The double angle connection (sometimes referred to as a cleat connection) is one of the most commonly used simple shear connections, and many investigations have been conducted on this type of connection. However, most of these investigations have focused on either the strength or the moment-rotation relationship under shear loading. Several investigations have recently been performed on the behavior of double angle connections subjected to shear plus axial tensile loads. In these investigations, analytical models and design formulas have been proposed to model the complex behavior of these connections when subjected to the combined loading. However, a complete design model has not been developed. To fulfill the need for a design procedure, double angle connections were studied for three different loading cases. The first case was used to establish the load-displacement relationship under axial tensile loads. The second case was to establish the moment-rotation relationship under shear loads. Finally, the third case was to find the effects of combined axial tensile loads and shear loads on the behavior of double angle connections. For these purposes, 3D-nonlinear finite element models were developed to simulate the connection behavior under the three loading cases. The commercial software package, ABAQUS, was used for the study. The complex phenomena of contact problems and the pretension forces in the bolts were simulated. A simplified angle model and an equivalent spring model were developed from the 3D results. / Ph. D.

The prospects for enhanced Positron Emission Tomography imaging using liquid xenon (LXe) gamma ray detectors had been examined. Monte-Carlo simulations using GEANT4 were performed and the results were used to study the expected performance of a small animal PET scanner in comparison with a simulated conventional small animal scanner (LSO Focus 120). A NEMA-like cylinder phantom and an image contrast phantom were simulated with both scanners to compare performance characteristics. A Compton reconstruction algorithm was developed for the LXe scanner, and its performance and limitations studied.

The prospects for enhanced Positron Emission Tomography imaging using liquid xenon (LXe) gamma ray detectors had been examined. Monte-Carlo simulations using GEANT4 were performed and the results were used to study the expected performance of a small animal PET scanner in comparison with a simulated conventional small animal scanner (LSO Focus 120). A NEMA-like cylinder phantom and an image contrast phantom were simulated with both scanners to compare performance characteristics. A Compton reconstruction algorithm was developed for the LXe scanner, and its performance and limitations studied.

The prospects for enhanced Positron Emission Tomography imaging using liquid xenon (LXe) gamma ray detectors had been examined. Monte-Carlo simulations using GEANT4 were performed and the results were used to study the expected performance of a small animal PET scanner in comparison with a simulated conventional small animal scanner (LSO Focus 120). A NEMA-like cylinder phantom and an image contrast phantom were simulated with both scanners to compare performance characteristics. A Compton reconstruction algorithm was developed for the LXe scanner, and its performance and limitations studied. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The present dissertation contributes to advancing methods of determining the elastic and inelastic buckling resistance of compressive members with single angle and back-to-back double angle cross-sections with end conditions representative of those commonly used in steel construction. The first contribution develops an elastic buckling solution for members with asymmetric sections, such as unequal-leg angle members, connected to gusset plates at both ends and subjected to pure compression. In this case, the gusset plate connections at the member ends provide a fixity restraint to the member within the plane of the gusset and nearly a pin restraint in a plane normal to the gusset. Since both directions do not coincide with the principal directions of the member, the classical flexural-torsional buckling solutions provided in standards become inapplicable. In this context, a variational principle is formulated based on non-principal directions and then used to derive the governing differential equations and associated boundary conditions for the problem. The coupled equations are then solved analytically subject to the boundary conditions, and the characteristic equations are recovered and solved for the flexural-torsional buckling load of the member. The validity of the solutions derived is assessed against 3D shell elastic eigen-value buckling models based on ABAQUS for benchmark cases and the solution is shown to accurately predict the elastic buckling load and mode shapes. The effect of non-principal end restraints on the buckling load of compression members is then investigated for members with angle and zed cross-sections in a parametric study. It is observed that when a member end is fixed about a non-principal direction and pinned about the orthogonal direction, the flexural-torsional buckling load of the member is significantly influenced by the angle of inclination between the fixity axis and the minor principal axis. The second contribution aims to obtain the inelastic buckling resistance for single angle compression members with end gusset plate connections by taking into consideration the effects of material and geometric nonlinearity, initial out-of-straightness, residual stresses, and load eccentricity induced by the offset of the member centroidal axis from the end gusset plate connection. Towards this goal, a series of 3D shell models based on ABAQUS are developed and validated through comparisons against experimental results by others and then used to generate a database of compressive capacities for over 900 eccentrically loaded angle members with various geometrical dimensions and load eccentricities. The database is then used to investigate the effect of slenderness ratio, leg width ratio, connected leg width-to-thickness ratio and gusset plate-to-angle thickness ratio on the compressive resistance of the members, assess the accuracy of solutions available in present design standards, and develop improved design expressions for the compressive resistance for the members. The third contribution develops solutions for predicting the elastic buckling resistance of back-to-back double angle assemblies with end gusset plates and intermediate interconnectors subjected to compressive loads. Towards this goal, two novel models are developed. (1) A thin-walled finite element buckling solution is formulated and implemented into a MATLAB code. The formulation treats each angle member as a line of 1D thin-walled beam elements where then both angle members are connected at intermediate points along the span at the locations of interconnectors. The formulation is equipped with a multi-point constraint feature to enforce the kinematic constraints at the interconnector locations and at both extremities of the member. The model captures the tendency of both angles to open relative to one another in between interconnectors while undergoing flexural-torsional buckling. (2) An analytical buckling solution is developed for the limiting case where enough interconnectors are provided between members to force the two angles to essentially behave as a monolithic entity. The resistance predicted by the former model was then shown to asymptotically approach that predicted by the later model as the number of interconnectors is increased. The validity of the finite element model is assessed against 3D shell models based on ABAQUS and published experimental results, and then used to assess the validity of present design rules based on the effective slenderness concept. The present models are then used to carry out a parametric study of 1250 runs while varying the member slenderness ratio, leg width ratio, connected leg width-to-thickness ratio, and angle spacing-to-thickness ratio. The database of results generated is used to develop a simple expression to characterize the elastic buckling load/stress of the assembly. The possible integration of the new expression with present design provisions in standards to predict the inelastic buckling resistance of the member is illustrated through a design example.

