The University of Sheffield has a non-linear finite element analysis program called VULCAN which has been developed in-house over a number of years and has been thoroughly validated. A parametric study has been conducted using this software, which assesses the influence of such factors as load, geometric imperfection, material properties, temperature profile and axial and rotational restraint on the behaviour, of isolated steel columns in fire. This study is then extended to investigate the behaviour of steel columns as part of a larger multi-storey frame, in which axial restraint to thermal expansion of the heated column is provided by the floors above. A method of modelling these effects in VULCAN using a linear spring element to provide axial restraint has been developed and validated. An experimental partner project has been carried out at the University of Ulster, in which steel columns were furnace-tested with various levels of load, slenderness and axial restraint. These tests have been paralleled with analyses using VULCAN and a good correlation with test results has been shown. The VULCAN program was then used to examine the effects of parameters outside the range of the physical constraints imposed by the test facility. A numerical model, capable of assessing the level of axial restraint imparted on a column by a general multi-storey framed structure has been developed, which has a number of levels of complexity, each giving a higher degree of accuracy. Once the level of restraint for a structure has been assessed, the parametric studies and test data can be applied, and conclusions drawn about the behaviour of the frame. The applicability of different mathematical solution procedures to the analysis of these columns, which exhibit snap-through and snap-back behaviour, has been conducted. The arc-length method has been identified as applicable in such cases and a skeleton version of the procedure introduced into the VULCAN program. The program structure of VULCAN has been improved and the format for data input and output has been developed to allow flexibility. A graphical file-viewer program has also been created. Details of these changes are shown in appendices.

Steel beams with web openings are frequently used in construction to achieve attractive, flexible and optimised design solutions. These beams are used to provide passages for building services, to reduce the overall construction height and to achieve long spans. However, the presence of the openings may lead to a substantial reduction in the load carrying capacity of the beam at both ambient and elevated temperatures and introduce additional failure modes including shear-moment interaction at the location of the openings causing the Vierendeel mechanism. Steel beams in practical construction are axially restrained and the presence of this axial restraint can drastically change the behaviour of the beams in comparison to those without axial restraint. One particular issue is premature buckling of the compressive tee-sections around the openings. The aim of this research is to investigate the effects of openings on axially restrained steel beams at elevated temperatures so as to develop an analytical method for design consideration. The analytical derivation will be based on the results of extensive numerical simulations. The research starts with the behaviour of steel beams with web openings under combined axial compression, bending moment and shear force at ambient temperature. The results show that buckling of the compressive tee-sections at the openings can reduce the plastic moment capacity of the openings; and an analytical method has been proposed to incorporate the influences of axial compression and tee-section buckling into the existing shear-moment design equations. The elevated temperature simulations show that axially restrained steel beams with web openings may enter catenary action at much lower temperatures than the commonly accepted critical failure temperatures calculated assuming no axial restraint and no tee-section buckling. Therefore, at the commonly accepted critical failure temperatures, many perforated steel beams exert tensile forces on the adjacent connections. It is important that the connections have the strength and deformation (rotation) capacity to enable catenary action to develop. The parametric study examines, in detail, how changing the different design parameters may affect the elevated temperature behaviour of perforated beams. The examined parameters including load ratio, level of axial restraint, cross-section temperature distribution profile, opening shape, opening size and opening position. Based on the results of the numerical parametric study, an analytical method has been derived to obtain the complete axial force-temperature relationship for axially restrained perforated steel beams. The key points of the analytical method include initial stiffness, point of initial failure under combined axial compression, bending moment and shear force, transition temperature at which the axial force on the beam changes from compression to tension and the magnitude of the tensile force resulting from the beams going into catenary action. Using the analytical method, it is possible to assess the maximum tensile force in the beam and the corresponding temperature so that the safety of the connections can be checked.

