Dissertations / Theses on the topic 'Open cross section'

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Em virtude de sua eficiência, elementos estruturais de paredes finas com seções abertas são comuns em estruturas de aço, sendo secção em I, L, C e T usuais na prática de engenharia. A maior parte das vigas de parede fina tem uma boa resistência à flexão em relação ao eixo principal de inércia, mas uma baixa rigidez à flexão em relação ao eixo de menor inércia e uma baixa rigidez em torção. É por isso que estes elementos apresentam em geral uma instabilidade que leva a um acoplamento de flexo-torção. Muitas destas estruturas trabalham em um regime não linear e uma formulação não linear que leve em conta grandes deslocamentos e os acoplamentos inerentes é necessária. Neste trabalho um modelo não linear para vigas de seção aberta e paredes finas, considerando grandes deslocamentos, os efeitos de encurtamento e acoplamentos em flexão e torção é adotado. Inicialmente um estudo das frequências naturais, das cargas críticas e da relação frequência-carga axial é apresentado para diversos perfis. Com base nestes resultados, faz-se um estudo detalhado do comportamento dinâmico não linear destes perfis destacando o efeito do acoplamento não linear na região de ressonância e sua influência na estabilidade dinâmica da estrutura. Para isto são usadas diversas ferramentas de dinâmica não linear, tais como diagramas de bifurcação, respostas no tempo e plano de fase e bacias de atração. Os resultados mostram que a consideração dos acoplamentos não lineares é essencial para se avaliar o nível de segurança destas estruturas.
Due to its efficiency, thin-walled structural elements with open sections, such as I, L, C and Z profiles, are common in steel structures, being usual in engineering applications. Most thin-walled beams have a good flexural strength around of the principal axis of inertia, but a low one around the axis of lower inertia as well as low torsional stiffness. That is why these elements, generally, show instabilities that lead to flexural torsional coupling. Many of these structures do not work in a linear range and a non-linear formulation that takes into account large displacements and associated couplings is required. This dissertation presents a nonlinear model for extensional beams with thin-walled open section, considering large displacements, and flexural-torsional couplings. Initially a study of the natural frequencies, critical load and axial load vs. frequency relation is presented for different profile kinds. Based on these results, a detailed study of the dynamic behavior of non-linear profiles is made, highlighting the effect of non-linear coupling in the resonance region and its influence on the dynamic stability of the structure. For this, various tools of nonlinear dynamics are used, such as bifurcation diagrams, time histories and phase-space portraits and basins of attraction. The results show that the consideration of non-linear couplings is essential to availed the safety level of these structures.

A turbulence model was developed for computing surface velocity coefficients and discharge under steady, uniform flow conditions for rectangular and compound open-channel cross sections. Reynolds-Average Navier-Stokes (RANS) equations, Reynolds stress equations, and kinetic energy and dissipation equations were applied in the model using the finite-volume method with the SIMPLER algorithm. The models show graphical results of the velocity distributions in the longitudinal bed slope direction, secondary velocities, pressure, turbulence kinetic energy, and kinetic energy dissipation rate across the cross section. Also, the surface velocity coefficients were computed at increments of one-eighth of the base width from the vertical walls to the center of the cross section, and the submergence depth of the floating object from zero to 30 cm, with a 5-cm depth increment. Four different sets of Reynolds stress equations (one set by Boussinesq hypothesis and three sets of algebraic stress model) were used to calculate the results. Only one version of the algebraic stress model was successful in predicting the depression of the maximum streamwise velocity below the water surface. The model was calibrated and verified using laboratory data collected at Utah State University. Calculated discharges from the turbulence model had very good agreement with the laboratory data. The surface velocity coefficients from model results were generally lower than the results from the laboratory data, but higher than the values published by the United States Bureau of Reclamation. Standard cross sections of rectangular and compound cross sections were defined to simulate the model results and model sensitivity to parameter changes. The model results were summarized to show the relationship between surface velocity coefficient and channel characteristics compared with the published values by the USBR. For rectangular cross sections, the coefficients from the model are higher than the published USBR values. But the coefficients from the model and USBR are in very close agreement for the tested compound cross sections. The published coefficients by the USBR are a function of only average water depth. However, the model results show that the coefficients are also related to channel size, surface roughness height, float submergence depth, and lateral location of the float object. These factors should be included in the determination of the surface velocity coefficient to improve the discharge estimations from the application of the float method.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Estruturas com elementos de seção aberta e paredes delgadas são amplamente utilizados em estruturas metálicas. Estes elementos têm, em geral, baixa rigidez a torção. Para seções monosimétricas e assimétricas, quando o centro de cisalhamento não coincide com o centro de gravidade, pode ocorrer acoplamento entre flexão e torção. Devido à baixa rigidez à torção, podem ocorrer grandes rotações das seções transversais da viga. Assim, uma análise do comportamento de tais elementos estruturais, levando em consideração a não linearidade geométrica, é desejável. Com este objetivo, equações diferenciais parciais de movimento que descrevem o acoplamento flexão-flexão-torção são utilizadas, em conjunto com o método de Galerkin, para se obter um conjunto de equações discretizadas de movimentos, que é resolvido pelo método Runge-Kutta. A partir das equações linearizadas, obtêm-se as frequências naturais, cargas críticas axiais e a relação entre carga axial e frequência para vigas com diferentes condições de contorno. A seguir, estudam-se as oscilações não lineares e bifurcações de uma viga engastada-livre submetida a cargas laterais harmônicas. Uma análise paramétrica detalhada, usando várias ferramentas de dinâmica não linear, investiga o comportamento dinâmico não linear e não planar da viga nas três primeiras regiões de ressonância e a influência da não linearidade, posição do carregamento, restrições à torção e parâmetros de controle do carregamento na estabilidade dinâmica da estrutura.
Structural elements with open and thin-walled section are widely used in metal structures. These elements have, in general, low torsional stiffness. For monosymmetric and asymmetric sections, when the shear center does not coincide with the center of gravity coupling between bending and torsion may occur. Due to the low torsional stiffness, large twist beam cross sections may arise. Thus, an analysis of the behavior of such structural elements, taking into account the geometric nonlinearity, is desirable. For this purpose, partial differential equations describing the flexural-flexural-torsional coupling are used in conjunction with the Galerkin method to obtain a set of discretized equations of motion, which is solved by the Runge-Kutta method. From the linearized equations, we obtain the natural frequencies, axial critical loads, and the axial load and frequency relationship for beams with different boundary conditions. Next, we study the nonlinear oscillations and bifurcations of a clamped-free beam subjected to harmonic lateral loads. A detailed parametric analysis, using various nonlinear dynamics tools, investigates the nonlinear dynamic behavior and nonplanar motions of the beam for the first three regions of resonance and the influence of the non-linearity, loading position, torsional restraints and load control parameters on the dynamic stability of the structure.

