Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature ($theta,partial_s theta$) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points. / Master of Science

O presente trabalho foi realizado por meio de uma abordagem tríplice do problema de compressão dinâmica em risers, fundamentado em ensaios em um Calibrador Hidrodinâmico, com posterior confrontação dos resultados com formulações analíticas e o uso de programas comerciais dedicados ao estudo da estática e dinâmica de linhas flexíveis. O principal objetivo foi a determinação acurada, a partir de uma instrumentação pouco invasiva, dos comprimentos das ondas de flexão geradas no TDP, durante a compressão dinâmica. Esse objetivo, de per si, encerra o caráter de ineditismo da presente tese. Os ensaios consistiram na realização de movimentos circulares no topo de um modelo flexível lançado em catenária, sob diversas configurações, totalizando um total de 72 experimentos: foram utilizados três frequências de movimento, três amplitudes, quatro ângulos de topo e dois sentidos de rotação. Um sistema de monitoramento óptico foi utilizado como principal instrumentação. Além desse equipamento, foi utilizada uma célula de carga, posicionada entre o equipamento que prescrevia os movimentos ao modelo flexível e uma rótula, que permitia que a célula de cargas e movimentasse solidariamente ao sistema. Rotinas numérica próprias foram utilizadas para o pós-processamento dos dados obtidos. Os resultados foram, então, comparados com formulações analíticas constantes da literatura, bem como a adaptação da equação para a carga crítica de flambagem de vigas curvas, para as condições de contorno dos ensaios realizados. Como resultado principal, é possível citar a confirmação experimental da suposição corrente com relação ao número de onda associado às ondas de flexão geradas na compressão dinâmica, até então assumida como uma hipótese ad hoc. Além disso, o procedimento adotado, embasado teoricamente, foi utilizado desde o estabelecimento do material com que o modelo foi construído, passando pela elaboração racional da matriz de ensaios e finalizando com as análises realizadas, quando os resultados experimentais foram confrontados com as previsões analíticas. / This work was carried out through a threefold approach to dynamic compression in risers, based on tests in a Hydrodynamic Calibrator, with subsequent comparison of results with analytical formulations and the use of commercial softwares dedicated to the study of static and dynamic flexible lines. The main aim was an accurate determination, from a minimally invasive instrumentation, the lengths of flexural waves generated in the TDP, during dynamic compression. This goal, in itself, is the novelty of this thesis. The tests consisted in performing circular motion on top of a flexible catenary model launched under several conditions, amounting to a total of 72 experiments: three motion frequencies, three imposed amplitudes , four top angles and clockwise and counter-clockwise rotation. A tracking monitoring system was used as main instrumentation. In such equipment, a load cell was used, positioned between rotor used to prescribe top movements at the top of a flexible model, allowing the load cell jointly move around a bar conected to the shaft motor. Numerical routines, made by author, were used for data post-processing. The results were then confronted with analytical formulations from specialized literature, as well as the adaptation of the equation for the buckling critical load for curved beams under the boundary conditions of the tests. As a main result, it is possible to mention the experimental confirmation of the current assumption with respect to the wave number associated with bending waves generated during the dynamic compression, hitherto assumed as an ad hoc hypothesis. In addition, the procedure adopted, based in analytical theories, was used since the establishment of the material with which the model is built, through the rational development of the test matrix and ending with the analyzes carried out when the experimental results were compared with analytical predictions.

