The P-delta effect, which is a second order effect, is experienced by a structure mostly when the structure is subjected to lateral forces like earthquake and wind. In addition to earthquake and wind loads, when the structure is subjected to various live load patterns other than symmetrical loading, the structure experiences side sway or lateral translation. In this thesis, P-delta effects due to symmetrical and asymmetrical live loads is studied on a three-bay, two-story steel moment frame. The main objective of this research is to investigate P-delta effects on the column which is subjected to critical load case. The effect is analyzed based on the value of the moment magnification factor, B2. Besides, the story drift due to asymmetrical loading is also investigated. For the purpose of this study, “Approximate Second-Order Analysis” specified in “Appendix 8” of AISC Steel Construction Manual (AISC 2011) is used to amplify the first order effects to account for the second-order effects in the steel moment frame. Additionally, computer software is used to calculate the first order moments and axial forces.

Several different approaches to determining second-order moments in plane frames were studied during this research. The focus of the research was to compare the moments predicted by four different commercially available computer analysis programs and the current design specification, the AISC LRFD moment magnification method. For this research, the second-order moments for ten commonly designed frames were compared. An overview of various second-order analysis procedures is presented first. The solution procedure utilized by each computer program and the AISC moment magnification method are explained. Also, the frames considered in the research are described. Next the frames are analyzed and the results between each of the computer programs and the current design specifications are compared. Finally, conclusions are drawn concerning the consistency of the second-order moments predicted by each of the solution procedures and recommendations for their use are discussed. In general, each of the four computer analysis programs evaluated and the AISC moment magnification method can consistently and adequately predict the second-order moments in plane frames. / Master of Science

A análise de segunda ordem global de edifícios é indispensável nos dias atuais, em que as estruturas são cada vez mais esbeltas. No mercado, há diversos sistemas computacionais que realizam essa análise, e alguns dos novos engenheiros estruturais podem não saber os conceitos em que ela se baseia. Portanto, este trabalho pretende: avaliar os efeitos de segunda ordem em edifícios por meio dos coeficientes \'gama\'z e FAVt, este desenvolvido pela TQS, e por meio do processo P-Delta; mostrar como este processo P-Delta funciona e como o sistema computacional CAD/TQS o considera; e analisar também os esforços de segunda ordem calculados a partir dos de primeira ordem multiplicados por O,95 \'gama\'z. Em relação à avaliação da estabilidade global, serão comparados os resultados obtidos com os parâmetros \'alfa\', \'gama\'z, FAVt e RM2M1, este último gerado a partir do processo P-Delta. Pretende-se, assim, fornecer subsídios para que os novos engenheiros tenham condições de atuar com base conceitual bem fundamentada, tanto na escolha do método quanto na análise dos resultados. / The overall second-order analysis of buildings is essential nowadays, in which the structures are each time more slender. In the market, there are several computer systems that perform this analysis, and some new structural engineers can not know the concepts on which it rests. Therefore, this study aims: to evaluate the second-order effects in buildings making use of the coefficients \'gama\'z and FAVt, this developed by TQS, and using P-Delta process; to show how this P-Delta process works and how the computer system CAD/TQS considers it; and also analyze the second order efforts obtained from the first-order ones multiplied by O,95 \'gama\'z. Regarding the evaluation of overall stability, will be compared the results obtained with the parameters \'alfa\', \'gama\'z, FAVt, and RM2M1, the latter generated from the P-Delta process. It is intended, therefore, to provide subsidies for new engineers to be able to work with well-founded conceptual base, both in the choice of method and analysis of results.