À hautes températures, les propriétés de l’acier sont affectées et sa résistance est donc moindre que sa résistance à température ambiante. Des méthodes de calculs différentes doivent donc être utilisées pour prédire la résistance dans la situation exceptionnelle d’incendie. Les normes actuelles proposent des méthodes simplifiées pour prédire la résistance de l’acier à haute température. Toutefois, ces méthodes sont inspirées des méthodes de dimensionnement à froid et ne sont donc généralement pas adéquates pour prédire de façon précise la résistance des éléments en situations d’incendie. Ce mémoire présente les recherches effectuées pour la proposition d’une nouvelle méthode de calcul pour les sections d’acier ouvertes soumises à de hautes températures en utilisant l’Overall Interaction Concept (O.I.C). Cette méthode est basée sur l’interaction entre la résistance et la stabilité et permet de considérer les imperfections géométriques et matérielles. Entre autres choses, l’avantage de cette nouvelle méthode est qu’elle permet d’obtenir des résultats précis et de conserver une continuité entre les prédictions. Un modèle numérique a été utilisé pour prédire la résistance de l’acier à hautes températures. Ce modèle a été validé en comparant les résultats avec des résultats expérimentaux. À la suite de la validation, le modèle a été utilisé pour conduire des simulations dans lesquelles plusieurs géométries, températures, limites élastiques et cas de chargement ont été considérés. Les résultats ont ensuite été utilisés pour proposer de nouvelles équations dans le format O.I.C. La performance de la nouvelle proposition a été évaluée et comparée avec la performance de normes existantes. Cette évaluation a permis de conclure que la proposition donne des résultats beaucoup plus précis. Finalement, l’évolution du comportement de l’acier entre la température ambiante et les hautes températures a brièvement été analysé. Puisque ce point est abordé de façon sommaire, il ouvre la porte vers de futures études sur le sujet.
At high temperatures, steel suffers from great lossesin strength and stiffness. Different design methods must therefore be considered to predict the resistance of steel in the exceptional situation of fire. Current standards propose simplified methods to predict the resistance of steel at high temperatures. However, these methods are inspired by steel design equations used at room temperature and are therefore generally not suitable to predict accurately the resistance of steel elements in fire situation. This thesis presents research investigations pursued to propose a new design method for open steel cross-sections subjected to high temperatures by means of the Overall InteractionConcept (O.I.C.). This calculation method is based on the interaction between resistance and stability and allows to consider geometrical and material imperfections. The advantage of this new calculation method is that it allows to obtain precise results and to keep continuity between predictions contrarily to standards that use the cross-section classification. A numerical model, initially developed for open steel cross-sections at ambient temperature,was improved to predict the resistance of steel at high temperatures. It was then verified against experimental test results to ensure its accuracy. After validation, the numerical model was used to conduct simulations using different geometries, temperatures, yield limits andload cases. Results were then used to formulate new design proposals for cross-sections at high temperatures in the O.I.C. format. The performance of the new proposal was then evaluated et compared with the performance of existing standards. This evaluation allowed to conclude that the proposition is much more accurate than existing standards. Finally, the evolution of the behaviour of steel between cold and high temperature was briefly analysed. As this point was only briefly discussed, it opens the door for future studies on the subject.

Uniform open-channel flow in a pipe of circular cross-section with a flat bed, is studied by experiment and numerical modelling. A pipe of diameter D= 305 nun, and mild bed slopes So = 4.63 x 10-4and 9.27 x 10-4was, studied - the former slope only by experiment. The bed thicknesses( e), e/D = 0.141, and 0.285 were studied experimentally and numerically, with e/D = 0.020, studied only numerically. Five flow depths (Y. ) were studied; (Y. +e)/D = 0.3,0.4 (and 0.416), 0.5,0.667, and 0.751. A smooth bed and bed roughnessesd,5 o= 0.93,4.20, and 1.71 mm were also used. Mono-chromatic Laser Doppler Anemometry (ILDA) was used to measure the local mean longitudinal (primary), and vertical velocities, and their respective turbulence intensifies. The primary velocity contours display dipped maxima and bulging towards the comer. The inwardly-curving side-walls slightly modify these contours. In each channel half there is a surface cell and a bottom cell. These move high momentum fluid away from the centreline towards the comer zone. The primmy and secondary flows are largely similar to those in rectangular channels. The wall shear force ratios obtained by the Vanoni-Brooks separation technique follow the empirical trend from various channel types. Similarity laws for the longitudinal mean velocity in the comer-influenced zones are proposed. The numerical model is based on the SIMPLE technique, and computes the flow on a Cartesian grid, using a non-linear k-e turbulence model with wall functions. The model boundary conditions were modified to reflect the effects of the comers, the curved side-wall, and a roughened bed. Model predictions of the primary mean velocities, and centreline turbulence intensities, are close to the experimental and empirical distributions. Primary velocity predictions for e/D = 0.020 compare well to the case of a clear pipe flowing part-fiffl. The predicted secondary flows are largely similar to the experimental patterns. Usage of a small mesh size (e. g. when (YO + e)/D < 0.5) results in side-wall points lying within the larninar sublayer, leading to inaccurate secondary flow prediction by the k-e model. As in rectangular channels, the predicted local boundary shear stress decreases from the centreline along the bed and minimises at the comer. On the side-walls, the model overpredicts the local boundary shear stresses. Nonetheless, computed wall shear force ratio values follow the empirical trend.

