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A concrete beam is rarely subjected to pure torsion loading. However, in many design applications a beam is subjected to torsional loads in addition to bending and shear loading. The American Concrete Institute has developed a specification for the design of beams subjected to torsion. These specifications are found in ACI 318-83. In this research report, a computer program is presented, using these specifications, which will aid engineers in the design of reinforcement for concrete beams subjected to torsional loading. The provisions of the ACI 318-83 specification and their implementation into the computer program are presented. A sample problem is solved to compare the results of normal hand calculations to the results of the computer program. A listing of the computer program, written in Microsoft's GW BASIC, is provided. The designer enters information pertaining to the beams cross sectional properties, material properties and loading conditions. The program computes the concrete and reinforcement strength requirements and determines the amount of reinforcement required. The stirrup spacing and longitudinal reinforcement required are then determined and output to the designer.

<p>Existence of closed geodesics on compact manifolds was first proved by Lyusternik and Fet in the 1950s using Morse theory, and the corresponding problem for orbifolds was studied by Guruprasad and Haefliger, who proved existence of a closed geodesic of positive length in numerous cases. In this thesis, we develop an alternative approach to the problem of existence of closed geodesics on compact orbifolds by studying the geometry of group actions. We give an independent and elementary proof that recovers and extends the results of Guruprasad and Haefliger for developable orbifolds. We show that every compact orbifold of dimension 2, 3, 5 or 7 admits a closed geodesic of positive length, and we give an inductive argument that reduces the existence problem to the case of a compact developable orbifold of even dimension whose singular locus is zero-dimensional and whose orbifold fundamental group is infinite torsion and of odd exponent. Stronger results are obtained under curvature assumptions. For instance, one can show that infinite torsion groups do not act geometrically on simply connected manifolds of nonpositive or nonnegative curvature, and we apply this to prove existence of closed geodesics for compact orbifolds of nonpositive or nonnegative curvature. In the general case, the problem of existence of closed geodesics on compact orbifolds is seen to be intimately related to the group-theoretic question of finite presentability of infinite torsion groups, and we explore these and other properties of the orbifold fundamental group in the last chapter.</p> / Doctor of Philosophy (PhD)

The level of safety associated with the ACI Standard 318-83 design criteria for torsional reinforced concrete members is evaluated. Advanced first-order, second-moment reliability analysis is used to compute the reliability index. Reinforced concrete beams, subjected to both equilibrium and compatibility torsion, are analyzed. The uncertainties associated with the various torsion design parameters are included in the reliability-based formulation. For beams designed to carry equilibrium torsion, reliability indices ranging from 3.10 to 3.65 are obtained. The reliability indices for the compatibility torsion designs, analyzed in this study, vary from 1.88 to 2.09. For a given beam section, the reliability index is found to decrease with an increase in beam reinforcement. When the live load is reduced for members having a load influence area greater than 400 ft 2, the reliability index is found to increase with increase in basic live load to nominal dead load ratio. / M.S.

