This research study is conducted on one bay-one story non-sway frames where the effects of the rotational restraint and slenderness ratio on the post-buckling strength of the axially restraint column under thermal load are studied. Geometric non-linear analysis of the structures is performed using a research program based on the beam-column theory. A total 32 models are created considering two different bottom end conditions: fixed and hinged, slenderness ratios: 50 and 125, and the beam to column length ratios: 0.5,1,1.5 and 2, to account for the variation in the rotational restraint. All models are subjected to thermal loads and numerical results are obtained to study the post-buckling behavior of the columns of the frames under thermal loads.

The objective of this study is to examine the effect of rotational restraints on thermal post-buckling response of sway columns using geometrically nonlinear analysis. The present design approach considers columns to have failed once they buckle. However, the columns under fire load are found to exhibit significant post-buckling strength which could be utilized for more economical design. The past researchers on the nonlinear thermal analysis used isolated columns with idealized support conditions which mean the columns are assumed to be free or fully restrained in the rotation, lateral and, axial directions. However, that is seldom the case in real structures and the restraint at an end of the column depends upon the members connected at that joint. The restraint provided to the column by the members connected at the joint will be in between the free case and fully restrained case. This study incorporates the variation in rotational restraint due to changes in the properties of members connected at the ends of the column. The columns are assumed to be fully restrained in the axial direction. Since the study is being carried out on sway columns, the restraint in the lateral direction is zero.

The purpose of this study is to investigate the footing fixity effect on the lateral deflection of a bridge pier for different types of soil. Generally, the rotational restraint coefficient at top and bottom of pier (degree of fixity of the pier) is used to compute the effective length factor of pier which is in turn used to determine the pier deflection. The magnitude of the deflection is used to determine whether the p-delta force effect should be considered while designing the pier. However, the pier deflection is usually computed by assuming that the pier footing is completely fixed to the ground. In case of soil under footing, rotational restraint coefficient is taken as five for all types of soils. In this study, finite element analysis method was used to determine the pier deflection by providing three actual soil environments and compare the results with the traditional approach. Hence, the rotational restraint coefficient will be modified according to the deflection computed from the finite element analysis.

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.