Des barres en acier à section ouverte sont, dans la majorité des cas, soumises à une combinaison d’effort normal et de flexion bi-axiale. Cependant, en raison de leur utilisation elles peuvent également être soumises à un moment de torsion. Même si les barres à section ouverte peuvent être soumises à des charges de torsion en pratique, l’Eurocode 3, ne définit pas comment la résistance de la barre peut être déterminée dans ces conditions. Ce pourquoi, l’objectif principal de cette thèse est de remplir cette lacune. Pour atteindre cet objectif, le comportement des barres métalliques soumises à une combinaison complexe de charges est étudié par voie théorique, expérimentale et numérique. Tout d’abord, la résistance plastique des barres est étudiée. En cas de torsion, il a été montré que les barres à section ouverte possèdent une réserve plastique importante qui ne peut pas être mise en évidence à l’aide d’une simple analyse élastique. Afin de tenir compte de l’effet bénéfique de la réserve plastique en torsion, une méthode d’analyse simplifiée est développée et validée par des analyses numériques. Ensuite, l’interaction plastique entre les efforts internes est étudiée. Des essais en laboratoire ont été réalisés afin de caractériser l’interaction entre l’effort tranchant et le moment de flexion. L’étude est ensuite étendue à l’aide de simulations numériques sur des cas d’interaction plus complexes incluant notamment des moments de torsion. Les essais accompagnés par l’étude numérique ont permis de mettre au point un modèle de résistance basé sur la méthode « Partial Internal Force Method » développée dans le passé. La dernière partie de la thèse concerne la résistance des barres à l’instabilité. Un modèle de résistance incluant l’effet de l’instabilité élasto-plastique est développé pour les barres métalliques en présence de torsion. Cette méthode est basée sur une extension des formules d’interaction proposées dans l’Eurocode. Afin de franchir certaines limitations liées à cette méthode, un deuxième modèle de résistance est développé pour les barres en I dans le format du « Overall Interaction Concept »
Structural steel members with open cross-section are, in the majority of cases, subject to a combination of axial forces and mono- or bi-axial bending. Nonetheless, owing to specific use they may be subject to torsion as well. Even if torsional loads are of practical interest for steel members of open section, the European standard for the design of steel structures, Eurocode 3, does not contain a generally accepted design method addressing the resistance of these members. Consequently, the main objective of this thesis is to close the lack in the current standard. So as to attain this objective the behaviour of members of open section subject to a complex load combination has been studied theoretically, experimentally and numerically. First, the plastic resistance of steel members has been analysed. It has been shown that members subject to torsion may possess a high plastic system reserve that cannot be predicted by simple elastic analysis. So as to account for the beneficial effect of the plastic reserve, a simplified analysis method has been developed and validated with numerical simulations. After this, the plastic interaction between all internal forces and moments has been studied. Several laboratory tests have been performed to characterise the interaction between bending moments and the shear force. The study is then extended to more complex interaction cases including torsion by means of numerical simulations. The laboratory test and the numerical simulations allowed the development of a precise resistance model based on the “Partial Internal Force Method” developed in the past. The last part of this thesis was dedicated to the member resistance including instability. A resistance model has been developed based on the Eurocode 3 interaction equations. So as to overcome some of the limitations linked to this method, a second design approach is developed based on the “Overall Interaction Concept”

The transnational traffic of narcotics has had undeniable impacts on international development, for instance, stagnant economic growth in Myanmar (Chin, 2009), unsustainable agricultural practices in Yemen (Robins, 2016), and human security threats in Columbia (Thoumi, 2013). Furthermore, globalization is a catalyst for the transnational narcotics traffic (Robins, 2016; Aas, 2007; Kelly, Maghan & Serio, 2005). Several qualitative studies exist on the transnational narcotics traffic, yet few quantitative studies examine the issue. There is thus an opportunity for novel quantitative studies on the general question: “what are the main economic factors that influence the transnational traffic of narcotics between countries?” This study looked at the specific question: “are distance and economic size correlated with the volume of narcotics traffic between countries?” This study chose the gravity model as it centres on bilateral trade (Tinbergen, 1962), accounts for trade barriers (Kalirajan, 2008) and is empirically robust (Anderson 2011). This study defined a basic functional gravity model relating a proxy of the narcotics traffic to distance and economic size. Four augmented functional gravity models were also advanced to address omitted variable bias. The research was limited conceptually to cross sectional and pooled time series data. In addition, the data was also limited practically to a convenience sample of secondary data drawn from: the United Nations Office on Drugs and Crime’s (UNODC) (2016a) Individual Drug Seizures (IDS); the World Bank’s (2016) World Development Indicators; and the CEPII’s GeoDist (2016) datasets. This study used a novel “dosage” approach to unit standardization to overcome the challenge posed by the many measures and forms of narcotics. The study used the Poisson pseudo maximum likelihood (PPML) estimator as its estimations of the gravity model are consistent (Gourieroux et al., 1984), allow heteroscedasticity (Silva & Tenreyro, 2006) and avoid back transformation bias (Cox et al., 2008). The evidence analyzed in this study seem to indicate that the gravity model may not be applicable in its current form to the transnational narcotics traffic among countries that report drug seizures to the UNODC. However, the sampling method and the choice of proxy are likely to influence these findings. Moreover, the low explanatory power of the gravity model for the narcotics traffic, reflected in the values of the pseudo-R-squared coefficient of determination, indicates that other factors are at play. For instance, authors such as Asad and Harris (2003) and Thoumi (2003) argue that institutions could be a key factor in the narcotics traffic. Future empirical research into this topic could build on the theses findings to introduce new proxies and to explore alternate theoretical frameworks.

