L'une d'une bibliothèque C++ de calcul dynamique de solides rigides existante, Chrono::Engine, permet la simulation de la chaîne cinématique soumise à cette pression. L'outil numérique fournit l'ensemble des paramètres nécessaires aux ressources de calcul et pilote la co-simulation entre ces ressources (programme Scilab de combustion et calcul mécanique Chrono::Engine). L'identification des paramètres des modèles mis en oeuvre nécessite de caractériser expérimentalement le comportement des sous-systèmes, comme le générateur de gaz, et des composants déformables (barre de torsion intégrée dans la chaîne cinématique et ceinture de sécurité). Des dispos tifs d'essais conçus spécifiquement permettent l'identification le comportement de ces composants, soumis à des sollicitations dynamiques. La validation du démonstrateur réalisé en C++ est basée sur la comparaison des résultats des simulations avec les résultats d'essais expérimentaux du système entier l'enrouleur de ceinture. / The simulation of a pyromechanism is a complex task because of its multi-physics intrinsic nature. Consequently, various computing resources are needed to simulate each physical aspect. The goal of this project is to provide a numerical tool able to model a pyromechanism and to interface the different computing resources in order to simulate an equipment. Feasibility of such a tool is illustrated with a specific pyromechanism : pyrotechnic belt retractor. The design of the numerical tool is based on an Object Oriented Approach (OOA) to model both the technological aspects of the pyromechanism and the interfaces with computing resources. The technological OO model is based on “Core Product Model” (CPM) and on “Open Assembly Model” (OAM) of the NIST (National Institute of Standards and Technology). Thanks to CPM-OAM model, any mechanism can be described as a hierarchy of assemblies and parts, linked by associations (connections, kinematic link,...). The full simulation of the pyromechanism requires external computing resources: - a model for simulating a gas generator implemented under Scilab. It computes the pressure produced by the gas generator, coupled with displacement of the mechanical load. - a C++ library for mechanical simulation of rigid bodies : ChronoEngine the response of the mechanical system computed kinematic response under pressure from gas generator. The resulting software provides all parameters needed by these external computing resources and drives the ballistic and mechanical co-simulation. Parameter identifications of models ask for experimental characterization of sub-system, as gas generator and deformable part (torsion bar and safety belt). Experimental devices has been developed for identifying behavioral law under dynamic load. Validation of demonstrator, written in C++, is based on comparison between simulation results and experimental results of the pyrotechnic retractor.

Parafusos corticais são uns dos implantes mais utilizados na prática cirúrgica e são normalmente compostos por ligas metálicas como o aço inoxidável F-138 e a liga de titânio 6Al-4V e, quando inseridos no organismo humano, são submetidos a diversos esforços mecânicos. Assim, é necessário avaliar as propriedades mecânicas desses implantes. Portanto, o objetivo deste estudo foi analisar o comportamento mecânico de parafusos corticais de aço inoxidável e de liga de titânio, de fabricação nacional, em ensaio de torção. Vinte parafusos de aço inoxidável foram divididos em quatro grupos (1,2,3,4) e o mesmo foi feito com os parafusos de liga de titânio. Primeiramente, suas medidas-padrão foram analisadas de acordo com a Norma Brasileira NBR ISO 5835:1996. Nos dois grupos 1 (de aço inoxidável e de liga de titânio), o ângulo de rotação foi mensurado por um goniômetro e o ensaio de torção foi manual. Já os parafusos dos dois grupos 2 foram ensaiados em uma máquina de torção. Os parafusos dos grupos 3, primeiramente, foram inseridos em cortical óssea suína e, posteriormente submetidos à torção. Nos dois grupos 4, os parafusos foram submetidos à torção sucessiva e, posteriormente submetidos à torção na máquina. Na análise estatística das propriedades mecânicas, os resultados apresentaram diferença significativa no torque no limite de proporcionalidade entre o grupo 1 e os demais grupos de aço inoxidável e entre o grupo 1 e os demais grupos de liga de titânio, sugerindo um possível erro metodológico no ensaio de torção manual. No torque no limite máximo houve diferença significativa entre o grupo 4 de liga de titânio e os grupos 2 e 3, mostrando que a torção sucessiva pode comprometer esta propriedade. Na rigidez torcional, foi demonstrada diferença estatística significativa entre os grupos 1 e 3 de liga de titânio. Na tenacidade torcional, houve