This thesis investigates the torsional performance of steel structures with and without rigid diaphragm constraints through numerical simulations and evaluates the appropriateness of relevant design provisions in current seismic design codes. In the first part of the work, six theme structures with different (1) in-plane stiffness of diaphragm, and (2) horizontal configurations of vertical braced frames were designed and their performance evaluated through both nonlinear static and dynamic analyses. Comparisons of the analytical results between the structures with and without rigid diaphragm constraints indicate that the in-plane rigidity of the diaphragms affects the efficiency of in-plane force transfer mechanisms, resulting in different global ductility and strength demands. Rigid diaphragm structures exhibit higher global strengths as well as higher torsional rotation capacity because of the infinite in-plane stiffness of the diaphragm. Semi-rigid diaphragm structures have higher ductility demands due to the finite in-plane diaphragm stiffness. The inclusion of bi-axial forces in the analyses reduces the structural strength and increases the ductility demands on the peripheral frames. The axial forces in the collectors and chords that make up the diaphragm depend on (1) the sequence of brace buckling and (2) vertical configuration of the braced frames. The results show higher axial forces in collectors in the roof diaphragms, and higher chord axial forces in the third floor diaphragms. The shear connections in the beams that make up both the collectors and chords are susceptible to failure due to the significant increment of axial forces in those members. The conventional beam analogy used in design can severely underestimate the axial forces in chords and collectors when the structures step into the inelastic stage. / Ph. D.

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Recent advancements in earthquake engineering have caused a movement toward a probabilistic quantification of the behavior of structural systems. Analysis characteristics, such as ground motion records, material properties, and structural component behavior are defined by probabilistic distributions. The response is also characterized probabilistically, with distributions fitted to analysis results at intensity levels ranging from the maximum considered earthquake ground motion to collapse. Despite the progress toward a probabilistic framework, the variability in structural analysis results due to modeling techniques has not been considered. This work investigates the uncertainty associated with modeling geometric nonlinearities and Rayleigh damping models on the response of planar frames at multiple ground motion intensity levels. First, an investigation is presented on geometric nonlinearity approaches for planar frames, followed by a critical review of current damping models. Three frames, a four-story buckling restrained braced frame, a four-story steel moment resisting frame, and an eight-story steel moment resisting frame, are compared using two geometric nonlinearity approaches and five Rayleigh damping models. Static pushover analyses are performed on the models in the geometric nonlinearities study, and incremental dynamic analyses are performed on all models to compare the response at the design based earthquake ground motion (DBE), maximum considered earthquake ground motion (MCE), and collapse intensity levels. The results indicate noticeable differences in the responses at the DBE and MCE levels and significant differences in the responses at the collapse level. Analysis of the sidesway collapse mechanisms indicates a shift in the behavior corresponding to the different modeling assumptions, though the effects were specific to each frame. The FEMA P-695 Methodology provided a framework that defined the static and dynamic analyses performed during the modeling uncertainties studies. However, the Methodology is complex and the analyses are computationally expensive. To expedite the analyses and manage the results, a toolkit was created that streamlines the process using a set of interconnected modules. The toolkit provides a program that organizes data and reduces mistakes for those familiar with the process while providing an educational tool for novices of the Methodology by stepping new users through the intricacies of the process. The collapse margin ratio (CMR), calculated in the Methodology, was used to compare the collapse behavior of the models in the modeling uncertainties study. Though it provides a simple scalar quantity for comparison, calculation of the CMR typically requires determination of the full set of incremental dynamic analysis curves, which require prohibitively large analysis time for complex models. To reduce the computational cost of calculating the CMR, a new parallel computing method, referred to as the fragility search method, was devised that uses approximate collapse fragility curves to quickly converge on the median collapse intensity value. The new method is shown to have favorable attributes compared to other parallel computing methods for determining the CMR. / Ph. D.