[EN] Classically, the study of the contact with hyperplanes and hyperspheres has been realized by using the family of height and distance squared functions. On the first part of the thesis, we analyze the Taylor expansion of the exponential map up to order three of a submanifold $M$ immersed in $\r n.$ Our main goal is to show its usefulness for the description of special contacts of the submanifolds with geometrical models. As we analyze the contacts of high order, the complexity of the calculations increases. In this work, through the Taylor expansion of the exponential map, we characterize the geometry of order higher than $3$ in terms of invariants of the immersion, so that the effective computations in specific cases become more affordable. It allows also to get new geometric insights. On the second part of the thesis, we introduce the concept of critical point of a smooth map between submanifolds. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its focal set can also be interpreted as the image of the critical points of the {\it normal map} $\nu(m,u): NM\to \r{k+n}$ defined by $\nu(m,u)=\pi_N(m,u)+ u,$ for $m\in M$ and $u\in N_mM,$ where $\pi_N:NM\to M$ denotes the normal bundle. In the same way, the parabolic set of a differential submanifold is given through the analysis of the singularities of the height functions over the submanifold. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its parabolic set can also be interpreted as the image of the critical points of the {\it generalized Gauss map} $\psi(m,u): NM\to \r{k+n}$ defined by $\psi(m,u)= u,$ for $u\in N_mM.$ Finally, we characterize the asymptotic directions as the tangent set of a $k$-dimensional manifold $M$ immersed in $\r{k+n}$ throughout the study of the singularities of the tangent map $\Omega(m,y): TM\to \r{k+n}$ defined by $\Omega(m,y)=\pi(m,y)+y,$ for $y\in T_mM,$ where $\pi:TM\to M$ denotes the tangent bundle. We describe first the focal set and its geometrical relation to the Veronese of curvature for $k$-dimensional immersions in $\r{k+n}.$ Then we define the $r$-critical points of a differential map $f:H \to K$ between two differential manifolds and characterize the $2$ and $3$-critical points of the normal map and generalized Gauss map. The number of these critical points at $m\in M$ may depend on the degeneration of the curvature ellipse and we calculate those numbers in the particular case that $M$ is an immersed surface in $\r{4}$ for the normal map and $\r{5}$ for the generalized Gauss map. / [ES] En general, el estudio del contacto con hiperplanos e hiperesferas se ha llevado a cabo usando la familia de funciones altura y la función distancia al cuadrado. En la primera parte de la tesis analizamos el desarrollo de Taylor de la aplicación exponencial hasta orden 3 de una subvariedad $M$ inmersa en $\r n.$ Nuestro principal objetivo es mostrar su utilidad en el estudio de contactos especiales de subvariedades con modelos geométricos. A medida que analizamos los contactos de orden mayor, la complejidad de las cuentas aumenta. En este trabajo, a través del desarrollo de Taylor de la aplicación exponencial, caracterizamos la geometría de orden mayor que $3$ en términos de invariantes geométricos de la inmersión, por lo que el trabajo con las cuentas en casos especiales se convierte en más manejable. Esto nos permite también obtener nuevos resultados geométricos. En la segunda parte de la tesis se introduce el concepto de punto crítico de una aplicación regular entre subvariedades. Si consideramos una variedad diferenciable $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto focal puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación normal} $\nu(m,u): NM\to \r{k+n}$ definida por $\nu(m,u)=\pi_N(m,u)+ u,$ para $m\in M$ y $u\in N_mM,$ donde $\pi_N:NM\to M$ denota el fibrado normal. De la misma manera, el conjunto parabólico de una subvariedad diferencial viene dado por el análisis de las singularidades de la función altura sobre la subvariedad. Si consideramos una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto parabólico puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación generalizada de Gauss} $\psi(m,u): NM\to \r{k+n}$ definida por $\psi(m,u)= u,$ donde $u\in N_mM.$ Finalmente, caracterizamos las direcciones asintóticas como el conjunto de direcciones del tangente de una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n}$ a través del estudio de las singularidades de la aplicación tangente $\Omega(m,y): TM\to \r{k+n}$ definida por $\Omega(m,y)=\pi(m,y)+y,$ para $y\in T_mM,$ donde $\pi:TM\to M$ denota el fibrado tangente. Describimos primero el conjunto focal y su relación geométrica con la Veronese de curvatura para una variedad $k$ dimensional inmersa en $\r{k+n}.