This thesis presents the results of a numerical investigation of the whole range, large deflection behaviour of axially and rotationally restrained RC beams and interactions between beams and columns in RC frame structures exposed to fire. The dynamic explicit time integration algorithm implemented in the general finite element package ABAQUS/Explicit solver was used so as to overcome various modelling challenges including temporary instability, local failure of materials, non-convergence and long simulation time. Either load factoring or mass scaling may be used to speed up the simulation process. Validity of the proposed simulation model was checked by comparison of simulation results against relevant test results of restrained RC beams at ambient temperature and in fire. The validated ABAQUS/Explicit model was then used to conduct a comprehensive study of the effects of different levels of axial and rotational restraints on the whole range behaviour of RC beams in fire, including combined bending and compression due to restrained thermal expansion, bending failure, transition from compression to tension when catenary action develops and complete fracture of reinforcement at ultimate failure. The numerical results show that different bending failure modes (middle span sagging failure, end hogging failure due to fracture of tensile reinforcement, end hogging failure due to concrete crushing) can occur under different levels of boundary restraints. Furthermore, release of a large amount of energy during the rapid transition phase from compression to tension in a beam prevents formation of a three hinge mechanism in the beam under bending. The numerical results have also revealed that reliable catenary action develops at large deflections following bending failure only if bending failure is governed by compressive failure of concrete at the end supports whereby a continuous tension path in the beam can develop in the top reinforcement. To allow fire engineering practice to take into consideration the complex restrained RC beam behaviour in fire, a simplified calculation method has been developed and validated against the numerical simulation results. The proposed method is based on sectional analysis and meets the requirements of strain compatibility and force equilibrium. The validation study results have shown that the simplified method can satisfactorily predict the various key quantities of restrained beam axial force and beam deflection-fire exposure time relationships, with the simplified method generally giving results on the safe side. The validated explicit finite element model in ABAQUS was also used to investigate structural interactions between beams and columns within an RC frame structure with different fire exposure scenarios. When fire exposure involves beams and columns located in edge bays of a frame, catenary action cannot develop. Also due to thermal expansion of the connected beam, additional bending moments can generate in the columns. Furthermore, very large hogging moments can be induced at the beam end connected to the internal bay. It is necessary to include these bending moments when designing beams and columns under such fire conditions. Catenary action can develop in interior beams of the frame when fire exposure is in interior bays where the beams have high degrees of axial restraint.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Li-Moon Wann. / M.S.

See appended files.

Variational techniques are used to develop a theory for the time evolution of a thin strand of viscous fluid suspended from two points. The shape of the strand is approximated to be a parabola and energy conservation is used to derive a differential equation modeling the change in height over time. Data is collected with a high resolution camera and a strobe light to obtain the position and shape of the strand over multiple intervals of time. Three very different and unexpected types of behaviors are observed depending on the initial thickness and shape of the filament. The approximation fits well with one type of behavior but variations in the thickness of the strand, and consequently in the center of mass, need to be factored in to predict the others.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-09-05T18:40:22Z No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T19:46:16Z (GMT) No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T19:46:22Z (GMT) No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Made available in DSpace on 2017-09-20T19:50:58Z (GMT). No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) Previous issue date: 2017-03-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The current study aims to elaborate a didactic sequence to study the catenary curve through the dynamic geometry perspective. In onder to highlight the importance of using software/application to better understand the function and its graphical representation, a study has been made on its historical development, notation, construction as well as its properties. Therefore, a lesson plan on the curve will be applied to High School students. Based on their reports, we intend to analyze and discuss these results. / O principal objetivo deste trabalho é elaborar uma sequência didática para estudo da curva catenária, utilizando geometria dinâmica. Para isso, foi feito um estudo sobre seu desenvolvimento histórico, notação, construção e propriedades. Destacar a importância do uso de software/aplicativo para melhor compreensão da função e sua representação gráfica. Por fim, aplicar um plano de aula sobre a curva com alunos do Ensino Médio, coletar, analisar e discutir os resultados baseando-se nos relatos dos alunos envolvidos.