This dissertation presents work targeted to study the effects of diaphragm flexibility on the seismic performance of light frame wood structures (LFWS). The finite element approach is considered for modeling LFWS as it is more detailed and provides a way to explicitly incorporate individual structural elements and corresponding material properties. It is also suitable for capturing the detailed response of LFWS components and the structure as a whole. The finite element modeling methodology developed herein is in general based on the work done by the other finite element researchers in this area. However, no submodeling or substructuring of subassemblages is performed and instead a detailed model considering almost every connection in the shear walls and diaphragms is developed. The studs, plates, sills, blockings and joists are modeled using linear isotropic three dimensional frame elements. A linear orthotropic shell element incorporating both membrane and plate behavior is used for the sheathings. The connections are modeled using oriented springs with modified Stewart hysteresis spring stiffnesses. The oriented spring pair has been found to give a more accurate representation of the sheathing to framing connections in shear walls and diaphragms when compared to non-oriented or single springs typically used by most researchers in the past. Fifty six finite element models of LFWS are created using the developed methodology and eighty eight nonlinear response history analyses are performed using the Imperial Valley and Northridge ground motions. These eighty eight analyses encompass the parametric study on the house models with varying aspect ratios, diaphragm flexibility and lateral force resisting system. Torsionally irregular house models showed the largest range of variation in peak base shear of individual shear walls, when corresponding flexible and rigid diaphragm models are compared. It is also found that presence of an interior shear wall helps in reducing peak base shears in the boundary walls of torsionally irregular models. The interior walls presence was also found to reduce the flexibility of diaphragm. A few analyses also showed that the nail connections are the major source of in-plane flexibility compared to sheathings within a diaphragm, irrespective of the aspect ratio of the diaphragm. A major part of the dissertation focuses on the development of a new high performance nonlinear dynamic finite element analysis program which is also used to analyze all the LFWS finite element models presented in this study. The program is named WoodFrameSolver and is written on a mixed language platform Microsoft Visual Studio .NET using object-oriented C++, C and FORTRAN. This tool set is capable of performing basic structural analysis chores like static and dynamic analysis of 3D structures. It has a wide collection of linear, nonlinear and hysteretic elements commonly used in LFWS analysis. The advanced analysis features include static, nonlinear dynamic and incremental dynamic analysis. A unique aspect of the program lies in its capability of capturing elastic displacement participation (sensitivity) of spring, link, frame and solid elements in static analysis. The program's performance and accuracy are similar to that of SAP 2000 which is chosen as a benchmark for validating the results. The use of fast and efficient serial and parallel solver libraries obtained from INTEL has reduced the solution time for repetitive dynamic analysis. The utilization of the standard C++ template library for iterations, storage and access has further optimized the analysis process, especially when problems with a large number of degrees of freedom are encountered. / Ph. D.

<p> This study deals with a method of analysis and the associated computer program that can capture the full nonlinear response of twodimensional reinforced concrete and steel plane frames subjected to dynamic loads, including blast and impact. Most of the relevant parameters that are normally neglected by similar available analysis tools have been considered in the present study. These include tension stiffening and concrete cracking, confinement effect and strain rate effect. Interaction between axial and bending deformations has also been accounted for. Four different constitutive models for concrete have been used and compared to each other together with multiple formulae accounting for the strain rate effect. The proposed analysis procedure was verified against other sophisticated software and experimental results and has proven to be a reliable means of analysis. </p> <p> The strain rate effect is shown to be a key parameter that plays an important role in the overall behaviour of structures under blast loads. Neglecting this effect does not necessarily lead to a more conservative design because it increases the overall stiffness of the structure which causes it to attract higher forces. This increase is proportional to the strain rate, which makes it particularly important in the case of blast loading where the strain rate can reach up to 1000 sec⁻¹. </p> / Thesis / Master of Applied Science (MASc)

A study on shape memory alloy materials as vibration dampers is reported. An important component is the strain rate-dependent and temperature-dependent constitutive behavior of shape memory alloy, which can significantly change its energy dissipation capacity under cyclic loading. The constitutive model used accounts for the thermo-mechanical strain rate-dependent behavior and phase transformation. With increasing structural flexibility, the hysteretic loop size of shape memory alloy dampers increases due to increasing strain rates, thus further decreasing the response of the structure to cyclic excitation. The structure examined is a beam, and its behavior with shape memory alloy dampers is compared to the same beam with conventional dampers. Parametric studies reveal the superior performance of the shape memory alloy over the conventional dampers even at the resonance frequency of the beam-damper system. An important behavior of the shape memory alloy dampers is discovered, in that they absorb energy from the fundamental and higher vibration modes. In contrast, the conventional dampers transfer energy to higher modes. For the same beam control, the stiffness requirement for the shape memory alloy dampers is significantly less than that of the conventional dampers. Response quantities of interest show improved performance of the shape memory alloy over the conventional dampers under varying excitation intensity, frequency, temperature, and strain rate.