$ Entonces, definimos los puntos $r$-críticos de una aplicación $f:H \to K$ entre dos subvariedades y caracterizamos los puntos $2$ y $3$ críticos de la aplicación normal y la aplicación generalizada de Gauss. El número de estos puntos críticos en $m\in M$ depende de la degeneración de la elipse de curvatura y calculamos ese número en el caso particular de una superficie inmersa en $\r{4}$ para la aplicación normal y $\r{5}$ para la aplicación generalizada de Gauss. / [CA] En general, l'estudi del contacte amb hiperplans i hiperesferes s'ha dut a terme utilitzant la família de funcions altura i la funció distància al quadrat. A la primera part de la tesi analitzem el desenvolupament de Taylor de l'aplicació exponencial fins a ordre 3 d'una subvarietat $M$ immersa en $\r n.$ El nostre principal objectiu és mostrar la seua utilitat en l'estudi de contactes especials de subvarietats amb models geomètrics. A mesura que analitzem els contactes d'ordre major, la complexitat dels comptes augmenta. En aquest treball, a través del desenvolupament de Taylor de l'aplicació exponencial, caracteritzem la geometria d'ordre major que $ 3 $ en termes d'invariants geomètrics de la immersió, de manera que el treball amb els comptes en casos especials es converteix en més manejable. Això ens permet també obtenir nous resultats geomètrics. A la segona part de la tesi s'introdueix el concepte de punt crític d'una aplicació regular entre subvarietats. Si considerem una varietat diferenciable $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt focal pot ser interpretat com la imatge dels punts crítics de la {\it aplicació normal} $ \nu (m, u): NM \to \r {k + n} $ definida per $ \nu (m, u) = \pi_N (m, u) + o, $ per $ m \in M $ i $ u \in N_mM, $ on $ \pi_N: NM \to M $ denota el fibrat normal. De la mateixa manera, el conjunt parabòlic d'una subvarietat diferencial ve donat per l'anàlisi de les singularitats de la funció altura sobre la subvarietat. Si considerem una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt parabòlic pot ser interpretat com la imatge dels punts crítics de la {\it aplicació generalitzada de Gauss} $ \psi (m, u): NM \to \r{k + n} $ definida per $ \psi (m, u) = u, $ on $ u \in N_mM. $ Finalment, caracteritzem les direccions asimptòtiques com el conjunt de direccions del tangent d'una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r{k + n} $ a través de l'estudi de les singularitats de l'aplicació tangent $ \Omega (m, y): TM \to \r {k + n} $ definida per $ \Omega (m, y) = \pi (m, y) + y, $ per $ y \in T_mM, $ on $ \pi: TM \to M $ denota el fibrat tangent. Descrivim primer el conjunt focal i la seva relació geomètrica amb la Veronese de curvatura per a una varietat $ k $ dimensional immersa en $ \r{k + n}. $ Llavors, definim els punts $ r $-crítics d'una aplicació $ f: H \to K $ entre dues subvarietats i caracteritzem els punts $ 2 $ i $ 3 $ crítics de l'aplicació normal i l'aplicació generalitzada de Gauss. El nombre d'aquests punts crítics en $ m \in M $ depèn de la degeneració de l'el·lipse de curvatura i calculem aquest nombre en el cas particular d'una superfície immersa en $ \r{4} $ per a l'aplicació normal i $ \r{5} $ per a l'aplicació generalitzada de Gauss. / García Monera, M. (2015). r-critical points and Taylor expansion of the exponential map, for smooth immersions in Rk+n [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/50935

Functionally graded structures have material properties that continuously vary in one or more directions. Examples include human teeth, seashells, bamboo stems and human organs, where the varying volume fraction of fibers and their orientations optimize functionality. Deformations of such structures typically involve bending, stretching, and shearing. An everyday example of shearing deformation is the twisting of wet fabrics to extract water. In this study, we analytically examine the large deformations of functionally graded Mooney-Rivlin circular cylinders, focusing on how radial grading of material moduli can be beneficially utilized. We investigate the finite deformations caused by pressures applied to the bounding surfaces and axial loads or twisting moments on the end faces. We also simulate residual stresses in a hollow cylinder either by inverting it inside out or by closing a longitudinal wedge opening parallel to the cylinder axis through axisymmetric deformation before other loads are applied. It is observed that the maximum shear stress in an initially stress-free Mooney-Rivlin cylinder can occur at an interior point. In the absence of axial forces on the end faces, the cylinder elongates when twisted, with the degree of elongation depending on the grading of the material moduli. These findings