Les poutres à parois minces à sections ouvertes sont des éléments de base des ouvrages courants en génie civil, de l'automobile et de l'aéronautique. En raison de leur élancement et la forme des sections, elles sont très sensibles à la torsion et aux instabilités aussi bien en statique qu’en dynamique. En dynamique, les modes de vibration en torsion sont plus dominants par rapport au modes de flexion classiques. Pour ces raisons, les défaillances planaires de telles structures sont connues pour être une exception plutôt qu'une règle. Dans ce travail de thèse, on s’intéresse au comportement dynamique de poutres à parois minces et à section ouvertes arbitraires. En se basant sur le modèle de Vlasov qui prend en compte de la torsion et du gauchissement, les équations de mouvement 3D sont dérivées à partir du principe d’Hamilton. Des solutions analytiques originales pour différentes conditions aux limites sont dérivées pour des modes supérieurs en vibrations libres. Dans ces solutions, les effets des termes de rotation inertiels en flexion et torsion sont pris en compte. Pour des cas généraux, un modèle élément fini de poutre 3D est décrit et implémenté. Dans le modèle, un degré de liberté (ddl) est affecté au gauchissement. Toutes les matrices de rigidité masse de base sont calculées par intégration numérique (intégration de Gauss). Dans le modèle, les calculs en vibrations libres et forcées sont possibles. Le modèle est validé par comparaison aux solutions numériques et expérimentaux de la littérature. Une comparaison aux simulations des codes commerciaux est aussi suivie. Afin de valider le modèle théorique et numérique utilisé, une campagne d’essais a été suivie au LEM3 à Metz. Des essais de vibration libre et forcée sont effectués sur des poutres à parois minces avec différentes conditions aux limites. Les solutions analytiques, numériques et les mesures expérimentales sont comparées et validées. Un bon accord entre les différentes solutions est constaté. Le modèle est étendu aux poutres 3D retenues latéralement par des entretoises. Des ressorts élastiques et visqueux 3D sont ajoutés dans le modèle numérique. L'effet des entretoises est étudié dans le but d’améliorer le comportement des poutres à parois minces vis-à-vis des modes indésirables de type flexion latérale et torsion
Thin-walled beams with open section constitute main elements in engineering applications fields as in civil engineering, automotive and aerospace construction. Due to slenderness and cross section shapes, these elements are very sensitive to torsion and instabilities in both statics and dynamics. In dynamics, the torsional and flexural-torsional modes of vibration are often lower frequencies compared to the classical plane pure bending modes. Thus, planar failures of such structures are known to be an exception rather than a rule. In torsion, warping is important and governs the behavior. In this thesis work, we are interested with the dynamic behavior of thin-walled beams with arbitrary open cross sections. Based on the Vlasov’s model accounting for warping, the 3D motion equations are derived from the Hamilton’s principle. Original analytical solutions for different boundary conditions are derived for higher free vibration modes. In these solutions, the effects of the inertial rotation terms in bending and torsion are taken into consideration. For more general cases, a 3D beam finite element model is described and implemented. Compared to conventional 3D beams, warping is considered as an additional Degree Of Freedom (DOF). The mass and stiffness matrices are obtained by numerical integration (Gauss method). In the model, free and forced vibration analyses are possible. The model is validated by comparison with benchmark solutions available in the literature and other numerical results obtained from simulation on commercial codes. In order to validate the present model, laboratory test campaign is undertaken at the LEM3 laboratory in Metz. Tests are carried out on thin-walled beams with different boundary conditions. Free and forced vibration tests are performed using impact hammer and shaker machine. In the presence of arbitrary sections, flexural-torsional vibration modes are observed. The analytical, the numerical and the experimental solutions are compared and validated. Moreover, the numerical and experimental dynamic response spectra are compared. A good agreement between the various solutions is remarked. The model is extended to 3D beams in presence of lateral braces. 3D elastic and viscous springs are added in the finite element model. The effect of the springs is studied in order to improve the behavior of thin-walled beams against undesirable lateral bending and torsion modes

Steel is a material commonly used in various constructions such as high-rise buildings, sport arenas, ships etc. Steel is a versatile building material due to its isotropic characteristics, e.g. both high tensile- and compressive strength. This allows steel to be formed into open section profiles which reduces material usage but simultaneously allows the tensile- and compressive stress resistance to be high in directions were loads are applied. Although steel has a high stress resistance its sensitivity to fire is larger than other building materials due to its high thermal conductivity. The strength of the material is reduced at higher temperatures and thereby makes the dimensioning of beams in fire cases vital in fire safety design of structural elements. An aspect to consider when dimensioning open section building elements in steel is the shadow effect. The shadow effect is the result of the open cross-section geometrical shape of beams and columns, e.g. H-profiles. The interior of the profile is screened from thermal radiation caused by fire which makes the characteristics of the thermal exposure different from closed cross-section profiles. A common way to estimate the temperatures of steel after a certain time of fire exposure is to use numerical calculations described in Eurocode. In these calculations the shadow effect is applied as a reduction of the total heat exchange, i.e. both convection and thermal radiation, from the fire exposure. A more realistic approach is to separate these boundary conditions and treat them as independent quantities. Wickström (2001) argues that a void is created within the flanges and that reduction factor thereby only should be applied to the radiative part of the total heat exchange, acting as a reduction of surface emissivity within the profile. This, since the convection is not affected by the shadow effect. Wickströms (2001) suggestion of application has been investigated in this thesis and has showed a better correlation than the approach suggested in Eurocode when compared to experimental tests. Shadow effects calculated on the premises of separated boundary conditions for the total heat exchange has of yet only been investigated in detail with TASEF+-simulations, but these simulations predicts steel temperatures with satisfactory results. It is possible to reproduce a similar setup in the program COMSOL Multiphysics in two-dimensional simulations, and further three-dimensional simulations. This possibility has been investigated in this thesis. COMSOL Multiphysics has proven to be an adequate tool when it comes to simulate fire exposure on slender steel beam with shadow effects considered. Both three- and two-dimensional models produced simulation results correlating well to simulations conducted in TASEF. Additionally, adequate correlations with experimental tests were obtained for COMSOL Multiphysics as well. Further work regarding fire simulations with the utilisation of COMSOL Multiphysics is thereby suggested.

The characteristics of fully developed turbulent flow in smooth open channels of simple trapezoidal cross-section have been examined experimentally in the range 0.5 < Fr < 3.5,1.9 x 104 < Re < 6.2 x 105 and 0.3 < 2b/H < 15.0. Subcritical flow in a compound trapezoidal channel has also been studied for relative depths between 0.05 < Dr 0.5. The effect of secondary flows and the interaction between the main channel and the flood plain flows have been shown to influence the boundary shear stress and velocity distributions significantly. For simple channels, the boundary shear stress distributions have been correlated with the geometry parameters 2b/H or Pb/Pw, and empirically derived equations are presented giving the percentage of the total shear force carried by the wall. Ancillary equations are also presented giving the correlation between the geometry parameters and the mean and maximum shear stresses. Attention is also focussed on the effect of the hydraulic parameters on flow resistance. A comparison is made between the data and traditional formulations for smooth pipes and rectangular channels. The Froude number effect is also examined and found to be important. For compound channels, the transfer of momentum between the main channel and the flood plain has been studied in detail. Boundary shear force results have been used to calculate the apparent shear forces on vertical, horizontal and inclined interfaces. An empirically derived equation relating the geometry parameters and the boundary shear force on the flood plain bed and walls is presented. In order to quantify the momentum transfer within the whole section, the Navier-Stokes equation for steady uniform flow is used, and an analytical solution to the depth averaged form of the equation compared with the experimental results. A comparison of the depth-averaged values of flow resistance with those values obtained from a one-dimensional formulation is also made, and distinct differences noted. Improvement may be made by using the resistance radius in place of the traditional hydraulic radius. Use is made of the apparent shear force results in assessing channel discharge calculation methods which are based on sub-dividing the flow area. Equations are presented giving the main channel discharge for both vertical and horizontal division planes. The methods for evaluating the critical depth in a compound channel are also reviewed and assessed against experimental data. The free overfall for simple trapezoidal channels has been studied and an analytical relationship obtained between the ratio of brink depth to critical depth and the channel bed slope. Experimental data confirm this relationship.