O método dos elementos finitos é o método numérico mais difundido na análise de estruturas. Ao longo das últimas décadas foram formulados inúmeros elementos finitos para análise de cascas e placas. As formulações de elementos finitos lidam bem com o campo de deslocamentos, mas geralmente faltam testes que possam validar os resultados obtidos para o campo das tensões. Este trabalho analisa o elemento finito T6-3i, um elemento finito triangular de seis nós proposto dentro de uma formulação geometricamente exata, em relação aos seus resultados de tensões, comparando-os com as teorias analíticas de placas, resultados de tabelas para o cálculo de momentos em placas retangulares e do ANSYSr, um software comercial para análise estrutural, mostrando que o T6-3i pode apresentar resultados insatisfatórios. Na segunda parte deste trabalho, as potencialidades do T6-3i são expandidas, sendo proposta uma formulação dinâmica para análise não linear de cascas. Utiliza-se um modelo Lagrangiano atualizado e a forma fraca é obtida do Teorema dos Trabalhos Virtuais. São feitas simulações numéricas da deformação de domos finos que apresentam vários snap-throughs e snap-backs, incluindo domos com vincos curvos, mostrando a robustez, simplicidade e versatilidade do elemento na sua formulação e na geração das malhas não estruturadas necessárias para as simulações. / The Finite Element Method (FEM) is the numerical method most commonly used in structural analysis. A number of shell and plate finite elements has been suggested in the last decades. Finite element formulations deal well with the displacements field, but they usually lack tests that can validate the results obtained for the stress field. This work analyzes the finite element T6-3i, a six-nodes triangular finite element derived from a geometrically exact theory, regarding its stress results, comparing them with analytic plate theories, results from tables of moments in rectangular plates and from ANSYSr, a commercial software for structural analysis, showing that T6-3i can present unsatisfactory results. In the second part of this work, the T6-3i potentialities are expanded as a dynamic formulation for nonlinear shell analysis is proposed. An updated Lagrangian framework has been used and the weak form is obtained from the Principle of VirtualWork. Several numerical examples of folding a thin dome, which present various snap-throughs and snap-backs are presented, including creased shells, showing the robustness, simplicity and versatility of the element formulation and in generation of the unstructured curved meshes indispensable for the simulations.

O tema está relacionado com o constante crescimento da necessidade em implantarnovas torres de telecomunicações devido ao crescimento acelerado da infraestrutura de telecomunicações no Brasil. Todos os dias, novos sistemas de transmissão e recepção de ondas eletromagnéticas estão sendo implantados no território brasileiro. O objetivo deste trabalho é propor um procedimento seguro e eficaz para a análise estrutural de torres de telecomunicações em concreto armado de grande esbeltez, com base em um modelo dinâmico não linear, submetendo à carga de vento. Estas cargas são simuladas pelo método do vento sintético proposto por Franco (1993). A análise do concreto armado será realizada de acordo com a NBR-6118 (ABNT, 2007). A fim de determinar com precisão os deslocamentos da estrutura submetida ao carregamento de vento, um método iterativo computacional será utilizado obter as respostas não lineares. Realiza-se uma análise linear e, a partir dos resultados de esforços solicitantes, as tensões e a porção fissurada de cada seção transversal é obtida e parte-se para a determinação dos deslocamentos de 2ª ordem da torre. Em cada iteração, um procedimento do tipo P-Delta será utilizado para levar em conta a não linearidade geométrica da estrutura. As condições de contorno do problema estão relacionadas com a restrição do nível de tensões, deslocamentos e frequências de vibração da estrutura. Ao fim, uma análise dinâmica em torno da configuração não linear será realizada, e o deslocamento total da torre será dado pela somatória da componente estática com a componente flutuante do vento. / The theme is related to the constant growth in the need to deploy new telecommunications towers due to the accelerated growth of telecommunications infrastructure in Brazil. Every day, new systems of transmission and reception of electromagnetic waves are being implanted in the Brazilian territory. The objective of this work is to propose a safe and efficient procedure for the structural analysis of telecommunication towers with high slenderness constructed in reinforced concrete, based on a dynamic nonlinear model, submitting it to the wind load. These loads are simulated by the synthetic wind method proposed by Franco (1993). The analysis of the reinforced concrete will be held according to NBR-6118 (ABNT, 2007). In order to determine accurately the displacements of the structure subjected to wind loading, an iterative computational method will be held to obtain non-linear responses. A linear analysis is carried out and, with the results of the forces, the tensions and the fissured portion of each cross section are obtained and then 2nd order displacements of the tower. In each iteration, a P-Delta type procedure will be held to take into account the geometric non-linearity of the structure. The boundary conditions of the problem are related to the restriction of the stress level, displacements and vibration frequencies of the structure. At the end, a dynamic analysis around the nonlinear configuration will be performed, and the total displacement of the tower will be given by the sum of the static component with the floating component of the wind.