should aid numerical analysts in verifying their algorithms for simulating large deformations of rubber-like materials modeled by the Mooney-Rivlin relation. / Master of Science / Functionally graded materials (FGMs) are composites whose properties vary in one or more directions to exploit the functionality of the individual components. An example would be a sheet of material that is fully metallic on one side and fully ceramic on the other, with properties changing gradually through the thickness. The Mooney-Rivlin model is used to capture the stress-strain response of rubber-like materials. Therefore, functionally graded Mooney-Rivlin cylinders are rubber-like composite cylinders whose properties change throughout their thickness. Functionally graded cylinders have a wide array of applications, including in pressure vessels, vibration damping systems and tires. Therefore, having a thorough understanding of the stresses induced in these cylinders when subjected to loads is essential for safe and reliable designs. This research aims to investigate the effects of material inhomogeneity on the stresses induced in functionally graded cylinders subjected to torsion, radial expansion, eversion, and various combinations of these. Furthermore, realizing that stresses induced during the fabrication process cannot be easily quantified, we study a problem in which these induced stresses can be determined and analyze their effect on subsequent deformations of the cylinder when subjected to torsion and radial expansion. To achieve this aim, we use a member of Ericksen's third family of universal deformations, which mathematically describes torsion, inflation, and eversion, along with the Mooney-Rivlin model to determine the stress state resulting from deformation. The results show that for cylinders of the same geometry in the stress-free undeformed state subjected to identical surface tractions, material inhomogeneities greatly influence the stresses in the cylinder. It was also found that the magnitude of the normal and shear stresses, axial stretch, and the geometry of the cylinder after deformation depend on the type of deformation and functional grading. Additionally, the results indicate that the normal stresses induced in an initially stressed cylinder are much greater than those in a cylinder that is initially stress-free when subjected to the same boundary conditions.

Les bâtiments avec retrait excentré en élévation deviennent de plus en plus populaires, dus à leurs avantages tant pratiques qu’architecturaux. Cependant, la géométrie particulière de ce type de bâtiment dans la direction perpendiculaire au retrait apporte une sensibilité accrue au comportement en torsion. Cette étude vise à élargir les connaissances concernant les effets du niveau et du degré de retrait sur le comportement couplé en translation-torsion des bâtiments avec retrait excentré en élévation dans la direction perpendiculaire au retrait ainsi qu’à évaluer la validité et la pertinence des exigences relativement à la sensibilité à la torsion proposées par les codes du bâtiment et la documentation scientifique. Les résultats suggèrent que la variation du niveau et le degré de retrait, c’est-à-dire la variation de la géométrie des bâtiments avec retrait excentré en élévation, dans la direction perpendiculaire au retrait, influence de manière significative leur comportement ainsi que leur sensibilité à la torsion. Mots-clés : Bâtiment avec retrait excentré en élévation, dynamique des structures, comportement sous sollicitation sismique, comportement couplé en translation-torsion, évaluation des exigences des codes du bâtiment. / Asymmetric setback buildings are becoming increasingly popular because of the architectural and practical advantages they offer. However, the characteristic geometry of this type of building comes, in the direction perpendicular to the setback, with an increased sensitivity to torsional motion. This study is concerned with the growth of the body of knowledge concerning the effects of the level and degree of setback on the coupled translational-torsional behaviour of asymmetric setback buildings in their direction perpendicular to the setback and the assessment of the torsional sensitivity requirements as proposed by the different building codes and the literature. Results suggest that the variation of the level and the degree of setback has a significant effect on the coupled translational-torsional behaviour of asymmetric setback structures in the direction perpendicular to the setback and thus on their sensitivity to torsional behaviour. Keywords : Asymmetric setback buildings, structural dynamics, seismic behaviour, translational-torsional behaviour, code requirements assessment.

