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Contribuição para a concepção e dimensionamento de novas estruturas em granito de alta resistência
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O presente trabalho constitui uma contribuição para a conceção de estruturas esbeltas em granito de alta resistência, nomeadamente para estruturas de cascas, vigas, pilares e arcos. São abordados conceitos fundamentais da mecânica aplicada à conceção de estruturas, como é o caso do conceito de força e do conceito de rigidez. As forças são consideradas como resultantes de sistemas de interações magnéticas intermoleculares cuja intensidade se altera com a ocorrência de deslocamentos relativos. O conceito de rigidez é associado à sensibilidade para que se verifiquem variações das intensidades das interações nesses deslocamentos relativos. Tendo por base o facto de as variações de forças estarem associadas a deslocamentos intermoleculares relativos, introduz-se o conceito de fase transitória em desequilíbrio, intervalo de tempo durante o qual a estrutura transita para uma nova configuração e se geram as forças internas equilibrantes. O funcionamento de uma estrutura em equilíbrio é associado a processos de transferência de informação e caminhos de forças, cuja representação faz uso de campos vetoriais e conceitos associados. Os conceitos de rigidez e de caminhos de forças conduzem à ideia de via construtiva de manipulação de rigidez para a conceção de estruturas. O procedimento corresponde à adição de material onde se pretendem criar os caminhos de forças, com manipulação dos parâmetros que influenciam a rigidez, de modo a que o sistema de forças resultante seja adequado às condicionantes presentes. O comportamento mecânico do granito de alta resistência foi estudado, com abordagem dos processos de destruição interna por formação e progressão de fissuras. É proposto que, sob solicitações longitudinais de compressão, as forças transversais de tração nas pontas das fissuras, responsáveis pela progressão, são resultantes do deslocamento relativo das suas faces irregulares encaixadas. Com base nesse modelo são estudados os diferentes fatores que influenciam a progressão de fissuras e, consequentemente, a resistência mecânica à compressão. Esses fatores são, nomeadamente, os gradientes das tensões de compressão, a velocidade do carregamento, a dimensão dos grãos, a composição química do granito e o nível de confinamento transversal. O conceito de “material” é entendido como um sistema estrutural, por exemplo, na forma de mini e micropilares interligados, não se considerando adequada a utilização geral de modelos e teorias idealizadas para domínios homogéneos e contínuos. O equilíbrio de estruturas de cascas é estudado através de campos vetoriais, sendo proposto um procedimento de obtenção de formas anti-funiculares para sistemas de forças internas predefinidos. Em cascas para coberturas, por exemplo, esses sistemas de forças correspondem a projeções horizontais dos esforços de membrana, que se podem associar ao equilíbrio de “parede”, e a sistemas de forças verticais associados a soluções de “laje”. O sistema de forças predefinido apenas se verifica na estrutura resultante através do recurso a pré-esforço, que garante que a fase transitória em desequilíbrio seja mínima. Caso contrário, existe uma dependência dos parâmetros de rigidez e a transição em desequilíbrio que a estrutura tem que verificar implica sempre diferenças entre o sistema de forças predefinido e o resultante. O procedimento proposto difere da obtenção de forma anti-funicular por inversão de membranas suspensas, em que existe dependência da rigidez do sistema. Nesse caso, as soluções podem ainda ser controladas, por exemplo, através da manipulação de rigidez nas zonas de apoio, em contraste com o procedimento alternativo em que o controlo é feito através do pré-esforço. As soluções propostas para pilares e vigas consistem na associação de escoras de cantaria a sistemas laterais de contraventamento na forma de cabos de pré-esforço e escoras de ligação. A rigidez do sistema de contraventamento confere-lhe capacidade de transferência de cargas transversais e resulta em importantes aumentos de carga crítica da escora. A capacidade de carga do conjunto é condicionada pela existência de defeitos de fabrico como, por exemplo, no contacto entre superfícies empenadas ou com rugosidade macroscópica. Para a implementação das soluções torna-se necessário um rigoroso controlo de qualidade no processo de corte e na montagem dos elementos de cantaria. São propostas soluções para pontes de arco articulado com vão da ordem de 250 m, composto por troços retos na forma de escoras de cantaria contraventadas por cabos laterais e escoras transversais de ligação. Nos nós articulados concorrem os troços do arco e os pilares de apoio das vigas do tabuleiro. Nas soluções propostas, a função de equilíbrio de sobrecargas rodoviárias ou ferroviárias é partilhada pelas vigas contínuas do tabuleiro e por sistemas adicionais de rigidez constituídos por cabos de pré-esforço. Essa solução permite reduções importantes das necessidades de rigidez e resistência das vigas do tabuleiro. Para arcos articulados com vãos da ordem dos 250 m sem os referidos sistemas de cabos, essas vigas resultariam demasiado volumosas, com secções transversais de dimensões desproporcionadas relativamente às dos restantes elementos da ponte. As soluções propostas para grandes vãos contrastam com as soluções que resultariam da simples ampliação de soluções “convencionais” de pontes de arco fino de pequenos vãos, que seriam mesmo inviáveis para utilizações mais exigentes como é o caso da utilização ferroviária. O reduzido consumo de material no arco que resulta da adoção dos sistemas laterais de contraventamento e o processo construtivo simplificado de um arco articulado apresentam-se vantajosos, tendo em conta as importantes reduções de peso e a maior adequação à pré-fabricação.