Research has argued that effortful cognitive functioning is more susceptible to age-related decline compared to tasks that can be performed with minimal cognitive effort. Aerobic exercise has also been associated with beneficial cognitive effects for tasks implicating higher order executive control processing. Therefore, the current study aims to investigate whether aerobic exercise selectively improves executive control processing which is known to be disproportionately effected by aging, potentially counteracting cognitive deterioration in healthy aging. Although behavioural studies have provided inconsistent findings, EEG/ERP studies investigating the effects of acute exercise intensity on neural activity during executive control tasks are limited in numbers and have mainly focused on younger rather than older populations. Ten healthy participants consisting of five young (mean age = 20±1 years, two male, three female) and five older adults (mean age = 67±4 years, three male, two female) performed a computerised Stroop test with continuous EEG following a 20 minute bout of acute cycling at 40% and 70% heart rate reserve, compared to a no exercise control. Behavioural reaction times showed no significant age effects for exercise condition or congruency, although moderate exercise was associated with the fastest reaction times for congruent trials. The P3b and N450 components also showed no significant higher order effects specific to trial congruency, although significant age effects were observed at the frontal region following acute exercise. The P3b and N450 amplitudes were reduced at the frontal region for the young group following moderate exercise compared to the control, suggesting processing efficiency was enhanced. However, for the older group P3b and N450 amplitudes increased at the frontal region following high intensity exercise compared to moderate, suggesting that high intensity exercise had a negative effect on cognitive processing. Acute exercise does not selectively improve executive control processing during the Stroop test, but rather seems to facilitate a non-specific global activation of neural resources at the frontal region. Acute moderate and high intensity exercise were associated with enhanced frontal processing for young adults, but impaired functioning for older adults. These findings are understood in terms of Compensatory-Related Utilization of Neural Circuits, the Posterior-Anterior Shift in Aging and Scaffolding Theory of Cognitive Aging.

碩士
淡江大學
水資源及環境工程學系碩士班
93
The objective of this study is to develop a linearized analytical model and solve the diffusion problems of pollutants. The water quality model includes unsteady discharge equations and continuity equation of concentration. Because the De Saint Venant equations which contain the continuity and momentum equations, and the continuity equation of contraction are nonlinear partial differential equations, it is difficult to obtain the exact solution. In this study, a linearized analytical technique is provided, not only apply to the scheme of the nonlinear differential equations, and also apply to the coefficients of the diffusion terms of the water quality model. The linearized analytical method has been used in solving regular rectangular cross sections of open channel successfully. Because the circular cross section of the open channel is more complicated than other rectangular or wide rectangular cross sections, the methods used before of obtaining coefficients of the diffusion equations of discharges and concentrations are using Taylor Series expansion which exist the infinite terms of the series. Therefore, it is impossible to obtain accurate solutions. In this study, an unsteady water quality model of open channel with circular cross section is proposed. By using the linearized analytical method to modify the coefficients of the diffusion equations of and concentration, the good results are obtained.

碩士
國立成功大學
水利及海洋工程學系碩博士班
92
The manhole (or junction box) in the sewer system is same the suddenly continuous expanded and contracted cross-section in the short distance of channel. In order to design the sewer system, effect on the flow due to a series of the suddenly continuous expanded and contracted cross-section in the prismatic channel is studied by the theoretical analysis and the hydraulic experimentations. 　　The backwater effect due to the suddenly expanded cross-section will make upstream depth higher than the normal depth. The hydraulic jump and the cross wave are induced by the separate phenomena on the downstream of the suddenly continuous expanded and contracted cross-section. The depth of both the suddenly continuous contracted and expanded cross-section and the upstream reach also will be increased by the choke due to the separate phenomena.

碩士
國立交通大學
機械工程系所
105
The geometrical nonlinear static behavior and infinitesimal free vibration around the static equilibrium position are studied using total Lagrangian finite element method for three dimensional thin-walled beams with point-symmetric open section subjected to axial load with its resultant passing through the centroid of beam cross section. The bimoment induced by axial load is considered in this study. The element employed here has two nodes with seven degrees of freedom per node. The element nodes are chosen to be located at the shear center of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis. The kinematics of the beam element is described in the current element coordinate system constructed at the current configuration of the element. The current element coordinate system is regarded as an inertial local coordinate system. Thus, the first and the second time derivative of the position vector defined in the element coordinates are the absolute velocity and absolute acceleration. The element deformation nodal forces and inertia nodal forces are systematically derived by the d'Alembert principle, the virtual work principle and consistent second order linearization in the current element coordinates. The equilibrium equations may be obtained by dropping the terms of the inertia forces in the equation of motion. The governing equations for linear vibration around the static equilibrium position are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of the nonlinear equilibrium equations. The subspace iterative method is used for the solution of natural frequencies and vibration modes for the free vibration. Numerical examples are studied to investigate the effects of the axial load and bimoment induced by axial load on the critical state, critical load and the natural frequencies of z cross section beams with different lengths and boundary conditions under axial loading. The objective of the paper is to analyze the influence of bimoment induced by constant axial loads on the free motion of thin-walled beams with point-symmetric open cross- section. For various boundary conditions, a closed-form solution for natural frequencies of free harmonic vibrations was derived by using a general solution of governing differential equations of motion based on Vlasov’s theory. In order to investigate the effect of the bimoment on natural frequencies, the numerical examples with symmetric Z cross-section are given. The obtained results, verified using an ANSYS finite element model, demonstrate that the influence of the bimoment is important in the assessment of torsional natural frequencies. A force with its resultant passing through the centroid of a particular section and being perpendicular to the plane of the section. A force in a direction parallel to the long axis of the structure

碩士
國立中興大學
水土保持學系
89
Open dams are usually built with long rectangular openings and are easily blockaded by boulders. To solve this problem, this study investigated the downstream scouring response of an open dam with compound cross-section under various combinations of three opening types, three bed slopes, three flow discharges, and three sediment types. Based on the flume experiments and regression analysis for the results, this study found that the relationship among scouring factors (i.e., maximum scouring depths, maximum length from the deepest point of the scouring pool to the dam, scouring length, energy dissipation rate, channel slope, diameter of bed-load sediment, and water run-through area) and concluded empirical formulas for their relationships. Meanwhile, experimental findings indicated that the extreme scouring depth would increase with the flow discharge and channel slope, while mix sediments provided better armoring function for downstream channel bed. Besides, this study also discovered that the scouring length and energy dissipation rate would decrease with higher flow discharge and increased with steeper channel.