En soudage en phase solide, si la température peut avoir un rôle favorable, une sollicitation mécanique est également nécessaire pour s’affranchir de la couche d’oxyde recouvrant naturellement l’aluminium. Dans ce travail, on a ainsi cherché à comprendre l’importance de la sollicitation mécanique vis-à-vis de la création des jonctions métalliques. Dans ce but, 2 essais de soudabilité à froid ont été mis en place. L’essai de compression plane (CP) a pour but d’augmenter la surface à l’interface de soudage, de sorte à morceler la couche d’oxyde. Grâce à la microscopie, à une analyse par EF et à un modèle tensoriel de caractérisation de l’évolution des surfaces, les essais ont montré que, plus que l’importante déformation globale, le soudage se produit dans les zones de cisaillement maximum.Par conséquent, le second essai repose sur le cisaillement de l’interface de soudage : un tube sectionné est soumis à un effort de compression et de torsion alternée. Comme pour l’essai de CP, l’influence de divers paramètres a été étudiée. Parmi ceux-ci, l’état de surface (rugosités et propreté), l’angle de torsion (faible amplitude) et le nombre de cycles ont un rôle prépondérant. Les assemblages soudés ont ensuite été caractérisés mécaniquement et observés en microscopie (MEB-FEG, EBSD). Par rapport à l’essai de CP, on a pu constater une meilleure quantité et qualité des jonctions en compression-torsion alternée. De plus, un modèle thermodynamique a permis de conclure que les énergies mises en jeu sont trop faibles pour permettre un échauffement significatif : le soudage, sur environ 50% de l’interface en l’état actuel des choses, n’est réalisé que par des effets mécaniques locaux. / In solid-state welding, if the temperature generally has an important role (diffusion, recrystallization, etc.), a mechanical load is also necessary to override the oxide layer which naturally covers aluminium alloys. This work aims to understand the influence of the mechanical load on the formation of metallic bonds. To this end two cold weldability tests have been introduced. Firstly the plane strain channel-die compression of two cuboids sample aims to increase the surface at the welding interface in order to break up the oxide layer. Thanks to microscopy, a FEA model and a tensorial model of surfaces evolution, those results showed that, more than the important global deformation, welds were created in areas with maximum shear. Subsequently the second test aims to shear the welding interface: a tube is cut through its section and undergoes both a compression and a cyclic torsion load. As for our first weldability test, the influence of some parameters has been studied. Among them, the surface condition (roughness and cleanliness), the torsion angle (low amplitude) and the number of cycles are the most influential. Then the welded joints have been mechanically tested and microscopically observed (FEG-SEM and EBSD). In comparison with our first test, a higher quality and quantity of the joining has been showed. Moreover, a thermodynamic model concludes that the energies involved in this experimental process are too low to imply any local heating: the joining, on 50% of the welding interface as things stand, is only achieved thanks local mechanical effects.

L’extraction des cellules cancéreuses d’un fluide corporel est une procédure importante lors d’un diagnostic clinique et d’une thérapie. En particulier, lorsque la technique de séparation est basée sur la chromatographie cellulaire, il est important de disposer de connaissances précises sur les capacités de liaison des cellules cibles avec le milieu poreux. Pour cette raison, des expériences utilisant la tomodensitométrie à résolution temporelle ont été́ conçues et réalisées à l’Installation Européenne de Rayonnement Synchrotron. Les distributions des courbures et des torsions des trajectoires de cellules situées dans suspension s’écoulant à travers un milieu poreux sont des informations précieuses pour caractériser l’efficacité́ des procédés chromatographiques. Cependant, le calcul de la torsion est un défi car étant basé sur des dérivées d’ordre supérieur qui sont très sensibles au bruit de discrétisation. Cette thèse présente deux nouvelles méthodes d’estimation des courbures et des torsions de trajectoires de particules données respectivement sous la forme de points discrets connectes ou non connectes. La première méthode est basée sur une approche dite d’approximation de Fourier. Des études de cas ont mis en lumière une diminution de l’erreur d’estimation des torsions d’au moins 65% par rapport à la méthode de référence d’approximation par les splines. Par ailleurs, le paramètre de lissage de l’approximation de Fourier peut rester constant pour une large plage de résolutions latérales et pour différentes valeurs de courbures et de torsion. La méthode dite d’approximation de Fourier n’étant pas applicable à des courbes échantillonnées avec un pas variable, une deuxième méthode basée sur la discrétisation des formules