No description available.

Barras compostas em dupla cantoneira são constituídas por duas seções idênticas dispostas paralelamente, afastadas entre si e ligadas uma a outra apenas em alguns pontos ao longo do comprimento, por meio de chapas separadoras. O sistema aqui apresentado é bastante utilizado, principalmente em estruturas treliçadas leves, no entanto, não existem estudos específicos sobre seu comportamento, como conseqüência as normas de cálculo não fornecem subsídios para o projeto desse componente estrutural. É relevante estudar o comportamento de barras em dupla cantoneira, já que neste caso, além dos modos de instabilidade associados à cantoneira isolada, poderão ocorrer modos de instabilidade associados à barra composta em função da presença das chapas separadoras, que tendem a modificar o comportamento do sistema. Apresenta-se no trabalho análises numérica e experimental sobre o comportamento de barras submetidas à compressão centrada e excêntrica. Nas análises variou-se o número de chapas separadoras buscando estudar a eficiência das mesmas na força normal resistente das barras. Os resultados mostraram que a introdução de chapas separadoras melhorou significativamente o comportamento das barras, principalmente para compressão excêntrica. Foram observados modos de instabilidade por flexo-torção, por flexão e combinação dos dois modos. Para comparação dos resultados, inicialmente foram adotadas duas hipóteses de cálculo com base no procedimento da ABNT NBR 14762:2010, considerando compressão centrada. No primeiro procedimento considerou-se cada cantoneira como uma barra isolada independente da presença das chapas separadoras, admitiu-se instabilidades local, por flexo-torção e por flexão; no segundo considerou-se barra composta admitindo-se apenas instabilidades local e por flexão em relação ao eixo principal de menor inércia do conjunto. Em geral, os resultados das análises numérica e experimental apresentaram valores intermediários aos obtidos pelas duas hipóteses adotadas inicialmente. Com os resultados obtidos nas análises numérica e experimental são recomendados procedimentos para o dimensionamento desse componente estrutural. / Double-angle members with batten plates consist of two identical angles set up in parallel, spaced apart, and connected to each other by batten plates at specified points along the length. The system presented herein is widely used, especially in light truss structures; however, there are no standard design procedures specific for the design of this structural component. Studying the behavior of double angle members is interesting, because in this case, besides the critical modes of the single angle, they also show critical modes, due to the presence of the batten plates that sometimes interfere with the behavior of the system. This work presents a numerical and experimental study of members under concentric and eccentric axial compression. The number of batten plates is changed to study the influence on the nominal axial strength. The use of batten plates significantly increases the strength of the system, especially for members under eccentric compression. The buckling modes observed were flexural-torsional, flexural and combination of the modes. Initially, two design hypotheses are compared to the results obtained: (i) non-composite action (no interaction between angles), with only local, flexural, and flexural-torsional buckling considered; (ii) composite action (full interaction between angles), and only considering local and minor-axis flexural buckling of the pair of angles. The two design hypotheses ignore load eccentricity. The hypotheses are based upon recommendations in ABNT NBR 14762:2010. In general, numerical and experimental results for angles connected by bolted batten plates fall in between the design curves defined by methods (i) and (ii). With the results obtained in numerical and experimental analysis, procedures are recommended for the design of this structural component.