碩士
淡江大學
水資源及環境工程學系
87
In the study, an analytical solution is proposed for simulating unsteady open channel flow with circular cross section, and the linearized of the Saint-Venant equation by small perturbation is used to obtain analytical solution . The proposed analytical method is tested for circular channel. It can also be applied to different flow conditions, such as the downstream boundary condition is approximately by a normal flow. The sensitivity analysis of reference central angle, using the reference discharge to solve the concentration routing problem to obtain the best solution. This result shows that the analytical solution is good, economic, efficient approximation in practical cases.

The Large Hadron Collider (LHC) at CERN is the world’s highest energy hadron collider, providing proton- proton collisions currently at a centre-of-mass energy √s = 8 TeV and Pb-Pb collisions at √sNN = 2.76 TeV. This opens a new energy regime, which allows the study of QCD in elementary pp-collisions and in the extreme environment of Pb-Pb collisions, as well as providing a discovery potential for rare and exotic particles. ALICE is the dedicated heavy-ion experiment at the LHC. The experiment is optimised to provide excellent tracking and particle identification capabilities, in particular at low-pt, where the bulk of the particles is produced in heavy-ion collisions as well as in proton-proton collisions. The production of heavy quarks is described in proton-proton collisions by next-to-leading order per- turbative QCD (pQCD) calculations. Thus, the measurement of heavy-quark production in proton-proton collisions serves as a test of pQCD. Measurements performed at SPS, RHIC, and Tevatron experiments showed a good agreement with pQCD, where the data were usually at the upper limit of the prediction. In addition, measurements in proton-proton collisions serve as reference for heavy-ion collisions, in which heavy quarks are essential probes for parton energy loss in a deconfined medium. Heavy-quark produc- tion can be studied either with hadronic or in semi-leptonic decay channels. The analysis presented in this thesis is performed in the semi-electronic decay channel with the ALICE apparatus. A crucial device for the electron selection is the Transition Radiation Detector (TRD), which provides an important contribution to the electron-pion separation for momenta larger than 1 GeV/c. In November 2010, the first data were recorded with the experiment. The electron selection performance was studied for the first time on real data using data-driven methods. A pion-rejection factor of 23 at a momentum of 2 GeV/c was obtained using a likelihood method on the total charge deposit in the detector for tracks with the maximum amount of charge deposit measurements. The inclusive electron pt-spectrum, which contains contributions from heavy-flavour hadrons as well as from various background sources, was measured for 0.5 GeV/c < pt < 8 GeV/c in proton-proton collisions at √s = 7 TeV at midrapidity (|y| < 0.5). The contribution of background electrons was quantified using a cocktail method, and it was subtracted from the inclusive spectrum. For the resulting spectrum of electrons from heavy-flavour hadron decays a signal-to-background ratio of 1 was observed at pt = 2 GeV/c. This ratio grows with increasing electron pt up to ≈5 at pt = 8 GeV/c. The pt-differential cross section of electrons from heavy-flavour hadron decays obtained by this method is in good agreement with fixed-order plus next-to-leading logarithm pQCD (FONLL) predictions. The total charm cross section in proton-proton collisions obtained from this analysis is σc = 7.6 ± 0.3(stat) ± 2.9(sys) -2.5 +3.2(extr) ± 0.3(norm) ± 0.3(br) mb.