The present work constitutes a contribution for the design of slender structures in high strength granite as shell structures, beams, columns and arches for bridges. Fundamental concepts of mechanics are applied to the design of structures, like the concepts of forces and stiffness, being the basis for the developed work. Forces are considered as resultants of systems of intermolecular magnetic interactions whose intensity varies with the occurrence of relative displacements. The concept of stiffness is associated to the sensitivity of the variation of the interactions intensity with the relative displacements. Because the forces are associated to intermolecular relative displacements, the concept of transitory phase in disequilibrium is introduced, being a time interval in which the structure moves to a new equilibrium configuration and the internal equilibrium forces are generated. The structural equilibrium is associated to information transmission processes and to force paths, whose representation utilizes vector fields and related concepts. The perspective of stiffness and force paths results in an idea of a constructive process of stiffness manipulation in structural design. The procedure corresponds to the addition of the material in which the load paths are generated, with manipulation of the stiffness parameters to warrantee a system of forces that is adequate to the actual conditions. The mechanical behaviour of granite was analysed, essentially in terms of the internal destruction processes by formation and progression of cracks. It is proposed that, under longitudinal compression, the transversal tensile forces in the crack tips, responsible for the progression, are generated by relative displacement of their irregular faces in contact. Based in that proposal, the different factors that have influence in the crack progression, the failure modes and the compressive strength are analysed. Those factors are namely the compression stress gradients, the loading rate, grain size, grain distribution and type and existence of transversal confinement. The concept of “material” is considered as a structural system, composed for example by interconnected micro and mini-pillars, in which is not adequate the “blind” application of “compact” models and theories developed for homogeneous continuum. For the analysis of equilibrium of structural shells vector fields are used. A procedure to obtain anti-funicular shapes for predefined systems of forces is proposed. For roof shells, those systems of forces correspond to horizontal projections of the membrane forces, which can be associated to a “wall equilibrium”, and to systems of vertical forces related to the equilibrium of a slab solution. The predefined system of forces can only occur in the obtained structure through the application of prestress. Otherwise, there exists a stiffness dependency and an unavoidable transition in disequilibrium that originates differences between the predefined and the resultant systems of forces. The proposed procedure differs from the classical shape inversion of suspended membranes, in which there exists a dependency between the forces and the stiffness distribution. In this last case the solutions are influenced by the supports, in contrast with the proposed procedure, where the control is possible through prestress. An innovative solution for columns and beams is proposed, consisting in the association of ashlar struts to lateral bracing systems, composed by prestressing cables and transversal connection struts. The stiffness of the bracing system results in capacity for the equilibrium of transversal loads and results in a significant increase of the critical axial buckling loads. The loading capacity is conditioned by the existence of imperfections like the contact between non-planar or rough surfaces. A rigorous quality control during the cutting process and assembling of the ashlar elements is therefore necessary. In the present work hinged arch solutions with 250 m span are proposed, being composed by ashlar struts braced by lateral cables and transversal steel connection struts. In the hinged nodes the braced struts of the arch and the columns that support the deck are connected. In the proposed solutions the equilibrium of non-uniform traffic loads is distributed between the continuous beams of the deck and additional stiffening systems composed by prestressing cables. Those solutions permit to reduce the needs of stiffness and strength of the deck, which, for big spans, would result too big and with disproportionate dimensions in comparison to the other elements of the bridge. The proposed solution differ from a simple application of scale factors to the “conventional” thin arch and stiff deck bridges, which are normally adequate for smaller spans. Magnified solutions can even result non-viable for long span railway bridges. The reduced material consumption in the arch, due to the transversal bracing systems, and the hinged solution are also advantageous in the construction process, having in consideration the high self-weight reductions and the adequacy for prefabrication and assembling.