géométriques différentielles (DDGF) a été́ développée. L’approximation par les splines et la DDGF conduisent à des erreurs moyennes similaires. Cependant, le masque filtrant reste inchangé́ pour le DDGF, alors que le paramètre de lissage de l’approximation par les splines doit être adapté à la forme ainsi qu’au pas d’échantillonnage de la courbe / The extraction of cancerous cells from body uids is an important procedure in clinical diagnostics and therapy. Notably, when the separation technique is based on cell chromatography, it is important to have precise knowledge about binding capacities of target cells in porous media. Therefore, experiments using time-resolved micro-computed tomography were designed and carried out at the European Synchrotron Radiation Facility. The curvature and torsion distributions of cell paths in a two-phase ow through a porous medium are valuable information to characterize the efficiency of chromatographic processes. However, the computation of torsion is very challenging, since it is based on higher order derivatives which are very sensitive towards discretization noise. In this thesis, two new curvature and torsion estimation methods of particle paths are presented. The first method is based on a Fourier approximation. Case studies showed a decrease of the torsion estimation error of at least 65% compared to the commonly used spline approximation. Moreover, the smoothing parameter of the Fourier approximation can remain unchanged for both a wide range of lateral resolutions and curvatures and torsion values. Since this Fourier approximation approach cannot be applied at non-equidistant points, a second method based on the discretization of the differential-geometric formulas (DDGF) was developed. The spline approximation and the DDGF led to similar mean torsion errors. However, the filter mask remains unchanged for the DDGF, whereas the smoothing parameter of the spline approximation must be adapted to the curve shape and discretization

Les algies pelviennes aigues constituent le premier motif de consultation aux urgences gynécologiques. Les étiologies possibles de ces algies pelviennes aigues sont nombreuses et incluent à la fois des affections gynécologiques et non gynécologiques. Certaines de ces affections peuvent, en l’absence de diagnostic précoce et d’un traitement adapté, avoir des conséquences très graves. Dans ce travail, nous avons développé un autoquestionnaire standardisé de manière qualitative dédié aux urgences gynécologiques par des entretiens structurés. Nous avons ensuite construit des modèles de prédiction clinique dédiés (i) au diagnostic de rupture tubaire chez les patientes porteuses de grossesses extra-utérines et (ii) au diagnostic de torsion d’annexe à partir de cet autoquestionnaire. Après avoir défini le concept d’urgence potentiellement à risque en gynécologie, nous avons proposé (iii) un modèle de prédiction clinique de celles-ci basé sur notre autoquestionnaire standardisé. A l’issue du développement de ces modèles, nous avons sélectionné certains items de l’autoquestionnaire standardisé afin d’en proposer une version simplifiée. L’utilisation de nos modèles pour le tri et le diagnostic des patientes aux urgences gynécologiques pourrait permettre d’optimiser la prise en charge des patientes. Dans les groupes à haut risque de pathologie, les patientes pourraient bénéficier d’une prise en charge plus rapide avec une éventuelle diminution de la morbidité secondaire à la pathologie. Pour les patientes classées à bas risque, une désescalade des examens complémentaires et des chirurgies inutiles pourrait aussi permettre une diminution de la morbidité d’origine iatrogène. / Acute pelvic pain is the main reason for emergency gynecologic consultation. The possible etiologies of acute pelvic pain are numerous and include both gynecological and non gynecological diseases. Some of these conditions may, in the absence of early diagnosis and appropriate treatment, have very serious consequences. In this work, we developed qualitatively a standardized self-assessed questionnaire dedicated to gynecological emergencies by structured interviews. We then developed clinical prediction rules for (i) the diagnosis of tubal rupture in patients who have ectopic pregnancies and (ii) the diagnosis of adnexal torsion. After a definition of the concept of potentially at risk emergencies in gynecology, we have proposed (iii) a clinical prediction rule based on our questionnaire. Following the development of these models, we selected items from the self-assessed questionnaire in order to propose a simplified version. Using our models for triaging and diagnosis of patients with gynecologic emergencies may optimize the management of patients. In groups at high risk of disease, patients may benefit from faster medical management with a possible decrease in morbidity. For patients classified as low risk, decrease of complementary tests and unnecessary surgery could also allow a reduction of iatrogenic morbidity.