This thesis presents the results of a research study to investigate the behaviour of axially restrained composite beams at ambient and elevated temperatures, and how composite beams and their connections contribute to the robustness of composite framed structures in fire. The commercial finite element analysis package (ABAQUS, 2010) was used to develop the numerical simulation models. This research includes the following four main parts: (1) validation of the simulation model; (2) behaviour of axially restrained composite beams with partial shear interaction at ambient and elevated temperatures; (3) behaviour of composite beams with realistic connections at elevated temperatures and methods of increasing composite beam survival temperatures; and (4) response and robustness of composite frame structures with different extents of damage at elevated temperatures. Based on the results of composite beams, it was found that the survival of axially restrained beams is dominated by the development of catenary action. By utilising catenary action, it is possible for composite beams to develop load carrying capacity significantly above that based on bending resistance. During the development of catenary action, the compression force in the concrete flange of the composite beam decreases, thus reducing the forces in the shear connectors. As a result, the behaviour of shear connector failures ceases to be an issue during the catenary action stage. The results further show that, the load carrying capacities/survival temperatures of composite beams increase by increasing the level of axial restraint up to a certain limit and then decrease at higher levels. Typical realistic composite structures can provide composite beams with sufficient axial restraint to develop catenary action. For detailed composite beams with composite connections, three different beam sizes were investigated using flushed and extended end plate connections with different amounts of slab reinforcement, different load ratios and different bolt sizes. It has been found that the most important method to increase the survival time of composite beams is to use extended end plate connections with sufficient top and bottom reinforcement meshes in the concrete slab, i.e. increasing the amount of slab reinforcement is more beneficial than increasing the bolt size or the number of bolts. Based on the results of modelling a four bay (9 m each, two storey, 4 m high) composite frame with different extents of fire damage to different members, it was found that whenever any of the columns failed, progressive collapse of the frame would occur. Therefore, damages to columns should be prevented or the columns should be designed and constructed to allow for possible damage. If the beams are damaged, it is still possible for the damaged frame to achieve the reference fire resistance time of the undamaged structure (which is used as the criterion to accept that the damaged frame has sufficient robustness) by developing catenary action in the damaged beam. For this to happen, the columns should be designed to resist the catenary tensile force (tying force) in the beams, in addition to the compressive force.

The aim of this diploma thesis is a set of methodical materials for geometry education on primary, secondary schools and possibly during the basic courses on a university. This materials will be based on real geometry phenomenon which we meet every day. The knowledge and understanding of this phenomenon might play an important part during studies of mathematics and geometry. It also shows mathematics and geometry in their close relationship with the real world. The part of the description this phenomenon presented will be solved examples, examples for demonstration and also examples for practise. They are prepared a task, solution and a methodical reviews for each exercise. When preparing this work, it was used his current knowledge of methodology of mathematics and it was selected such forms, means and didactics procedures, which will go together with requirements on a visual solution (mathematical and geometrical software, an interactive whiteboard, worksheets, ) and with the purpose of the example presented (it´s interpretation, practise, testing, ). The part of this diploma thesis are worksheets. This worksheets can help get to know with geometrical phenomena in this work. The worksheets have primary and secondary school level.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-24T12:38:17Z No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-25T11:12:06Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) / Made available in DSpace on 2015-11-25T11:12:06Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) Previous issue date: 2015-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we present a study about the Hyperbolic functions and their applications. We start with analysis of how these functions are approached in some di erential calculus books commonly used in graduate courses in exact sciences, noting that are made through its exponential setting. Then we exposed an approach using hyperbole as generating curve from the study of hyperbolic angles. The de nitions given it in parallel with the construction of the circular trigonometric functions, analyzing their similarities and di erences. Finally we present some of its applications, in particular and in more detail the catenary shape. / Neste trabalho apresentaremos um estudo das Funções Hiperbólicas e suas aplicações. Iniciamos com uma análise de como essas funções são abordadas em alguns livros de cálculo diferencial comumente usados nos cursos de graduação na área de exatas, constatando que são feitas através de sua defi nição exponencial. Em seguida expusemos uma abordagem utilizando-se da hipérbole como curva geratriz a partir do estudo de ângulos hiperbólicos. As de finições se deram paralelamente à construção das funções trigonométricas circulares, analisando suas semelhanças e diferenças. Por m apresentamos algumas de suas aplicações, em especial e de forma mais detalhada a catenária.