Model order reduction is necessary even in a time where the parallel processing is usual in almost any personal computer. The recent Model Reduction Methods are useful tools nowadays on reducing the problem processing. This work intends to describe a combination between POD (Proper Orthogonal Decomposition) and Ritz vectors that achieve an efficient Galerkin projection that changes during the processing, comparing the development of the error and the convergence rate between the full space and the projection space, in addition to check the stability of the projection space, leading to an adaptive model order reduction for nonlinear dynamical problems more efficient. This model reduction is supported by a secant formulation, which is updated by BFGS (Broyden - Fletcher - Goldfarb - Shanno) method to accelerate convergence of the model, and a tangent formulation to correct the projection space. Furthermore, this research shows that this method permits a correction of the reduced model at low cost, especially when the classical POD is no more efficient to represent accurately the solution. / A Redução de ordem de modelo é necessária, mesmo em uma época onde o processamento paralelo é usado em praticamente qualquer computador pessoal. Os recentes métodos de redução de modelo são ferramentas úteis nos dias de hoje para a redução de processamento de um problema. Este trabalho pretende descrever uma combinação entre POD (Proper Orthogonal Decomposition) e vetores de Ritz para uma projecção de Galerkin eficiente que sofre alterações durante o processamento, comparando o desenvolvimento do erro e a taxa de convergência entre o espaço total e o espaço de projeção, além da verificação de estabilidade do espaço de projeção, levando a uma redução de ordem do modelo adaptativo mais eficiente para problemas dinâmicos não-lineares. Esta redução de modelo é assistida por uma formulação secante, que é atualizado pela formula de BFGS (Broyden - Fletcher- Goldfarb - Shanno) com o intuito de acelerar a convergência do modelo, e uma formulação tangente para a correção do espaço de projeção. Além disso, esta pesquisa mostra que este método permite a correção do modelo reduzido com baixo custo, especialmente quando o clássico POD não é mais eficiente para representar com precisão a solução.

Deficient concrete structures are serious danger in seismic zones. In order to minimize economical and human loss, these structures should be retrofitted. Selecting suitable retrofitting schemes requires detailed investigation of these systems. Considering these facts, this study aims to calibrate analytical models of systems with chevron braces and internal steel frames / and evaluate their seismic performances. First, analytical models of the frames with braces and internal steel frames were prepared and then their responses were compared with cyclic responses of experimental studies. Results of these models were used to determine performance limits by the methods proposed by TEC2007 and ASCE/SEI-41. Then, calibrated models were employed for time history analyses with various scales of Duzce ground motion and analytical results were compared with experimental findings. Seismic performance of these systems was also evaluated by using aforementioned codes. Finally, evaluated retrofitting schemes were applied to a 4-story 3-bay reinforced concrete frame that was obtained from an existing deficient structure and effectiveness of applied retrofitting schemes was investigated in detail.