Dentro do conjunto de aspectos relacionados à elaboração de projetos em estruturas de aço e mistas de aço e concreto, destaca-se como de grande importância e interesse, para fins de dimensionamento, a consideração de elementos estruturais submetidos a temperaturas elevadas. Nesse sentido, o presente trabalho tem como objetivo principal propor a construção de modelos numéricos tridimensionais de pilares de aço pertencentes a sistemas estruturais correntes da construção civil, para análise em situação de incêndio, com vistas a simular numericamente a evolução dos níveis de temperatura ao longo do tempo com posterior acoplamento termoestrutural. Considera-se uma análise paramétrica com vista a variar as restrições axiais totais e parciais da barra, no referente aos deslocamentos axiais, contemplando desde a situação de extremidade livre até a restrição completa em resposta à consideração de apoio do tipo fixo, por exemplo. Os resultados numéricos são comparados a ensaios experimentais de outros autores, bem como com outros trabalhos numéricos já publicados. São obtidas respostas de deslocamentos axiais e laterais do modelo termoestrutural para diversas disposições de paredes em relação ao perfil, bem como gráficos do acréscimo de força axial introduzido no sistema pela restrição axial. Os estudos aqui realizados poderão servir como base para novas pesquisas tanto no campo numérico quanto experimental, assim como para futuras revisões da ABNT NBR 14323:1999, buscando contemplar situações de interesse não abordadas neste documento normativo. Os resultados da pesquisa apontam que a consideração do campo térmico com a inclusão da alvenaria no modelo termoestrutural pode melhorar consideravelmente o desempenho do elemento estrutural em situação de incêndio. / Within the set of aspects related to the development of researches in steel and composite steel and concrete structures, stands out with great importance and interest, aiming to dimension, the consideration of structural elements subjected to high temperatures. In this way, the present work has as main objective to propose the construction of three-dimensional numerical models of steel columns that belong to current structural systems of civil construction, for examination in fire situation, aiming to simulate numerically the evolution of temperature levels throughout of time with later termoestrutural coupling. It will be considered a parametric analysis in order to vary the total and partial axial restraint in respect to the axial displacements, since the free end situation until the complete restriction in response to the consideration of support for the fixed type, for example. The numerical results are compared to experimental tests made by other authors, as well as with others numerical works already published. Answers are obtained from axial and lateral displacements of the thermo structural model to many displacement of wall related to the profile, also charts of adding axial force introduced into the system by the axial restraint. The results of the current research could serve as a basis for further research in both the numerical field or experimental, also for future revisions of ABNT NBR 14323:1999, aiming to see situations of interest not studied in the same normative document. The results of this work show that consideration of thermal field with the inclusion of masonry in the thermo structural model can, significantly, improve the performance of the structural element in a fire situation.

Dentro do conjunto de aspectos relacionados à elaboração de projetos em estruturas de aço e mistas de aço e concreto, destaca-se como de grande importância e interesse, para fins de dimensionamento, a consideração de elementos estruturais submetidos a temperaturas elevadas. Nesse sentido, o presente trabalho tem como objetivo principal propor a construção de modelos numéricos tridimensionais de pilares de aço pertencentes a sistemas estruturais correntes da construção civil, para análise em situação de incêndio, com vistas a simular numericamente a evolução dos níveis de temperatura ao longo do tempo com posterior acoplamento termoestrutural. Considera-se uma análise paramétrica com vista a variar as restrições axiais totais e parciais da barra, no referente aos deslocamentos axiais, contemplando desde a situação de extremidade livre até a restrição completa em resposta à consideração de apoio do tipo fixo, por exemplo. Os resultados numéricos são comparados a ensaios experimentais de outros autores, bem como com outros trabalhos numéricos já publicados. São obtidas respostas de deslocamentos axiais e laterais do modelo termoestrutural para diversas disposições de paredes em relação ao perfil, bem como gráficos do acréscimo de força axial introduzido no sistema pela restrição axial. Os estudos aqui realizados poderão servir como base para novas pesquisas tanto no campo numérico quanto experimental, assim como para futuras revisões da ABNT NBR 14323:1999, buscando contemplar situações de interesse não abordadas neste documento normativo. Os resultados da pesquisa apontam que a consideração do campo térmico com a inclusão da alvenaria no modelo termoestrutural pode melhorar consideravelmente o desempenho do elemento estrutural em situação de incêndio. / Within the set of aspects related to the development of researches in steel and composite steel and concrete structures, stands out with great importance and interest, aiming to dimension, the consideration of structural elements subjected to high temperatures. In this way, the present work has as main objective to propose the construction of three-dimensional numerical models of steel columns that belong to current structural systems of civil construction, for examination in fire situation, aiming to simulate numerically the evolution of temperature levels throughout of time with later termoestrutural coupling. It will be considered a parametric analysis in order to vary the total and partial axial restraint in respect to the axial displacements, since the free end situation until the complete restriction in response to the consideration of support for the fixed type, for example. The numerical results are compared to experimental tests made by other authors, as well as with others numerical works already published. Answers are obtained from axial and lateral displacements of the thermo structural model to many displacement of wall related to the profile, also charts of adding axial force introduced into the system by the axial restraint. The results of the current research could serve as a basis for further research in both the numerical field or experimental, also for future revisions of ABNT NBR 14323:1999, aiming to see situations of interest not studied in the same normative document. The results of this work show that consideration of thermal field with the inclusion of masonry in the thermo structural model can, significantly, improve the performance of the structural element in a fire situation.

