[pt] A utilização de estruturas espaciais metálicas como solução estrutural para cobertura de edificações no Brasil tem sido cada vez mais difundida.Esses sistemas são basicamente compostos pela união de barras através de nós de ligação, formando uma malha tridimensional de barras no espaço. A principal diferença existente entre os vários sistemas espaciais metálicos até hoje desenvolvidos corresponde principalmente aos diferentes tipos de nós de ligação adotados. A complexidade dos diferentes tipos de nós de ligação tem sido o principal fator diferencial de custo entre cada sistema. No Brasil, por motivos econômicos o tipo de nó de ligação mais utilizado é o de ponta amassada.O nó de ligação de ponta amassada é o mais simples e mais barato para ser fabricado, porém, possui duas desvantagens principais: este tipo de nó gera o aparecimento de excentricidades na aplicação dos esforços e provoca a redução de inércia nas extremidades das barras, devido ao processo de amassamento. As normas geralmente adotadas para o dimensionamento de estruturas espaciais metálicas [2, 11, 20] ainda não consideram adequadamente os efeitos da redução de inércia e das excentricidades. Tem sido cada vez mais freqüente a constatação de problemas de instabilidade estrutural em obras recentes, que podem causar colapsos parciais ou até mesmo totais. Estes fatos motivaram o estudo do comportamento estrutural dos nós de ligação com pontas amassadas, observando a influência da redução de inércia nas extremidades das barras e das excentricidades na resistência global das estruturas. Inicialmente apresenta-se um breve histórico dos sistemas estruturais espaciais metálicos, seguido de uma descrição dos principais nós de ligação existentes. A seguir são apresentadas informações gerais sobre a classificação dos diferentes tipos de treliças espaciais mais utilizados. Em seguida são descritos e apresentados três séries de ensaios, realizados em escala real, visando o estudo do comportamento estrutural e a avaliação de reforços estruturais com o objetivo de aumentar a capacidade de carga,diminuir os deslocamentos ou recuperar uma estrutura que apresente subdimensionamento.Finalmente os resultados são comparados com valores de projeto recomendados pelas normas de projeto de estruturas de aço. / [en] The use of spatial structures as a natural structural system for long spans is becoming more frequent in Brazil. These structural systems, basically composed of bars and nodes, enable the development of a very efficient tri- dimensional mesh. The main difference between the major spatial systems is associated with the adopted structural connections being the node complexity the main factor for the cost difference between each system.In Brazil, by economic reasons, the most adopted connections uses the end- flattened bar converging into the node connected with a single bolt. This type of joint is the simplest and cheaper to be manufactured, but it has two main disadvantages, the generated eccentricity force and the bar`s inertia reduction due to the flattening process.Nowadays the structural design codes still do not properly tackles the inertia reduction and eccentricities effects previously mentioned. On the other hand, structural instability problems that can cause local or even global collapses have being more frequently noticed in recently executed structures. This was the main motivation for the investigation of the structural behaviour of spatial structures with flattened edges connections.A brief history of spatial structural systems is initially presented, followed by a description of the more usual splice joints. This is followed by a general description of the spatial trusses use and classification. This work continues with a depiction of an experimental program, consisting of three series of full-scale tests was performed to enlighten the structural behaviour. This work also presents a study of the structural reinforcements; created to improve the structural load capacity, minimize deflections or recuperate structures under-designed. Finally the experimental results are compared with design codes provisions.