diferença significativa entre o grupo 1 e os demais grupos de liga de titânio, entre o grupo 2 e os grupos 3 e 4 de aço inoxidável e entre todos os grupos de aço inoxidável e todos os grupos de liga de titânio. Conclui-se que, em geral, os parafusos de aço inoxidável apresentaram tenacidade torcional superior aos parafusos de liga de titânio, mas nas demais propriedades estes dois biomateriais apresentaram resultados semelhantes / Cortical bone screws are one of the most used implants in the surgical practice and the stainless steel (ASTM F-138) and titanic (6Al-4V) are the most common alloys used to manufacture them. When inserted into the bone such implants undergo several types of mechanical stress and, therefore, it is very useful to know their mechanical behavior. The purpose of the present study was to compare the mechanical properties of cortical bone screws made up of stainless steel and titanic alloy as tested in torsion. Twenty stainless steel screws were divided into four groups (1,2,3,4) and the same was made for the titanic alloy screws. First, the screw dimension were checked in accordance to the brazilian standard regulations. In groups 1 (either stainless steel or titanic alloy) the angle of rotation was measured with a goniometer and the torsion test was manual. For groups 2 the screws were tested in torsion in a testing machine. In groups 3, firstly, the screws were inserted into suine bone and, later, removed and submitted to torsion. In groups 4 the screws were tested in successive loading and unloading cycles in torsion and, later, submitted to torsion. The results showed statistically significant difference for the yield torque among the group 1 and the other groups of stainless steel and among the group 1 and the other groups of titanic alloy, which suggest a possible methodological error in manual torsion. For the ultimate torque there was difference among titanic groups 4, 2 and 3, showing that repeated torsion can affect such property. For the torsional stiffness there was statistical difference between titanic groups 1 and 3. The torsional tenacity was different among the 1 and the other titanic groups, also there was difference among stainless steel groups 2, 3 and 4. Finally, there was statistical difference among all stainless steel and titanic alloy groups, that, in general, the stainless steel screws showed greater torsional tenacity in comparison with the titanic alloy screws, but for the other torsional properties they displayed a similar behavior

Parafusos corticais são uns dos implantes mais utilizados na prática cirúrgica e são normalmente compostos por ligas metálicas como o aço inoxidável F-138 e a liga de titânio 6Al-4V e, quando inseridos no organismo humano, são submetidos a diversos esforços mecânicos. Assim, é necessário avaliar as propriedades mecânicas desses implantes. Portanto, o objetivo deste estudo foi analisar o comportamento mecânico de parafusos corticais de aço inoxidável e de liga de titânio, de fabricação nacional, em ensaio de torção. Vinte parafusos de aço inoxidável foram divididos em quatro grupos (1,2,3,4) e o mesmo foi feito com os parafusos de liga de titânio. Primeiramente, suas medidas-padrão foram analisadas de acordo com a Norma Brasileira NBR ISO 5835:1996. Nos dois grupos 1 (de aço inoxidável e de liga de titânio), o ângulo de rotação foi mensurado por um goniômetro e o ensaio de torção foi manual. Já os parafusos dos dois grupos 2 foram ensaiados em uma máquina de torção. Os parafusos dos grupos 3, primeiramente, foram inseridos em cortical óssea suína e, posteriormente submetidos à torção. Nos dois grupos 4, os parafusos foram submetidos à torção sucessiva e, posteriormente submetidos à torção na máquina. Na análise estatística das propriedades mecânicas, os resultados apresentaram diferença significativa no torque no limite de proporcionalidade entre o grupo 1 e os demais grupos de aço inoxidável e entre o grupo 1 e os demais grupos de liga de titânio, sugerindo um possível erro metodológico no ensaio de torção manual. No torque no limite máximo houve diferença significativa entre o grupo 4 de liga de titânio e os grupos 2 e 3, mostrando que a torção sucessiva pode comprometer esta propriedade. Na rigidez torcional, foi demonstrada diferença estatística significativa entre os grupos 1 e 3 de liga de titânio. Na tenacidade torcional, houve diferença significativa entre o grupo 1 e os demais grupos de liga de titânio, entre o grupo 2 e os grupos 3 e 4 de aço inoxidável e entre todos os grupos de aço inoxidável e todos os grupos de liga de titânio. Conclui-se que, em geral, os parafusos de aço inoxidável apresentaram tenacidade torcional superior aos parafusos de liga de titânio, mas nas demais propriedades estes dois biomateriais