In real conditions, a great majority of machine and structure elements and parts (shafts, pins, axis, etc.) are subjected to bending. That’s why the study of elastic plastic bending has a wide engineering science background and a very broad field of application. This work presents analytical research of elastic plastic pure bending of rectangular cross-section element. The simple power relation expresses stress strain curve in the region of uniform plastic deformation. Derived mathematical relations allow to calculate deviation of dimensionless stress neutral axis from symmetry axis of an element and dimensionless pure bending moment versus monotonic strain. Theoretical curves for different material constants are drawn. Theoretical curves of dimensionless pure bending moment give tolerable coincidence with experimental date. Derived relationships can be also fitted to analysis of rectangular cross-section element loaded by low cycle pure bending.

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.

The objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castigliano's second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the spring's stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the spring's geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castigliano's second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the spring's axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented. / Master of Science

<p> An experimental study of turbulent flow of air around a 90º bend is reported in this thesis. Four 90º bends of aspect ratio 1, 3, 5 & 10 and radius ratio 1.0 have been tested in the Reynolds number range of 1 × 10⁵ to 5 × 10⁵. The loss in total pressure across the bend (or elbow) is reported for two discharge conditions (1) and the elbow discharging to a plenum chamber through a constant area duct of a length equal to 4 hydraulic diameters; (2) the elbow discharging to the plenum chamber directly. A comparison of the experimental results is made with the curves given in NACA report L4F26 which have been reproduced in the recently published SAE Aero-Space Manual. </p> <p> Various other flow parameters, such as velocity profiles, turbulence levels and pressure distributions are also given in this thesis. </p> / Thesis / Master of Engineering (ME)

Os Polímeros Reforçados com Fibras (PRF) são materiais compósitos constituídos por fibras unidas por uma matriz polimérica. São leves, não corrosivos, possuem alta resistência à tração e são de simples execução. O PRF em forma de tecido é utilizado para envolver o pilar de concreto armado promovendo a restrição das deformações laterais pelo efeito de membrana. Nos pilares com seção transversal circular, esse efeito de membrana é desenvolvido ao longo de todo o seu perímetro. Já para seções quadradas ou retangulares, esse efeito de membrana se desenvolve apenas nos cantos arredondados, reduzindo, assim, a eficiência do confinamento. Por conta dessa limitação, esta pesquisa propõe a utilização de um mecanismo auxiliar constituído por tirantes transversais de aço ancorados por perfis longitudinais, que juntamente com o PRF vão promover o confinamento nos maiores lados de seções de pilares retangulares. Foram realizados ensaios experimentais de dez pilares de concreto, cujos resultados confirmaram o maior incremento de força e ductilidade nos pilares devido à presença dos tirantes, verificando também que os perfis longitudinais contribuem diretamente com a força axial no pilar. Por meio da análise numérica em elementos finitos foi possível observar o acréscimo de regiões de concreto efetivamente confinado devido à presença dos tirantes. Com a análise paramétrica realizada foram identificados os parâmetros e como eles influenciam no comportamento dos pilares reforçados com a técnica: a relação entre os lados da seção transversal, a taxa de PRF; a taxa de tirantes de aço e a rigidez do perfil de ancoragem. Por fim, foi desenvolvido um modelo analítico que possibilita calcular a parcela de força resistida pelo concreto confinado e pelos perfis de ancoragem de modo independente, indicando boas correlações com os resultados experimentais e numéricos. / Fiber Reinforced Polymers (FRP) are composite materials consisting of fibers bonded by a polymer matrix. They are lightweight, non-corrosive, have high tensile strength and simple to apply. The FRP jacket is used to wrap the concrete column and restrict the lateral expansion by the membrane effect. In columns with circular cross section, the membrane effect is developed along its entire perimeter. However, in square or rectangular sections this effect is only developed at the rounded corners, resulting in a decrease of the confinement efficiency. Due this limitation, this research proposes the use of an auxiliary mechanism made up of transverse steel ties anchored by longitudinal bars, which together with the FRP, promote confinement on the biggest sides of rectangular sections of columns. Experimental tests were carried out on ten concrete columns, whose results confirmed the greatest force increase and ductility due to the presence of the steel ties and that the anchor bars contribute directly with the axial force. Through the numerical analysis in finite elements methods it was possible to observe the effective confined concrete regions due to the presence of the ties. With the parametric analysis performed some parameters were identified and how they influence in behavior of columns reinforced with this technique: the relationship between the sides of the cross section; the PRF rate; the steel ties rate and the stiffness of the anchor bar. Finally, an analytical model was developed allowing calculate the force resisted by the confined concrete and the anchor bars forces independently, indicating good correlations with the experimental and numerical results.