<p> An oblique four bar structural model with fixed member ends, being the most general building for space frames, is analysed under free and steady-state vibrations, using discrete mass method. </p> <p> Experimental techniques for measurement of free and steadystate vibrations are described. </p> <p> Experimental results have been compared against analytical ones. </p> / Thesis / Master of Engineering (MEngr)

<p> An oblique four bar structural model with fixed member ends, being the most general building block for space frames, is analysed for establishing its influence coefficients, using the Finite Element Matrix Method. </p> <p> Experimental techniques for measurement of the flexibility influence coefficients of the model are described. </p> <p> Experimental results have been compared against analytical ones. </p> / Thesis / Master of Engineering (MEngr)

[pt] As estruturas espaciais tubulares padronizadas vem sendo cada vez mais utilizadas na construção civil brasileira; observa-se porém, que o tipo das ligações que comumente estão presentes nestas construções são as do tipo excêntrica com ponta amassada, decorrentes do baixo custo econômico que estas oferecem. Pouco se sabe sobre o comportamento estrutural destas ligações, já que as normas que geralmente são adotadas para o cálculo das resistências das barras componentes do reticulado não levam em consideração a redução de inércia que é feita nas extremidades destas para a formação deste tipo de ligação. A não consideração da redução da inércia nas extremidades das barras tem levado à constatação de que é cada vez mais freqüente a presença de problemas de instabilidade estrutural que pode levar ao colapso parcial ou até mesmo total da estrutura. Por outro lado ainda existem estudos que comprovem a veracidade das hipóteses de cálculo que foram assumidas para este tipo de ligação. Com o objetivo de melhor compreender este comportamento, são abordados neste trabalho alguns aspectos estruturais e construtivos das estruturas metálicas espaciais, através de uma série de ensaios experimentais. Inicialmente apresenta-se um breve histórico dos sistemas estruturais. Isto é seguido de informações gerais a respeito da classificação das estruturas espaciais e do tipo de ligação mais usadas. A seguir é feito um estudo dos programas existentes na PUC-RIO e que foram utilizados para à análise estrutural da treliça espacial a ser ensaiada. Apresenta-se também um breve roteiro de cálculo para uma cobertura em treliça espacial. Finalmente são apresentados resultados experimentais de testes em escala real de uma estrutura de 12,0 x 12,0 m, avaliando os modos de ruínas presentes. Estes resultados são confrontados com os valores das resistências nominais de projeto seguindo as recomendações de norma. / [en] This work presents an investigation of the structural behaviour of tubular space trusses composed of continuous end flattened members stacked above each other and joined together by a single bolt. One of the main motivations for this work comes from the fact that this structural solution is very commonly used in Brazil. The main reasons for that are the economy achieved in fabrication and the simplicity of erection associated with that structural solution. This solution also proves to be competitive when compared to other commercial systems. On the other hand, the structural design of these trusses are still subjected to some criticism since the loss of stiffness in the bars´ extremities is not taken into account. To enlighten this problem a full-scale experimental programme was performed in a 12m x 12m space structure. The adopted structure consisted of a diagonal on square mesh with top and bottom chord members of 2000mm and 1414mm and a 1500mm mesh height. The aim of the this programme was to investigate the ultimate compression resistance of the structural members taking into account the effect of the flattened ends and the type of connection used. The experiments ranged from tests where all the structural nodes used a single eccentric bolt to others where plated connectors were used in the supports to eliminate second- order moments. The experimental results demonstrated that the ultimate resistance of the structure with the eccentric connections only presented a small reduction when compared to other non-eccentric systems. The tests also confirmed that the flattened end of the members and the geometric characteristics of plated connectors are very significant parameters in the structure´s ultimate behaviour. / [es] Las extructuras espaciales tubulares padronizadas han ganado mayor espacio en la construcción civil brasilera. No obstante, se observa que en estas construcciones, conmúnmente se utilizan uniones tipo excéntrica con punta suavizada, debido a su bajo costo. Poco se sabe sobre el comportamiento extructural de estas uniones, ya que las normas que generalmente se adoptan para el cálculo de las resistencias de las barras que componen el reticulado no consideran la reducción de inercia en las extremidades de las barras para la formación de este tipo de unión. Se ha constantado que al no considerar la reducción de la inercia en las extremidades de las barras aparecen com mayor frecuencia problemas de inestabilidad extructural que pueden llevar al colapso parcial o incluso total de la extructura. Por otro lado, existen estudios que comprueban la veracidad de las hipótesis de cálculo que fueron asumidas para este tipo de unión. Con el objetivo de comprender mejor este comportamiento, se abordan en este trabajo algunos aspectos extructurales y constructivos de las extructuras metálicas espaciales, a través de una serie de ensayos experimentales. Inicialmente se presenta un breve histórico de los sistemas extructurales, con informaciones generales sobre clasificación de las extructuras espaciales y los tipos de unión más usadas. Seguidamente se presentan los programas existentes en la PUC-RIO que fueron utilizados para el análisis extructural de la celosía espacial que sería ensayada. Se presenta también un breve algoritmo para el cálculo para una cobertura en celosía espacial. Finalmente se presentan los resultados experimentales de pruebas en escala real de una extructura de 12,0 x 12,0 n, evaluando los modos de ruínas presentes. Estes resultados se comparan con los valores de las resistencias nominales del proyecto siguiendo las recomendaciones de la norma.