apresentaram resultados semelhantes / Cortical bone screws are one of the most used implants in the surgical practice and the stainless steel (ASTM F-138) and titanic (6Al-4V) are the most common alloys used to manufacture them. When inserted into the bone such implants undergo several types of mechanical stress and, therefore, it is very useful to know their mechanical behavior. The purpose of the present study was to compare the mechanical properties of cortical bone screws made up of stainless steel and titanic alloy as tested in torsion. Twenty stainless steel screws were divided into four groups (1,2,3,4) and the same was made for the titanic alloy screws. First, the screw dimension were checked in accordance to the brazilian standard regulations. In groups 1 (either stainless steel or titanic alloy) the angle of rotation was measured with a goniometer and the torsion test was manual. For groups 2 the screws were tested in torsion in a testing machine. In groups 3, firstly, the screws were inserted into suine bone and, later, removed and submitted to torsion. In groups 4 the screws were tested in successive loading and unloading cycles in torsion and, later, submitted to torsion. The results showed statistically significant difference for the yield torque among the group 1 and the other groups of stainless steel and among the group 1 and the other groups of titanic alloy, which suggest a possible methodological error in manual torsion. For the ultimate torque there was difference among titanic groups 4, 2 and 3, showing that repeated torsion can affect such property. For the torsional stiffness there was statistical difference between titanic groups 1 and 3. The torsional tenacity was different among the 1 and the other titanic groups, also there was difference among stainless steel groups 2, 3 and 4. Finally, there was statistical difference among all stainless steel and titanic alloy groups, that, in general, the stainless steel screws showed greater torsional tenacity in comparison with the titanic alloy screws, but for the other torsional properties they displayed a similar behavior

Cette thèse concerne les homéomorphismes de surfaces.Soit f un difféomorphisme d'une surface M préservant l'aire et isotope à l'identité. Si f a un point fixe contractile isolé et dégénéré z0 avec un indice de Lefschetz égal à 1, et si l'aire de M est finie, nous prouverons au chapitre 3 que z0 est accumulé non seulement par des points périodiques mais aussi par des orbites périodiques au sens de la mesure. Plus précisément, la mesure de Dirac en z0 est la limite en topologie faible-étoile d'une suite de probabilités invariantes supportées par des orbites périodiques. Notre preuve est totalement topologique et s'applique au cas d'homéomorphismes en considérant l'ensemble de rotation local.Au chapitre 4, nous étudierons des homéomorphismes préservant l’aire et isotope à l’identité. Nous prouverons l’existence d'isotopies maximales particulières: les isotopies maximales à torsion faible. En particulier, lorsque f est un difféomorphisme ayant un nombre fini de points fixes tous non-dégénérés, une isotopie I joignant l'identité à f est à torsion faible si et seulement si pour tout point z fixé le long de I, le nombre de rotation (réel) ρ(I,z), qui est bien défini quand on éclate f en z, est contenu dans (-1,1). Nous démontrerons l'existence d'isotopies maximales à torsion faible, et nous étudierons la dynamique locale de feuilletages transverses à l'isotopie près des singularités isolées.Au chapitre 5, nous énoncerons une généralisation d'un théorème de Poincaré-Birkhoff local au cas où il existe des points fixes au bord. / This thesis concerns homeomorphisms of surfaces.Let f be an area preserving diffeomorphism of an oriented surface M isotopic to the identity. If f has an isolated degenerate contractible fixed point z0 with Lefschetz index one, and if the area of M is finite, we will prove in Chapter 3 that z0 is accumulated not only by periodic points, but also by periodic orbits in the measure sense. More precisely, the Dirac measure at z0 is the limit in weak-star topology of a sequence of invariant probability measures supported on periodic orbits. Our proof is purely topological and will works for homeomorphisms and is related to the notion of local rotation set.In chapter 4, we will define a kind of identity isotopies: torsion-low isotopies. In particular, when f is a diffeomorphism with finitely many fixed points such that every fixed point is not degenerate, an identity isotopy I of f is torsion-low if and only if for every point z fixed along the isotopy, the (real) rotation number ρ(I,z), which is well defined when one blows-up f at z, is contained in (-1,1). We will prove the existence of torsion-low maximal identity isotopies, and we will deduce the local dynamics of the transverse foliations of any torsion-low maximal isotopy near any isolated singularity.In chapter 5, we will generalize a local Poincaré-Birkhoff theorem to the case where there exist fixed points on the boundary