As vigas de concreto armado sofrem deformações térmicas em situação de incêndio. Os comprimentos dos vãos se alongam resultando no deslocamento horizontal de seus respectivos apoios e elas passam a fletir de forma acentuada, o que gera a rotação nos mesmos. Se essas deformações forem impedidas pelas próprias condições de apoio da peça ou devido a elementos estruturais circundantes, por exemplo, esforços adicionais passarão a atuar nas vigas, modificando seu desempenho frente ao fogo. Estudos apontam que os efeitos desses esforços podem ser benéficos à resistência ao fogo (RF) das vigas aquecidas, contudo, nas poucas pesquisas voltadas à análise experimental dessa questão, as restrições foram admitidas apenas de forma isolada, i.e., ou as vigas estavam submetidas a restrições axiais ou a rotacionais. O efeito conjunto, mais representativo ao que ocorre na realidade, e a consideração de diferentes níveis de rigidezes impostos às deformações, foram avaliados em investigações numéricas sem dados experimentais apropriados para a validação dos resultados. Na presente Tese de Doutorado, avaliou-se experimentalmente o desempenho de vigas de concreto mediante a realização de ensaios de flexão em elementos em escala real e sob diferentes condições de apoio: sem restrições às deformações, com restrições apenas axiais e com restrições tanto axiais quanto rotacionais. Relativamente aos elementos restringidos, foram analisados dois níveis de rigidezes axial, 0,02 e 0,04EA/l, e rotacional, 1 e 2EI/l. Também houve ensaios de referência em vigas simplesmente apoiadas à temperatura ambiente para a verificação dos carregamentos e modos de ruptura. Os dados experimentais obtidos para diferentes esquemas estáticos de vigas motivaram a concepção de modelos numéricos que fossem representativos do comportamento dos mesmos. Com o auxílio do programa de computador DIANA, que tem base no método dos elementos finitos, foram criados modelos para as vigas ensaiadas à temperatura ambiente e ao fogo. Eles foram idealizados com a consideração de diversas propriedades características do comportamento não linear dos materiais e conduziram a boas correlações quando os seus resultados foram comparados aos obtidos em laboratório. A principal conclusão deste estudo numérico-experimental foi que a RF das vigas de concreto armado sempre aumentam quando admitido qualquer tipo de restrição (somente axial ou axial mais rotacional). Além disso, ao se fixar um valor para a restrição rotacional, as vigas com nível de restrição axial mais elevado apresentaram RF maiores do que aquelas com nível mais brando. O mesmo se verificou ao fixar a restrição axial e variar a rotacional. Vigas nos quais o efeito conjunto das restrições foi admitido conduziram a maiores RF do que aquelas apenas com restrição axial. Para a maior parte dos casos estudados, os aumentos das RF se mostraram significativos quando confrontados às vigas sem restrições. Assim, confirmou-se que os métodos simplificados normatizados que não consideram os efeitos provenientes das mesmas no dimensionamento para a situação de incêndio das vigas de concreto armado estão a favor da segurança. Os resultados numérico-experimentais aqui apresentados podem auxiliar na concepção de ferramentas alternativas para a consideração dos efeitos das restrições em projeto. / Reinforced concrete beams are submitted to thermal deformations when exposed to fire. The lengths of the spans elongate, a fact that triggers the horizontal displacement of their supports, and they begin to bend sharply, resulting in their rotation. If these deformations are hindered by the support conditions of the element or by surrounding structural elements, for instance, additional efforts will act on the beams in order to modify their performance when facing the action of fire. Studies have pointed out that the effects of such efforts may be beneficial to the fire resistance of the beams; however, in the few researches focused on the experimental analysis of this issue, the restraints were admitted only in an isolated way, i.e., the beams were either submitted to axial or to rotational restraints. Their coupled effect, more representative of what occurs in reality, and the consideration of different stiffness levels imposed on the deformations, were evaluated in numerical investigations, without suitable experimental data