[pt] Este trabalho tem como objetivo principal a aplicação do método híbrido dos elementos de contorno a problemas da mecânica da fratura linearmente elástica. São apresentados os desenvolvimentos de várias formulações e os principais aspectos das implementações computacionais referentes a cada uma delas. A consistência mecânica do método híbrido dos elementos de contorno facilita sobremaneira a compreensão dos diversos fatores envolvidos em sua aplicação à mecânica da fratura. Isto ocorre porque o apelo físico do método garante a interpretação adequada dos problemas presentes na análise dos mais diversos fenômenos da mecânica do contínuo. A contribuição mais relevante deste trabalho consiste na determinação de maneira rápida e direta do fator de intensidade de tensão em estruturas bidimensionais da elasticidade plana. Os efeitos de abertura e deslizamento das faces da trinca são considerados a partir da introdução de uma solução fundamental hipersingular, cujo entendimento físico é facilitado devido à consistência variacional do método híbrido. É proposta a utilização de uma função de Green, referente à série de Williams, nos nós do modelo estrutural correspondentes às pontas das trincas. Esta sistemática introduz os fatores de intensidade de tensão, modos I e II, como incógnitas do problema, sendo obtidos a partir da resolução do sistema de equações provenientes do método. Durante todo o desenvolvimento, são mostrados vários exemplos que validam e comprovam a aplicabilidade das formulações propostas, demonstrando a potencialidade do método quando aplicado à mecânica da fratura. / [en] Aim of this work is the application of the hybrid boundary element method to problems of the linear elastic fracture mechanics. Several formulations are introduced and the most relevant aspects of computational implementation are discussed. The mechanical consistency of the hybrid boundary element method enables the adequate mathematical description of the stress field related to a cracked continuum. The main attempt of this dissertation is to develop a computationally simples and fast procedure for the determination of stress intensity factors in two- dimensional elasticity. The effects of opening and sliding of the crack surfaces are considered by means of a hipersingular stress function, which are dealt with adequately in the frame of the variational formulation. It is shown that the stress series proposed by Williams for the local field around a crack tip may be considered as a Green´s function. As a consequence, the stress intensity factors corresponding to both Modes I and II are obtained as primary unknowns of the problem. Several numerical examples are presented in order top validate the formulations proposed. This shows the potentiality of the hybrid boundary element method for dealing with problems of the fracture mechanics. / [es] Este trabajo tiene como objetivo principal la aplicación del método híbrido de los elementos de contorno a problemas de mecánica de fracturas linealmente elásticas. Se describen varias formulaciones y los principales aspectos de su implementación computacional. La consistencia mecánica del método híbrido de los elementos de contorno facilita la comprensión de los diversos factores involucrados en su aplicación a la mecánica de fracturas. Esto ocurre porque el caracter físico del método garantiza la interpretación adecuada de los problemas que se presentan en el análisis de los más diversos fenómenos de la mecánica del contínuo. La contribuición más relevante de este trabajo consiste en la determinación de manera rápida y directa del factor de intensidad de tensión en extructuras bidimensionales de elasticidad plana. Son considerados los efectos de abertura y deslizamiento de las caras de la trinca a partir de la introducción de una solución fundamental hipersingular, cuya comprensión física se facilita debido a la consistencia variacional del método híbrido. Se propone la utilización de una función de Green, de la serie de Williams, en los nodos del modelo extructural correspondiente a las puntas de las trincas. Esta sistemática introduce los factores de intensidad de tensión, modos I y II, como incógnitas del problema, y se obtienen a partir de la resolución del sistema de ecuaciones provenientes del método. Durante todo el desarrollo, se muestran varios ejemplos que evalúan y comprueban la aplicabilidad de las formulaciones propuestas, demostrando la potencialidad del método cuando se aplica a la mecánica de fracturas.

Space structures are inevitable while covering large spans. Space structures are skeletal structures, which are lighter for the same stiffness when compared with RCC roofs. Till now, space structures, like any other metal structures have been designed assuming the joints as rigid, although there have been several publications about semi rigid joints. Of course, the publications mostly deal with 2D structures and there are very few reports on 3D structures. Space structures, by their nature fall into the latter category. The joints in a space structure are popularly called as "nodes". Generally, nodes, which ensure concentricity of member axes, are either solid or hollow. These are either cast or forged. There are other proprietary types, which do not come under the above classification, and have not been considered in this thesis. Hollow nodes are obviously more economical than solid nodes, but also more flexible. While it is prudent to prefer hollow nodes, it is equally necessary to assess their flexibility, because of its influence on the behaviour of the structure. The hollow spherical node is very popular because of its simplicity and adaptability to various forms of space frames. Double layer grids, which are the most popular forms for roofing applications, are being increasingly implemented. While the hollow spherical node is well suited for double layer grids, an evolutionary development has been what is called as the hollow octahedral node (this node is simply referred to as the 'Octa ' node in this thesis). Chapter 1 introduces space frames and double layer grids in particular, with the advantages of using double-layer grids. Jointing systems available around the world are briefed and the node connector used in the present study is introduced with a brief write-up on its advantages and disadvantages. This chapter also explores the available literature and, the scope and objectives of the thesis are mentioned. Chapter 2 introduces 3D finite element models of the hollow spherical and octahedral nodes. The stiffness