Barras compostas em dupla cantoneira são constituídas por duas seções idênticas dispostas paralelamente, afastadas entre si e ligadas uma a outra apenas em alguns pontos ao longo do comprimento, por meio de chapas separadoras. O sistema aqui apresentado é bastante utilizado, principalmente em estruturas treliçadas leves, no entanto, não existem estudos específicos sobre seu comportamento, como conseqüência as normas de cálculo não fornecem subsídios para o projeto desse componente estrutural. É relevante estudar o comportamento de barras em dupla cantoneira, já que neste caso, além dos modos de instabilidade associados à cantoneira isolada, poderão ocorrer modos de instabilidade associados à barra composta em função da presença das chapas separadoras, que tendem a modificar o comportamento do sistema. Apresenta-se no trabalho análises numérica e experimental sobre o comportamento de barras submetidas à compressão centrada e excêntrica. Nas análises variou-se o número de chapas separadoras buscando estudar a eficiência das mesmas na força normal resistente das barras. Os resultados mostraram que a introdução de chapas separadoras melhorou significativamente o comportamento das barras, principalmente para compressão excêntrica. Foram observados modos de instabilidade por flexo-torção, por flexão e combinação dos dois modos. Para comparação dos resultados, inicialmente foram adotadas duas hipóteses de cálculo com base no procedimento da ABNT NBR 14762:2010, considerando compressão centrada. No primeiro procedimento considerou-se cada cantoneira como uma barra isolada independente da presença das chapas separadoras, admitiu-se instabilidades local, por flexo-torção e por flexão; no segundo considerou-se barra composta admitindo-se apenas instabilidades local e por flexão em relação ao eixo principal de menor inércia do conjunto. Em geral, os resultados das análises numérica e experimental apresentaram valores intermediários aos obtidos pelas duas hipóteses adotadas inicialmente. Com os resultados obtidos nas análises numérica e experimental são recomendados procedimentos para o dimensionamento desse componente estrutural. / Double-angle members with batten plates consist of two identical angles set up in parallel, spaced apart, and connected to each other by batten plates at specified points along the length. The system presented herein is widely used, especially in light truss structures; however, there are no standard design procedures specific for the design of this structural component. Studying the behavior of double angle members is interesting, because in this case, besides the critical modes of the single angle, they also show critical modes, due to the presence of the batten plates that sometimes interfere with the behavior of the system. This work presents a numerical and experimental study of members under concentric and eccentric axial compression. The number of batten plates is changed to study the influence on the nominal axial strength. The use of batten plates significantly increases the strength of the system, especially for members under eccentric compression. The buckling modes observed were flexural-torsional, flexural and combination of the modes. Initially, two design hypotheses are compared to the results obtained: (i) non-composite action (no interaction between angles), with only local, flexural, and flexural-torsional buckling considered; (ii) composite action (full interaction between angles), and only considering local and minor-axis flexural buckling of the pair of angles. The two design hypotheses ignore load eccentricity. The hypotheses are based upon recommendations in ABNT NBR 14762:2010. In general, numerical and experimental results for angles connected by bolted batten plates fall in between the design curves defined by methods (i) and (ii). With the results obtained in numerical and experimental analysis, procedures are recommended for the design of this structural component.

<p>This report describes an annual line detection algorithm for the WoodEye quality control system. The goal with the algorithm is to find the positions of annual lines on the four surfaces of a board. The purpose is to use this result to find the inner annual ring structure of the board. The work was done using image processing techniques to analyze images collected with WoodEye. The report gives the reader an insight in the requirements of quality control systems in the woodworking industry and the benefits of automated quality control versus manual inspection. The appearance and formation of annual lines are explained on a detailed level to provide insight on how the problem should be approached. A comparison between annual rings and fingerprints are made to see if ideas from this area of pattern recognition can be adapted to annual line detection. This comparison together with a study of existing methods led to the implementation of a fingerprint enhancement method. This method became a central part of the annual line detection algorithm. The annual line detection algorithm consists of two main steps; enhancing the edges of the annual rings, and tracking along the edges to form lines. Different solutions for components of the algorithm were tested to compare performance. The final algorithm was tested with different input images to find if the annual line detection algorithm works best with images from a grayscale or an RGB camera.</p>

Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, Product-Sum Identities and Sum-Product Identities. These formulas provide effective tools to solve the problems in trigonometry. Chapter 2 handles the most important two theorems in trigonometry: The laws of sines and cosines and show how they can be applied to derive many well known theorems including: Ptolemy¡¦s theorem, Euler Triangle Formula, Ceva¡¦s theorem, Menelaus¡¦s Theorem, Parallelogram Law, Stewart¡¦s theorem and Brahmagupta¡¦s Formula. Moreover, the formulas of computing a triangle area like Heron¡¦s formula and Pick¡¦s theorem are also discussed. Chapter 3 deals with the method of superposition, inverse trigonometric functions, polar forms and De Moivre¡¦s Theorem.