for validating the results, though. In this PhD Thesis, the performance of concrete beams was evaluated experimentally by performing bending tests on full-scale elements under different support conditions: unrestrained, only with axial restraints and with both axial and rotational restraints. Regarding the restrained elements, two levels of axial and rotational stiffness were analyzed, 0.02 and 0.04EA/l; 1 and 2EJ/l. There were also reference tests on simply supported beams at ambient temperature to check the load-bearing capacities and failure modes. The experimental data obtained for different beam static schemes still motivated the conception of numerical models that would be representative of their behavior. With the aid of the DIANA software, which is based on the finite element and displacement methods, beam models to represent beams tested at ambient temperature and in fire conditions were created. These models were implemented considering several properties that characterize the nonlinear behavior of the materials and led to good correlations when their results were compared to those obtained in the laboratory. The main conclusion of this experimental and numerical study was that the fire resistance of RC beams always increases when any type of restraint (axial or axial plus rotational) is introduced. In addition, by fixing the rotational stiffness, the beams with higher axial stiffness level presented higher fire resistance than those with the lower level. The same was observed by fixing the axial stiffness and varying the rotational stiffness. Beams in which the combined effect of the restraints was admitted led to higher resistances than those with only axial restraint. For most of the studied situations, the increases of the resistances showed to be significant when confronted with the ones for unrestrained beams. Thus, it was confirmed that the standard simplified methods that allow the non-consideration of these effects during the fire design of the RC beams lead to conservative results. The numerical and experimental results presented herein may aid in the conception of alternative tools that allow applying restraint effects to design.

As vigas de concreto armado sofrem deformações térmicas em situação de incêndio. Os comprimentos dos vãos se alongam resultando no deslocamento horizontal de seus respectivos apoios e elas passam a fletir de forma acentuada, o que gera a rotação nos mesmos. Se essas deformações forem impedidas pelas próprias condições de apoio da peça ou devido a elementos estruturais circundantes, por exemplo, esforços adicionais passarão a atuar nas vigas, modificando seu desempenho frente ao fogo. Estudos apontam que os efeitos desses esforços podem ser benéficos à resistência ao fogo (RF) das vigas aquecidas, contudo, nas poucas pesquisas voltadas à análise experimental dessa questão, as restrições foram admitidas apenas de forma isolada, i.e., ou as vigas estavam submetidas a restrições axiais ou a rotacionais. O efeito conjunto, mais representativo ao que ocorre na realidade, e a consideração de diferentes níveis de rigidezes impostos às deformações, foram avaliados em investigações numéricas sem dados experimentais apropriados para a validação dos resultados. Na presente Tese de Doutorado, avaliou-se experimentalmente o desempenho de vigas de concreto mediante a realização de ensaios de flexão em elementos em escala real e sob diferentes condições de apoio: sem restrições às deformações, com restrições apenas axiais e com restrições tanto axiais quanto rotacionais. Relativamente aos elementos restringidos, foram analisados dois níveis de rigidezes axial, 0,02 e 0,04EA/l, e rotacional, 1 e 2EI/l. Também houve ensaios de referência em vigas simplesmente apoiadas à temperatura ambiente para a verificação dos carregamentos e modos de ruptura. Os dados experimentais obtidos para diferentes esquemas estáticos de vigas motivaram a concepção de modelos numéricos que fossem representativos do comportamento dos mesmos. Com o auxílio do programa de computador DIANA, que tem base no método dos elementos finitos, foram criados modelos para as vigas ensaiadas à temperatura ambiente e ao fogo. Eles foram idealizados com a consideração de diversas propriedades características do comportamento não linear dos materiais e conduziram a boas correlações quando os seus resultados