The present work constitutes a contribution for the design of slender structures in high strength granite as shell structures, beams, columns and arches for bridges. Fundamental concepts of mechanics are applied to the design of structures, like the concepts of forces and stiffness, being the basis for the developed work. Forces are considered as resultants of systems of intermolecular magnetic interactions whose intensity varies with the occurrence of relative displacements. The concept of stiffness is associated to the sensitivity of the variation of the interactions intensity with the relative displacements. Because the forces are associated to intermolecular relative displacements, the concept of transitory phase in disequilibrium is introduced, being a time interval in which the structure moves to a new equilibrium configuration and the internal equilibrium forces are generated. The structural equilibrium is associated to information transmission processes and to force paths, whose representation utilizes vector fields and related concepts. The perspective of stiffness and force paths results in an idea of a constructive process of stiffness manipulation in structural design. The procedure corresponds to the addition of the material in which the load paths are generated, with manipulation of the stiffness parameters to warrantee a system of forces that is adequate to the actual conditions. The mechanical behaviour of granite was analysed, essentially in terms of the internal destruction processes by formation and progression of cracks. It is proposed that, under longitudinal compression, the transversal tensile forces in the crack tips, responsible for the progression, are generated by relative displacement of their irregular faces in contact. Based in that proposal, the different factors that have influence in the crack progression, the failure modes and the compressive strength are analysed. Those factors are namely the compression stress gradients, the loading rate, grain size, grain distribution and type and existence of transversal confinement. The concept of “material” is considered as a structural system, composed for example by interconnected micro and mini-pillars, in which is not adequate the “blind” application of “compact” models and theories developed for homogeneous continuum. For the analysis of equilibrium of structural shells vector fields are used. A procedure to obtain anti-funicular shapes for predefined systems of forces is proposed. For roof shells, those systems of forces correspond to horizontal projections of the membrane forces, which can be associated to a “wall equilibrium”, and to systems of vertical forces related to the equilibrium of a slab solution. The predefined system of forces can only occur in the obtained structure through the application of prestress. Otherwise, there exists a stiffness dependency and an unavoidable transition in disequilibrium that originates differences between the predefined and the resultant systems of forces. The proposed procedure differs from the classical shape inversion of suspended membranes, in which there exists a dependency between the forces and the stiffness distribution. In this last case the solutions are influenced by the supports, in contrast with the proposed procedure, where the control is possible through prestress. An innovative solution for columns and beams is proposed, consisting in the association of ashlar struts to lateral bracing systems, composed by prestressing cables and transversal connection struts. The stiffness of the bracing system results in capacity for the equilibrium of transversal loads and results in a significant increase of the critical axial buckling loads. The loading capacity is conditioned by the existence of imperfections like the contact between non-planar or rough surfaces. A rigorous quality control during the cutting process and assembling of the ashlar elements is therefore necessary. In the present work hinged arch solutions with 250 m span are proposed, being composed by ashlar struts braced by lateral cables and transversal steel connection struts. In the hinged nodes the braced struts of the arch and the columns that support the deck are connected. In the proposed solutions the equilibrium of non-uniform traffic loads is distributed between the continuous beams of the deck and additional stiffening systems composed by prestressing cables. Those solutions permit to reduce the needs of stiffness and strength of the deck, which, for big spans, would result too big and with disproportionate dimensions in comparison to the other elements of the bridge. The proposed solution differ from a simple application of scale factors to the “conventional” thin arch and stiff deck bridges, which are normally adequate for smaller spans. Magnified solutions can even result non-viable for long span railway bridges. The reduced material consumption in the arch, due to the transversal bracing systems, and the hinged solution are also advantageous in the construction process, having in consideration the high self-weight reductions and the adequacy for prefabrication and assembling.
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Palavras-chave
Engenharia estrutural Estruturas em granito - Concepção Estruturas em granito - Dimensionamento