Tese no âmbito do Doutoramento em Engenharia Civil na Especialidade de Estruturas apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
The main body of the thesis is divided into two largely self-contained parts. The first one is devoted to the development of a continuous one-dimensional linear model for the stretching, bending and twisting of tapered thin-walled bars with open cross-sections under general quasi-static loading conditions. These bars are treated as two-dimensional Kirchhoff-Love shells, exhibiting both membrane and flexural behaviours. To achieve the necessary dimensional reduction, the classical assumptions of Vlasov and Kirchhoff-Love are regarded systematically as internal constraints, that is, a priori restrictions, of a constitutive nature, on the possible deformations of the bars (alternatively, they may also be viewed as holonomic-scleronomic constraints). Moreover, the internal forces are decomposed additively into active and reactive parts and this is shown to lead to a dual one-dimensional description of kinematics and statics. Two examples illustrate the application of the developed one-dimensional model, shed light on its physical aspects and demonstrate the shortcomings of piecewise prismatic models, regardless of the number of prismatic segments used (indeed, even in the limit when the length of these segments tends to zero). The main original contributions in this first part of the thesis may be summarized as follows: (i) The second fundamental form of the middle surface of a bar and the change of curvature tensor are established in general form. (ii) The displacement field of a whole bar (not just of its middle surface) is completely characterized, thus including the so-called through-the-thickness (or secondary) warping deformation. (iii) In the characterization of the internal forces in the bar, the shell bending and twisting moments and the transverse shear forces are taken into account, in addition to the membrane forces. (iv) The Saint-Venant contribution to the strain energy and the corresponding component of the total torque are derived consistently. (v) A set of fundamental inequalities concerning the cross-sectional properties is established. The second part of the thesis is restricted to the important special case of depth-tapered singly symmetric I-section bars and deals with one-dimensional models of the Hencky bar-chain type, whose nature is intrinsically discrete. Indeed, a Hencky bar-chain model consists of a finite number of rigid units linked by elastic springs (or, more generally, by rheological elements) – it can be thought of not only as an idealization of a (continuous) member, but also as an actual mechanical structure in its own right, the inherent simplicity and transparency of which make its qualitative behaviour more easily grasped. Two types of problem are addressed in successive chapters: (i) the linear mechanical behaviour in three-dimensional space under general quasi-static loading conditions and (ii) the linearized flexural-torsional buckling behaviour under bending (in the plane of symmetry, which is also the plane of greatest flexural rigidity) and compression, including the so-called Wagner effect associated with the asymmetry of the flanges. Particular attention is paid to the calibration of the spring stiffnesses and to the appropriate definition of boundary conditions. It is shown that the bar-chain models are consistent with (but not subordinate to or in any away dependent on) previously developed Vlasov-type continuum models, in the sense that the local truncation errors tend to zero as the length of the rigid units approaches zero. Several illustrative examples, including prismatic and flangeless members (i.e., members with narrow rectangular cross-sections), are solved in order to verify the discrete Hencky bar-chain models and to assess their convergence rates.
Contributos para a Modelação Unidimensional do Comportamento Tridimensional de Barras Não Prismáticas com Secção de Parede Fina Aberta A tese encontra-se dividida em duas partes em larga medida independentes. A primeira é dedicada ao desenvolvimento de um modelo linear unidimensional contínuo para a flexão e torção de barras com secção aberta de paredes finas, continuamente variável, submetidas a carregamentos quase-estáticos genéricos. Estas barras são tratadas como cascas de Kirchhoff-Love (bidimensionais), considerando tanto o comportamento de membrana como o de flexão. Para levar a cabo a necessário redução dimensional, as hipóteses clássicas de Vlasov e Kirchhoff-Love são tratadas sistematicamente como constrangimentos internos, isto é, restrições de natureza constitutiva às possíveis deformações de uma barra (alternativamente, aquelas hipóteses podem também ser vistas como constrangimentos holonómicos-escleronómicos). Assim, as forças internas são decompostas em parcelas activa e reactiva, o que conduz a uma descrição dual (unidimensional) da cinemática e da estática. São apresentados dois exemplos que ilustram a aplicação do modelo unidimensional desenvolvido, esclarecem os seus aspectos físicos e atestam as limitações dos modelos seccionalmente prismáticos (ou “em escada”), independentemente do número de segmentos prismáticos utilizados (de facto, estas limitações mantêm-se mesmo no processo de passagem ao limite quando o comprimento dos segmentos tende a para zero). Os principais contributos originais nesta primeira parte da tese podem ser resumidos da seguinte forma: (i) Obtêm-se expressões gerais para a segunda forma fundamental da superfície média de uma barra e para o tensor de mudança de curvatura (ii) Generaliza-se a definição do campo de deslocamentos da superfície média para todo a barra, incluindo assim a caracterização do empenamento na espessura das paredes (também designado por empenamento secundário). (iii) Na caracterização dos esforços internos, são tidos em consideração não apenas os esforços de membrana, mas também os momentos flectores e de torção e as forças de corte transversais “de casca”. (iv) A contribuição de Saint-Venant para a energia de deformação e a componente correspondente do momento torsor total são obtidas de forma consistente. (v) Estabelece-se um conjunto de desigualdades fundamentais relativas às propriedades mecânicas das secções transversais. A segunda parte da tese, cujo âmbito se restringe ao importante caso particular de barras com secção em I monossimétricas e altura variável, trata de modelos unidimensionais do tipo Hencky, cuja natureza é intrinsecamente discreta. De facto, um modelo de Hencky consiste num número finito de unidades rígidas ligadas por molas elásticas (ou, mais geralmente, por elementos reológicos) e pode ser encarado não apenas como uma idealização de um elemento estrutural contínuo, mas também como uma estrutura real por direito próprio. A sua simplicidade e transparência faz com que o seu comportamento, de um ponto de vista qualitativo, seja mais facilmente apreendido. São abordados dois tipos de problema em capítulos sucessivos: (i) o comportamento linear no espaço tridimensional, sob acções quase-estáticas genéricas e (ii) a encurvadura por flexão-torção (linearizada) de vigas e colunas-viga solicitadas à flexão no seu plano de simetria (que é também o plano de maior rigidez à flexão), incluindo o chamado efeito Wagner associado à assimetria dos banzos. É dada uma especial atenção à calibração das rigidezes da mola e à definição apropriada das condições de fronteira. Mostra-se que os modelos de Hencky, se bem que desenvolvidos de forma totalmente independente, são consistentes com modelos contínuos do tipo Vlasov previamente desenvolvidos, na medida em que os erros de truncatura locais tendem para zero à medida que o comprimento das unidades rígidas também se aproxima de zero. Apresentam-se vários exemplos ilustrativos, que incluem elementos prismáticos e elementos de secção rectangular fina, de forma a verificar os modelos discretos de Hencky e avaliar as suas taxas de convergência.

The present work deals with the unsteady galloping instability, which arises at low reduced flow velocities, for steel-concrete composite bridge decks during the incremental launching phase. In this particular situation, the light weight and bluff shape of the steel box, which is normally first launched, imply a high proneness to the risk of unsteady galloping. The main goal of this thesis is to understand the unsteady galloping with respect to these special cross sections, which have not been investigated in depth before, and to develop an analytical approach for the modeling of unsteady galloping as a basis for design of bridges.