Pour les panneaux de grande hauteur soumis à un fort gradient thermique associé à l’incendie, ils subissent des déplacements hors plan importants qui, du fait de l’excentrement du poids propre qui en résulte, vont engendrer des efforts de flexion venant s’ajouter aux efforts de compression déjà existants. Un tel changement de géométrie, d’autant plus prononcé que le panneau est de grande hauteur, combiné à une dégradation simultanée des propriétés de résistance des matériaux sous l’effet de l’élévation de température, peut conduire à un effondrement de la structure sous poids propre. L’évaluation de la résistance au feu d’éléments de structures de grandes dimensions, repose sur la théorie du calcul à la rupture, appliquée d’une part à la détermination d’un diagramme d’interaction au feu caractérisant la résistance du panneau en chacune de ses sections, d’autre part à l’analyse de la ruine globale du panneau dans sa configuration déformée. Le programme comporte deux volets complémentaires. Le premier volet concerne l’approche expérimentale. Un mur de 9 mètre a été testé sur le grand équipement Vulcain afin de valider le modèle de calcul d’une part, qui est en cours du développement, et à identifier des phénomènes locaux éventuels non accessibles par la modélisation d’autre part. Le deuxième volet concerne le développement d’outils de modélisation et de calcul performants. Basées sur une approche cinématique, des procédures itératives qui se reposent sur la méthode de perturbation ont été construit pour chercher une solution analytique pour prédire la configuration déformée d’une plaque soumis à un fort gradient thermique. Ensuite, des méthodes numériques fondées sur la discrétisation en éléments finis du panneau déformé, traité comme une coque à faible courbure, et l’utilisation de techniques d’optimisation non-linéaires, qui ont connu récemment des progrès importants, devront pouvoir être développées et appliquées à ce problème / High rise reinforced concrete walls under fire exhibit important out-of-plane displacements, which in turn lead to an eccentricity of the self-weight with respect to the initial undeformed configuration, resulting in supplementary bending moments. This geometrical change, combined with the degradation of the stiffness and strength properties of reinforced concrete due to severe temperature increase, may lead to the failure of walls under fire.Investigation on fire resistance of reinforced concrete walls will be based on the yield design approach in order to analyze the global stability of high rise walls, taking into account the geometry changes induced by the thermal loading.The program consists of two parts.Firstly, a 9-meter high reinforced concrete wall has already been tested under fire with the equipment Vulcan. This full size experiment aims at validating the modeling of plates under large out-of-plan displacement and identifying potential local phenomenon which has not been considered in the model.Secondly, a yield design approach will carried out to analyze the stability of reinforced concrete walls. By using the perturbation method, a recursive analytical procedure based on a kinematic approach is proposed to find the deformed configuration of reinforced concrete walls under fire. The deformed configuration will be later modeled as a shallow shell, on which a yield design procedure will be performed by a non-linear optimization

A análise de segunda ordem global de edifícios é indispensável nos dias atuais, em que as estruturas são cada vez mais esbeltas. No mercado, há diversos sistemas computacionais que realizam essa análise, e alguns dos novos engenheiros estruturais podem não saber os conceitos em que ela se baseia. Portanto, este trabalho pretende: avaliar os efeitos de segunda ordem em edifícios por meio dos coeficientes \'gama\'z e FAVt, este desenvolvido pela TQS, e por meio do processo P-Delta; mostrar como este processo P-Delta funciona e como o sistema computacional CAD/TQS o considera; e analisar também os esforços de segunda ordem calculados a partir dos de primeira ordem multiplicados por O,95 \'gama\'z. Em relação à avaliação da estabilidade global, serão comparados os resultados obtidos com os parâmetros \'alfa\', \'gama\'z, FAVt e RM2M1, este último gerado a partir do processo P-Delta. Pretende-se, assim, fornecer subsídios para que os novos engenheiros tenham condições de atuar com base conceitual bem fundamentada, tanto na escolha do método quanto na análise dos resultados. / The overall second-order analysis of buildings is essential nowadays, in which the structures are each time more slender. In the market, there are several computer systems that perform this analysis, and some new structural engineers can not know the concepts on which it rests. Therefore, this study aims: to evaluate the second-order effects in buildings making use of the coefficients \'gama\'z and FAVt, this developed by TQS, and using P-Delta process; to show how this P-Delta process works and how the computer system CAD/TQS considers it; and also analyze the second order efforts obtained from the first-order ones multiplied by O,95 \'gama\'z. Regarding the evaluation of overall stability, will be compared the results obtained with the parameters \'alfa\', \'gama\'z, FAVt, and RM2M1, the latter generated from the P-Delta process. It is intended, therefore, to provide subsidies for new engineers to be able to work with well-founded conceptual base, both in the choice of method and analysis of results.