Os Polímeros Reforçados com Fibras (PRF) são materiais compósitos constituídos por fibras unidas por uma matriz polimérica. São leves, não corrosivos, possuem alta resistência à tração e são de simples execução. O PRF em forma de tecido é utilizado para envolver o pilar de concreto armado promovendo a restrição das deformações laterais pelo efeito de membrana. Nos pilares com seção transversal circular, esse efeito de membrana é desenvolvido ao longo de todo o seu perímetro. Já para seções quadradas ou retangulares, esse efeito de membrana se desenvolve apenas nos cantos arredondados, reduzindo, assim, a eficiência do confinamento. Por conta dessa limitação, esta pesquisa propõe a utilização de um mecanismo auxiliar constituído por tirantes transversais de aço ancorados por perfis longitudinais, que juntamente com o PRF vão promover o confinamento nos maiores lados de seções de pilares retangulares. Foram realizados ensaios experimentais de dez pilares de concreto, cujos resultados confirmaram o maior incremento de força e ductilidade nos pilares devido à presença dos tirantes, verificando também que os perfis longitudinais contribuem diretamente com a força axial no pilar. Por meio da análise numérica em elementos finitos foi possível observar o acréscimo de regiões de concreto efetivamente confinado devido à presença dos tirantes. Com a análise paramétrica realizada foram identificados os parâmetros e como eles influenciam no comportamento dos pilares reforçados com a técnica: a relação entre os lados da seção transversal, a taxa de PRF; a taxa de tirantes de aço e a rigidez do perfil de ancoragem. Por fim, foi desenvolvido um modelo analítico que possibilita calcular a parcela de força resistida pelo concreto confinado e pelos perfis de ancoragem de modo independente, indicando boas correlações com os resultados experimentais e numéricos. / Fiber Reinforced Polymers (FRP) are composite materials consisting of fibers bonded by a polymer matrix. They are lightweight, non-corrosive, have high tensile strength and simple to apply. The FRP jacket is used to wrap the concrete column and restrict the lateral expansion by the membrane effect. In columns with circular cross section, the membrane effect is developed along its entire perimeter. However, in square or rectangular sections this effect is only developed at the rounded corners, resulting in a decrease of the confinement efficiency. Due this limitation, this research proposes the use of an auxiliary mechanism made up of transverse steel ties anchored by longitudinal bars, which together with the FRP, promote confinement on the biggest sides of rectangular sections of columns. Experimental tests were carried out on ten concrete columns, whose results confirmed the greatest force increase and ductility due to the presence of the steel ties and that the anchor bars contribute directly with the axial force. Through the numerical analysis in finite elements methods it was possible to observe the effective confined concrete regions due to the presence of the ties. With the parametric analysis performed some parameters were identified and how they influence in behavior of columns reinforced with this technique: the relationship between the sides of the cross section; the PRF rate; the steel ties rate and the stiffness of the anchor bar. Finally, an analytical model was developed allowing calculate the force resisted by the confined concrete and the anchor bars forces independently, indicating good correlations with the experimental and numerical results.

The scope of the presented Diploma thesis was the establishment of calculation model for shear design of textile reinforced concrete members with rectangular cross-section. To accomplish this task, it was necessary to acquire the knowledge of the principles of shear design for steel reinforced concrete and existing design methods for textile reinforced concrete. Based on these principles, an experiment was designed as 3-point bending test to obtain values of acting shear force in textile reinforced concrete beams. These beams were filled with textile reinforcement made of carbon and alkali resistant glass and cast in the laboratory of the Solidian Company. An important factor for the experiment design was the a/d ratio which was constant for all tested beams. The value of acting shear force as well as of concrete compressive strength was obtained from each experiment. These values were used for the optimization of mathematical equation for the shear design of textile reinforced concrete members with rectangular cross-section. This equation was first analyzed to gain the knowledge of every influential factor. After, the coefficient CRm,c was determined from the experimental data using the methods of optimization. The problem statement resulted in the formula for shear design of textile reinforced concrete members with rectangular cross-section which may be applied with respect to the conditions of usability of the shear model.

科学研究費補助金 研究種目:一般研究(A) 課題番号:63420036 研究代表者:後藤 俊夫 研究期間:1988-1990年度