foram comparados aos obtidos em laboratório. A principal conclusão deste estudo numérico-experimental foi que a RF das vigas de concreto armado sempre aumentam quando admitido qualquer tipo de restrição (somente axial ou axial mais rotacional). Além disso, ao se fixar um valor para a restrição rotacional, as vigas com nível de restrição axial mais elevado apresentaram RF maiores do que aquelas com nível mais brando. O mesmo se verificou ao fixar a restrição axial e variar a rotacional. Vigas nos quais o efeito conjunto das restrições foi admitido conduziram a maiores RF do que aquelas apenas com restrição axial. Para a maior parte dos casos estudados, os aumentos das RF se mostraram significativos quando confrontados às vigas sem restrições. Assim, confirmou-se que os métodos simplificados normatizados que não consideram os efeitos provenientes das mesmas no dimensionamento para a situação de incêndio das vigas de concreto armado estão a favor da segurança. Os resultados numérico-experimentais aqui apresentados podem auxiliar na concepção de ferramentas alternativas para a consideração dos efeitos das restrições em projeto. / Reinforced concrete beams are submitted to thermal deformations when exposed to fire. The lengths of the spans elongate, a fact that triggers the horizontal displacement of their supports, and they begin to bend sharply, resulting in their rotation. If these deformations are hindered by the support conditions of the element or by surrounding structural elements, for instance, additional efforts will act on the beams in order to modify their performance when facing the action of fire. Studies have pointed out that the effects of such efforts may be beneficial to the fire resistance of the beams; however, in the few researches focused on the experimental analysis of this issue, the restraints were admitted only in an isolated way, i.e., the beams were either submitted to axial or to rotational restraints. Their coupled effect, more representative of what occurs in reality, and the consideration of different stiffness levels imposed on the deformations, were evaluated in numerical investigations, without suitable experimental data for validating the results, though. In this PhD Thesis, the performance of concrete beams was evaluated experimentally by performing bending tests on full-scale elements under different support conditions: unrestrained, only with axial restraints and with both axial and rotational restraints. Regarding the restrained elements, two levels of axial and rotational stiffness were analyzed, 0.02 and 0.04EA/l; 1 and 2EJ/l. There were also reference tests on simply supported beams at ambient temperature to check the load-bearing capacities and failure modes. The experimental data obtained for different beam static schemes still motivated the conception of numerical models that would be representative of their behavior. With the aid of the DIANA software, which is based on the finite element and displacement methods, beam models to represent beams tested at ambient temperature and in fire conditions were created. These models were implemented considering several properties that characterize the nonlinear behavior of the materials and led to good correlations when their results were compared to those obtained in the laboratory. The main conclusion of this experimental and numerical study was that the fire resistance of RC beams always increases when any type of restraint (axial or axial plus rotational) is introduced. In addition, by fixing the rotational stiffness, the beams with higher axial stiffness level presented higher fire resistance than those with the lower level. The same was observed by fixing the axial stiffness and varying the rotational stiffness. Beams in which the combined effect of the restraints was admitted led to higher resistances than those with only axial restraint. For most of the studied situations, the increases of the resistances showed to be significant when confronted with the ones for unrestrained beams. Thus, it was confirmed that the standard simplified methods that allow the non-consideration of these effects during the fire design of the RC beams lead to conservative results. The numerical and experimental results presented herein may aid in the conception of alternative tools that allow applying restraint effects to design.