AN ABSTRACT OF THE THESIS OF

Symmetrical steel moment frames that are subjected to sidesway forces due to unsymmetrical live loads will undergo sidesway. The P-delta effects on a moment frame under the influence of sidesway forces is studied. The effective length method is used for the second-order analysis specified in the American Institute Steel Construction - Load and Resistance Factor Design (AISC-LRFD). This study investigates the P-delta effects on a multi-story, multi-bay steel moment frame subjected to sidesway forces caused by various unsymmetrical live load patterns. The study focuses on the interaction of axial and bending moment in the columns. The actual response of a moment frame is estimated by amplifying the results of a first-order elastic analysis using moment magnification factors. The moment magnification factors for each story of the steel moment frame are summarized.

Building engineering is called upon to keep up with the pace and challenges of modern design, which aims not only to build higher and greener, but also to fulfill the demands of the growing population and simple human curiosity. The main purpose of this study was to examine the global behavior of a slender and inclined (V-shaped) 300 m high rise building with different structural systems applied. In order to properly evaluate them, four different parametric studies were conducted. These included determining the appropriate inclination angle and the geometry of a simple beam system and later comparing fourteen different structural systems, namely trusses, diagrids, Tubed Mega Frames and moment frames. Parallel to this, a further investigation was made on a shell and beam element model, in order to assess the simplifications made and to control the obtained results. This study was based on various simulations in Finite Element Analysis programs, primarily ETABS, but also SAP2000 and Autodesk Robot Structural Analysis. The modelling included the definition of geometry and applied loads and results in extracting the desirable forces and deformations. Additionally, the automatic design for structural members was used for the purpose of a comprehensive study of the chosen structural systems. The designed structures were subjected to static analysis (dead, live, wind, seismic load), dynamic analysis (response spectrum and time history function) and nonlinear P-delta effect. A buckling analysis was also performed to determine the modes and associated load factors for buckling. In the end, the structural response in terms of displacement and acceleration was compared. The inclination angle study set the defining angle at 10° from vertical, with respect to the serviceability limit deflection. Comparing alternative truss geometries in a 2D parametric study resulted in the choice of four different systems (X, N, K and W trusses). In the 3D analysis, the chosen truss systems, together with three variations of diagrid systems, and seven Tubed Mega Frames with two moment frame structures were further analyzed. In both groups, the mass and the material of the systems were kept similar and the comparison was basically based on the obtained maximum displacement and natural periods of the buildings. The shell and frame model comparison gave a difference in displacements between 0 and 12%. Finally, the comprehensive study of the Tubed Mega Frame, X truss and diagrid structures showed that these buildings were performing similarly to vertical buildings with a top story displacement within the suggested limits (less than 673 mm). Further investigation should be made concerning the acceleration under synthetic earthquake, which exceeded the suggested norms, as well as the connecting nodes between the trusses and the inclined columns. The outcome of this study implied the possibility of construction and usability of inclined, slender, tall buildings with respect to the Ultimate Limit State and the Service Limit State, as specified in the American standard, ASCE 7-10, and opened new possible issues for further research.

During the months I have been at Virginia Tech, I have experienced the most exciting time of my life. There are many persons who helped me to pursue my Master's degree. I would like to take this opportunity to express my appreciations to them. I would like to thank my advisor and committee chairman, Dr Finley A. Charney. He has supported me for the entire duration of this project with all of his efforts. Without his assistance, it would have been very difficult for me to learn so many concepts in the field of nonlinear dynamic analysis and practical earthquake engineering. I would also like to acknowledge my other committee members, Dr. Raymond Plaut and Dr. W. Samuel Easterling, for taking the time to review the thesis and providing valuable insights and feedback on this thesis. I would like to thank my father, Chan Kwok Fung, who encouraged me to pursue my Master Degree, and my mother, Yu Yuk Ping, who brought me to life. I would like to thank my sister, Doris Chan, and my girlfriend, Ka Man Chan, for supporting and encouraging me during the past two years at Virginia Tech. Finally, I would like to give thanks to the rest of my family, friends, professors, and fellow graduate students for their help and encouragement during my stay at Virginia Tech. / Master of Science