Tese de doutoramento em Engenharia Civil, na especialidade de estruturas, apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Tapered thin-walled bars are extensively used in the fields of civil, mechanical and aeronautical engineering. The competitiveness of tapered structural members is hindered by the fact that their spatial behaviour is still poorly understood and by the lack of rational and efficient methods for their analysis and design. The present thesis aims at providing a contribution to overcome these drawbacks, by (i) developing one-dimensional models (i.e., models having a single independent spatial variable) to perform linear static, dynamic and lateral-torsional buckling analyses of tapered thin-walled bars with open cross-sections, (ii) supplying physical interpretations for the key behavioural features implied by these models and (iii) offering a detailed examination of several illustrative examples that will be useful for benchmarking purposes. The first part of the thesis is devoted to bars whose shape allows them to resist biaxial bending by the membrane action of their walls (I-section or C-section bars, for instance). It starts with the development, based on the induced-constraint approach, of a linear onedimensional model for the stretching, bending and twisting of tapered thin-walled bars with arbitrary open cross-sections under general static loading conditions. A two-dimensional linearly elastic membrane shell model is adopted as parent theory. The Vlasov assumptions, extended to the tapered case in such a way as to retain an intrinsic geometrical meaning, are treated consistently as internal constraints, that is, a priori restrictions, of a constitutive nature, on the possible deformations of the middle surface of the bar. Accordingly, (i) the membrane forces are decomposed additively into active and reactive parts, and (ii) the constitutive dependence of the active membrane forces on the membrane strains reflects the maximal symmetry compatible with the assumed internal constraints. For a large class of tapered thin-walled bars with open cross-sections, the membrane strain and force fields implied by the internal constraints do not have the same form as in Vlasov’s prismatic bar theory – they feature an extra term, involving the rate of twist. Consequently, the torsional behaviour (be it uncoupled or coupled with other modes of deformation) predicted by our tapered model is generally at odds with that obtained using a piecewise prismatic (stepped) approach. The discrepancies may be significant, as illustrated through examples. The developed linear model is then extended into the dynamic range. The contributions of rotatory inertia and torsion-warping inertia are fully taken into account. The inclusion of a viscous-type dissipative mechanism is briefly addressed. Subsequently, we derive a model for the elastic lateral-torsional buckling of singly symmetric tapered thin-walled beams with arbitrary open cross-sections, loaded in the plane of greatest bending stiffness. The adopted kinematical description rules out any local or distortional phenomena. Moreover, the effect of the pre-buckling deflections is ignored. Since isolated beams with idealised support conditions are seldom found in actual design practice, an archetypal problem is used to show how the presence of out-of-plane restraints can be accommodated in the one-dimensional buckling model. The restraints may (i) have a translational, torsional, minor axis bending and/or warping character, and (ii) be either linearly elastic or perfectly rigid. The second part of the thesis is concerned with strip members (i.e., members with a narrow rectangular cross-section) exhibiting constant thickness and varying depth. It deals with three problems of increasing complexity: (i) the elastic lateral-torsional buckling of cantilevered beams with linearly varying depth, acted at the free-end section by a conservative point load; (ii) the elastic lateral-torsional buckling of cantilevers (ii1) whose depth varies according to a non-increasing polygonal function of the distance to the support and (ii2) which are subjected to an arbitrary number of independent conservative point loads; (iii) the elastic flexural-torsional buckling of linearly tapered cantilever beam-columns, acted by axial and transverse point loads applied at the free-end section. These three problems are tackled analytically – we obtain exact closed-form solutions to the governing differential equations and, thereby, establish exact closed-form characteristic equations for the buckling loads. However, in the third problem, the analytical approach is successful only for certain values of the ratio between the minimal and maximal depth of the strip beam-column – in the remaining cases, it is necessary to resort to a numerical procedure.
As barras não prismáticas de parede fina são largamente utilizadas em engenharia civil, mecânica e aeronáutica. A competitividade destes elementos estruturais é prejudicada pelo facto de o seu comportamento espacial ser ainda mal compreendido e pela falta de métodos eficientes para a sua análise e dimensionamento. Esta tese visa dar um contributo para superar estas dificuldades, através (i) do desenvolvimento de modelos unidimensionais (isto é, modelos com uma única variável espacial independente) para efectuar análises lineares, em regime estático ou dinâmico, e de encurvadura lateral por flexão-torção de barras com secção de parede fina aberta continuamente variável, (ii) da interpretação física dos aspectos essenciais do comportamento destas barras, tal como previsto por estes modelos, e (iii) do exame detalhado de alguns exemplos ilustrativos, com utilidade para efeitos de verificação e validação. A primeira parte da tese é dedicada às barras cuja forma lhes permite resistir a flexão biaxial por acção de membrana das suas paredes (barras com secção em I ou em C, por exemplo). Começa com o desenvolvimento de um modelo linear unidimensional para a flexão e torção de barras não prismáticas com secção de parede fina aberta arbitrária, submetidas a carregamentos estáticos genéricos. Como ponto de partida, adopta-se um modelo bidimensional de membrana. As hipóteses de Vlasov, generalizadas ao caso não prismático de forma a manterem um significado intrínseco, são tratadas como constrangimentos internos, isto é, restrições de natureza constitutiva às possíveis deformações da superfície média da barra. Assim, (i) as forças de membrana são decompostas em parcelas activa e reactiva e (ii) a relação constitutiva entre as forças de membrana activas e as deformações de membrana reflecte a simetria máxima compatível com os constrangimentos internos impostos. Em geral, os constrangimentos internos admitidos implicam que as expressões analíticas que definem os campos de deformações e forças de membrana em barras não prismáticas incluem uma parcela adicional, associada à torção, em relação às da teoria de Vlasov para barras prismáticas. Assim, o comportamento torsional previsto pelo modelo unidimensional desenvolvido contrasta, em geral, com o obtido através de uma modelação “em escada”, em que uma barra não prismática é aproximada por uma sequência de segmentos prismáticos. Os exemplos ilustrativos apresentados permitem concluir que as diferenças podem ser significativas. O modelo linear desenvolvido é depois generalizado para o caso da análise dinâmica. As contribuições das inércias de rotação e de empenamento de torção são tomadas em consideração. Discute-se também a inclusão de um mecanismo de dissipação do tipo viscoso. Em seguida, estabelece-se um modelo unidimensional para a encurvadura lateral por flexão-torção de vigas monossimétricas não prismáticas com secção de parede fina aberta arbitrária. A descrição cinemática adoptada exclui a consideração de fenómenos locais ou distorcionais. O efeito dos deslocamentos de pré-encurvadura é também ignorado. Uma vez que, na prática, é raro encontrar vigas isoladas e com condições de apoio ideais, mostra-se ainda, através de um problema arquétipo, como se pode ter em consideração a presença de elementos de contraventamento. Estes elementos podem (i) restringir a translação, a torção, a rotação em torno do eixo de menor inércia e/ou o empenamento por torção e (ii) ser rígidos ou exibir um comportamento elástico linear. A segunda parte da tese diz respeito a elementos com secção rectangular fina de espessura constante e altura variável. São estudados três problemas de complexidade crescente: (i) a encurvadura lateral por flexão-torção de consolas com altura linearmente variável e submetidas a uma carga pontual transversal aplicada na extremidade livre; (ii) a encurvadura lateral por flexão-torção de consolas (ii1) com variação poligonal da altura e (ii1) submetidas a um número arbitrário de cargas pontuais transversais independentes; (iii) a encurvadura por flexão-torção de colunas-viga em consola com altura linearmente variável, actuadas por uma carga pontual axial e outra transversal, ambas aplicadas na extremidade livre. Estes três problemas são resolvidos analiticamente – obtêm-se soluções exactas para as equações diferenciais que os regem, o que permite estabelecer, também de forma exacta, as equações características para determinar as cargas de encurvadura. No entanto, no terceiro dos problemas elencados, a abordagem analítica só dá frutos numa determinada gama de relações entre as alturas mínima e máxima, sendo necessário recorrer a um procedimento numérico nos restantes casos.

碩士
中原大學
生物環境工程研究所
101
In this study, we examined the 3D free surface profiles with downstream cross section expanded or reduced the least-squares finite element method (LSFEM) has been used to solve the momentum and mass conservation equations. The experimental results were compared with the simulation results and shown in good agreement with each other. The flow phenomena in the open channel with downstream cross-section variation were discussed in detail. 　　By changing the inflow condition, the analysis between the simulation and experimental results stated that channel cross-sectional reduced will produce dramatically changes in water level, especially the water level in the upstream section where water accumulates in the corner. With the larger inlet velocity, the water level increasing phenomenon will be more obvious. 　　The level of free surface at the side walls is larger than at the central of channel when the cross-section is changed. Regardless of the cross-section is gradually expanded or shrunk, with the larger inlet velocity, the lower free surface level.