This report presents the degree project for a master's degree in Mechanical Engineeringat Luleå University of Technology performed by Emma Olsson at GKN ePowertrain in Köping. The aim of the thesis was to develop a calculation method to evaluate fatigue ina weld due to torsion. During the degree project, two di erent calculation methods weredeveloped - An analytical method and a numerical method. The analytical method is based on a calculation method already used at GKN for calculatingfatigue due to rotary bending, but with the adaptations required for when the weld issubjected to torsion. For this method, Wöhler's curve, Goodman and Gerber mean stresscorrection and Palmgren-Miner's rule have been used. The numerical method was performed in the commercial software FEMFAT, which hasbeen developed to calculate, among other things, fatigue and safety factors. This is asimulation program the company in question has, but previously not used for this purpose. During the process of developing these calculation methods, areas such as mean stresscorrection, fatigue strength and weld classi cation have been studied, and appropriatesettings for the simulation.This resulted in two calculation methods whose results differ greatly from each other.The analytical method is a very conservative method in which the fatigue damage that iscalculated becomes very high and according to the damage value the weld will fail. Forthe numerical method, on the other hand, the fatigue is very low and, according to thedamage value, will not fail. Based on this, it can be stated that the numerical method is the method considered mostreliable and should be further investigated and  nally used. However, it is not possible togive a precis conclusion of whether the methods correspond to the reality, since no physicaltesting have been performed.

[pt] Este trabalho de natureza experimental tem como objetivo estudar o comportamento de vigas de concreto submetidas à torção e reforçadas externamente com compósitos de fibras de carbono (CFC). Treze vigas de concreto com 2,0 m de comprimento e seção transversal de 30 cm х 60 cm foram testadas no Laboratório de Estruturas e Materiais do Departamento de Engenharia Civil (LEM/DEC) da Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio). As vigas foram divididas em quatro séries, sendo uma de referência, composta por quatro vigas sem reforço externo, e outras três séries constituídas por três vigas que foram reforçadas externamente com taxas crescentes de estribos de CFC. Com o propósito de estudar a contribuição do concreto e do reforço de CFC na resistência à torção de vigas, a armadura interna só foi colocada na região de aplicação de cargas e nos apoios para evitar a ruptura local e possibilitar o estudo da região central sem a parcela resistente devida à armadura interna de aço. Os resultados dos ensaios mostraram que as vigas reforçadas apresentaram aumento de carga de fissuração entre 16 por cento e 56 por cento e um acréscimo de resistência à ruptura entre 19 por cento e 47 por cento quando comparadas às vigas de referência. A rigidez das vigas na ruptura aumentou proporcionalmente ao crescimento da taxa de reforço como observado em outros ensaios encontrados na literatura. / [en] This research is an experimental study of torsion strengthening of concrete beams with carbon fibers composites. Thirteen concrete beams with 2.0 long and 30 x 60 cm cross section were tested in the Structures and Materials Laboratory of the Civil Engineering Department (LEM/DEC) of Pontifical Catholic University of Rio de Janeiro (PUC-Rio). The beams were divided in four series, the first one was called the reference series and consisted of four beams without external strengthening and each of the other three series was composed of three beams strengthened with increasing rates of external carbon fibers composites stirrups. In oder to allow the study of the central region without the contribution of the steel reinforcement, the internal steel reinforcement was placed only at points of loads application and supports to prevent the local rupture. The tests results showed that the strengthened beams had an increase of the cracking load between 16 per cent and 56 per cent, and an increase of the rupture load between 19 per cent and 47 per cent when compared to the reference beams. The ultimate resistance of the beams increased proportionally to the rate of external carbon fibers composites strengthening, as was observed by other researchers.