Este trabalho apresenta uma análise comparativa de diferentes sistemas estruturais para um edifício de 20 pavimentos. Cada um dos modelos foi dimensionado através dos princípios do método da análise direta, presente na ABNT NBR 8800:2008. O método da amplificação dos esforços solicitantes (MAES) foi usado para se obter de forma simplificada os esforços atuantes nos elementos do edifício considerando os efeitos locais e globais de segunda ordem. A incidência do vento foi simulada de duas formas diferentes. Na primeira, chamada de uniforme, o vento foi aplicado sem excentricidade, gerando apenas o efeito de tombamento nas estruturas. Na segunda hipótese, considerou-se uma excentricidade devida aos efeitos de vizinhança, prescrita pela ABNT NBR 6123:1988, responsável por ocasionar o tombamento e a torção dos edifícios. Todas as análises numéricas foram repetidas fazendo o uso de outro método simplificado de segunda ordem, conhecido como P-Delta. Por meio dos resultados obtidos, constatou-se que a possibilidade de se reduzir a sobrecarga para o dimensionamento de pilares proporciona uma economia de material, mas, por outro lado, tem como consequência o aumento do tempo de análise, pois exige a utilização de diferentes combinações de cálculo para o dimensionamento de vigas e pilares. A estratégia utilizada para simular os efeitos de vizinhança mostrou-se satisfatória, pois permitiu introduzir de maneira fácil e prática a torção ocasionada pela incidência excêntrica do vento. Observou-se também que esses efeitos ocasionaram o aumento dos momentos fletores e dos deslocamentos das estruturas analisadas. Em relação à avaliação dos efeitos de segunda ordem, comprovou-se que, para a classificação da deslocabilidade, a combinação de cálculo crítica é aquela que possui o maior carregamento gravitacional. Entretanto, para o dimensionamento dos elementos, foi constatado que outras hipóteses de cálculo, principalmente aquelas em que o vento é a ação variável principal, podem ser determinantes. Por fim, foi observado que os resultados obtidos pelo método P-Delta ficaram bastante semelhantes àqueles calculados pelo MAES, com desvios desprezíveis. O MAES, por sua vez, mostrou-se bastante trabalhoso, pois exige a modelagem de diferentes tipos de estruturas para a determinação dos esforços. / This work presents a comparative analysis of different structural systems for a 20-storey building. Each model has been designed using the principles of the direct analysis method (DAM), present in the ABNT NBR 8800:2008. The first-order amplification method (FOAM) was used to obtain, in a simplified manner, the forces acting on the building elements, including local and global second-order effects. The incidence of the wind was simulated in two different ways. In the first case, named uniform, the wind was applied without eccentricity, generating only structure overturning. In the second case, it was considered an eccentricity due to vicinity effects, prescribed by the ABNT NBR 6123:1988, responsible for causing twisting and building overturning. All numerical analysis were carried out a simplified second-order method known as P-Delta. From the results obtained it was found that the reduction of live loads in the design of columns provides material economy, but on the other hand, increases analysis time, since it requires different combinations for beams and columns. The strategy used to simulate the vicinity effects was satisfactory, because it allowed, in an easy and practical way, the consideration of the torsion produced by the wind eccentric impact. It was also observed that these effects increased the bending moments and the displacements of the structures. About the second-order effects, it was shown that, for sway or non-sway classification, the critical combination is one with greatest gravitational loading. However, for the design of the elements, it was observed that other loading conditions can be critical, especially those in which the wind is the main live load. Finally, the results obtained by the P-Delta method were very similar to those calculated by the first-order amplification method. The FOAM was, in turn, very laborious, because it requires the modeling of different types of structures for the determination of the forces.