matrixes of these nodes have been derived by conducting analyses on the computer for six sizes each of the Octa and spherical nodes. Using the stiffness matrix of the node, a new method of incorporating this into the regular analysis of a space truss has been developed. The new method proposed yields realistic values for the forces in the members and takes into account the elastic deflections in the node under the action of member forces. Implementation of the proposed method has been carried out by writing a custom program using state-of-the-art object oriented programming techniques. A sample problem has been analyzed using this program to demonstrate the effect of including joint flexibility. The effect of flexibility of nodes on the effective length of compression members in double-layer grids has been evaluated. The effect of compliance on the dynamic characteristics of a space frame has also been evaluated for the sample space frame with flexible joints. The analysis program has been modified to evaluate the natural frequencies of the system using rigid or flexible nodes. The study of the Octanode and spherical node under the action of uniaxial compression and tension dominates the contents of Chapter 3. The two types of nodes have been analyzed using commercially available finite element software considering material nonlinearity. The stress patterns from the analyses have been examined thoroughly. Two consistent methods for fixing the load at yield in both uniaxial compression and tension have been proposed using the load-displacement curve. Yield loads for all the nodes have been evaluated using both the methods and the results agree well between the two methods. Three material yield values have been selected for each of the node size for evaluating the yield values viz. 240,320 and 415 MPa. The members of a double layer grid are connected to the nodes by bolts and holes are drilled in the nodes for this purpose. The bolthole patterns differ between two popular types of double-layer grids. Both these bolthole patterns have been modeled separately in the above exercise and the results for these two have been shown to be approximately the same. The effect of varying diameters of the boltholes on the response of the nodes has been examined. Relationships between the yield load, diameter, thickness and material yield have been developed using the method of least squares. The differences in the behaviour of the nodes under uniaxial compression and tension have been discussed. Ramberg Osgood type of relationships have been worked out for all the load-displacement curves obtained from the analyses. The simulation of non-linear behaviour of nodes with cracks with plastic crack closing forces have been carried out with useful insights into the behaviour of the two types of nodes in uniaxial compression and tension. Chapter 4 is devoted largely for studying the two types of nodes under the influence of biaxial load combinations. The combinations studied are dual compression, dual tension and compression-tension. In all cases equal loads are applied along two orthogonal; directions in the horizontal plane. Stress patterns have been examined for each type of load combination and yield values for each case have been obtained using one of the methods proposed in chapter 3. These have been compared with the corresponding uniaxial values in both compression and tension. Some useful inferences have been possible by studying the behaviour of the nodes under the various biaxial load combinations. In each case, relationships between the biaxial yield load, uniaxial yield load, diameter of node, thickness of node and material yield of node have been obtained using the method of least squares. The nodes have been analyzed under some selected Multi-axial loading and combinations of load which cause yield based on the second method proposed in Chapter 3 have been obtained and tabulated. However, a proper and thorough study of the nodes under multi-axial loading proved to be beyond the scope of this thesis. Chapter 5 contains the contributions made towards developing new methods and algorithms for obtaining the several results of chapters 2, 3 and 4, using object oriented programming (OOP) techniques. The contributions have been in Object Pascal, the underlying language of Delphi, a popular RAD tool developed by Borland/Inprise of USA. Several new modules have been developed to reliably handle the large amounts of data generated by the hundreds of analyses detailed in chapters 2,3 and 4. The ease with which new methods were possible to be incorporated into existing software using OOP has been demonstrated, with source code examples. Comparisons with other types of tools available and die advantages of using OOP have also been demonstrated using the experience during the preparation of this thesis. A strong case for OOP as an indispensable tool for the researcher has been made. Chapter 6: Several important conclusions and suggestions for future work have been made. Appendix 1 contains a brief note on the Method of Least Squares. Appendix 2 contains a small write-up on Delphi and OOP. Concepts of OOP have been briefly described and comparisons between three popular OOP languages have been attempted. A brief description of the features in Delphi's Object Pascal has also been provided. Appendix 3 contains the listing of Unit Arrays, which is a general purpose unit developed to make handling of large arrays easy. Several matrix calculations have been implemented which make the unit extremely useful for programmers. Appendix 4 contains the full listing of program FormK, which has been developed for chapter 2 to derive the fall stiffness matrix of a space frame node. The program picks up results from several analyses, forms a few columns of the stiffness matrix and then fills up the rest using the cyclic symmetry present in the space frame node. This program is given in full, with the intention that other researchers may find it useful to use it as-is or use after making small alterations to suit their circumstances. OOP is known for fast, reliable and easy ways of implementing modifications to existing code. Appendix 5 provides the full listing of the Object Pascal program for extracting Eigenvalues of a space truss with rigid joints or flexible joints. The incorporation of flexibility of the joints proposed in chapter 2 has been implemented. Descriptions of the program's implementations have been provided in chapter 5. Bibliography contains the alphabetical list of references.